ICTS

Introduction to Quantum Optomechanics

I’ll use these lectures to provide a somewhat selective introduction to the field of cavity quantum optomechanics. Lec. 1 will give a general overview of the field and an introduction to the basic theory describing phenomena in the most experimentally-relevant "mean-field” regime, where a strong drive is required to see effects of the optomechanical interaction; we will discuss things like dynamical backaction, cavity cooling and optomechanically-induced transparency. Lec. 2 will focus on theory describing the quantum nonlinear regime, where the optomechanical coupling plays a role at the single photon and single phonon level; I will discuss proposals for how suitably chosen photonic and mechanical drives could help enhance these nonlinear quantum effects. Finally, in Lec. 3, I will turn to the general topic of reservoir engineering in quantum optomechanics, focusing on approaches for stabilizing squeezed and entangled states, and for generating non-reciprocal interactions and devices.
 

A discussion on quantum heat baths

The starting microscopic model of most quantum mechanical models of heat baths is the same, namely it consists of a gas of non-interacting particles in thermal equilibrium. The master equation approach and the Langevin equation approach are two different ways of studying the effective dynamics of a system coupled to such a bath. The talk will present a comparison of these two approaches in out-of-equilibrium applications.
 

Counter-diabatic driving in complex systems

In this talk I will discuss how one can construct approximate local counter-diabatic driving protocols, which can suppress dissipation and increase fidelity of the state preparation in interacting systems (both quantum and classical).
 

Anti-Kibble-Zurek Behavior in Crossing the Quantum Critical Point

TBA
 

Induced transparency in cyclic atomic systems in contact with a thermal bath

Electromagnetic (EM) waves are the fastest and least distortable information careers. Along with transport of information is the requirement for storage. This is usually done in a material medium often through lossy dipole interaction with the EM waves which in-turn produce induced atomic dipoles in matter. The phenomenon of electromagnetically induced transparency made such an interaction essentially lossless at the strongest coupling parameter regime of light and matter. In this talk, the effect of having both an electric and magnetic dipole interaction in the same system will be investigated with an emphasis on induced transparency effect. The talk is based on theoretical and experimental studies focusing on the influence of thermal photons which strongly affect coherence of levels connected by the magnetic dipole coupling.

[1] Effects of temperature and ground-state coherence decay on enhancement and amplification in a Δ atomic system. Phys. Rev. A 90, 043859 (2014)
[2] Demonstration of a high-contrast optical switching in an atomic Delta system (Accepted in Journal of physics B (2017))
 

Understanding the Born Rule in Weak Measurements

Projective measurement is used as a fundamental axiom in quantum mechanics, even though it is discontinuous and cannot predict which measured operator eigenstate will be observed in which experimental run. The probabilistic Born rule gives it an ensemble interpretation, predicting proportions of various outcomes over many experimental runs. Understanding gradual weak measurements requires replacing this scenario with a dynamical evolution equation for the collapse of the quantum state in individual experimental runs. We revisit the framework to model quantum measurement as a continuous nonlinear stochastic process. It combines attraction towards the measured operator eigenstates with white noise, and for a specific ratio of the two reproduces the Born rule. This fluctuation-dissipation relation implies that the quantum state collapse involves the system-apparatus interaction only, and the Born rule is a consequence of the noise contributed by the apparatus. The ensemble of the quantum trajectories is predicted by the stochastic process in terms of a single evolution parameter, and matches well with the weak measurement results for superconducting transmon qubits.
 

Electrical access to marginally protected conduction states in graphene

The zigzag (ZZ) edges of both single and bilayer graphene are perfect one dimensional (1D) conductors due to a set of zero energy gapless states that are topologically protected against backscattering. Competing effects of edge topology and electron-electron interaction in these channels have been probed with scanning probe microscopy, which reveal unique local thermodynamic and magnetic properties. A direct evidence of edge-bound electrical conduction, however, has remained experimentally elusive, primarily due to the lack of graphitic nanostructures with low structural and/or chemical edge disorder, as well as a clear understanding of the impact of edge disorder and confinement on electrical transport. In this talk I shall present a new method to observe ballistic edge-mode transport in suspended atomic-scale constrictions of single and multilayer graphene, created during nanomechanical exfoliation of graphite, which manifests in quantization of conductance close to multiples of e2/h even at room temperature [1]. I shall highlight the specific case of electrically biased bilayer graphene, where the conductance at low temperatures will be shown to possess non-trivial localization properties, as expected from topologically protected edge states in the presence of inter-valley scattering [2].

[1] A. Kinikar, T. P. Sai, S. Bhattacharyya, A. Agarwala, T. Biswas, S. Sarker, H. R. Krishnamurthy, M. Jain, V. Shenoy, A. Ghosh, Nature Nanotechnology (2017) doi:10.1038/nnano.2017.24.
[2] Md. A. Aamir, P. Karnatak and A. Ghosh (Under review).
 

Signature of Quantum Phase Transitions in highly excited non-equilibrium states

Quantum phase transitions refer to non-analytic changes in ground state properties of matter as a parameter of the system is tuned through a critical value. In this talk we will demonstrate that signature of such ground state transitions can have strong non-analytic signatures in highly excited non-equilbrium states with finite energy density and extensive entanglement entropy, created by quantum quenches.
 

Aperiodically driven integrable systems and their emergent steady states

Does a closed quantum many-body system that is continually driven with a time-dependent Hamiltonian finally reach a steady state? This question has only recently been answered for driving protocols that are periodic in time, where the long time behavior of the local properties synchronize with the drive and can be described by an appropriate periodic ensemble. Here, we explore the consequences of breaking the time-periodic structure of the drive with additional aperiodic noise in a class of integrable systems. We show that the resulting unitary dynamics leads to new emergent steady states in at least two cases. While any typical realization of random noise causes eventual heating to an infinite temperature ensemble for all local properties in spite of the system being integrable, noise which is self-similar in time leads to an entirely different steady state, which we dub as "geometric generalized Gibbs ensemble", that emerges only after an astronomically large time scale. To understand the approach to steady state, we study the temporal behavior of certain coarse-grained quantities in momentum space that fully determine the reduced density matrix for a subsystem with size much smaller than the total system. Such quantities provide a concise description for any drive protocol in integrable systems that are reducible to a free fermion representation.
 

On the entanglement spectrum: From the Levy distribution to the Tracy- Widom.

Coupling quantum systems whose dynamics is already non-integrable provides an interesting range of universal spectral behaviors for the reduced density matrices of the eigenstates. The spectra are interesting in as much as they determine the entanglement in these states. This talk explores the range of possibilities for the largest eigenvalue, from power- laws and the stable Levy distribution in the perturbative regime, to the more well-understood statistics governed by random matrix theory in the strong coupling regime. We look at two and many-body systems as examples.
 

Decay of quantum systems analysed with pseudomodes of reservoir structures

Reservoir structures result from certain types of non-uniform bath spectral density. When these structures are coupled to simple quantum systems the resulting decay can be analysed by the method of ""pseudomodes"", where the reservoir structure is replaced by an effective mode [1]. The approach is useful for strongly coupled, i.e. non-Markovian problems, since exact master equations can be derived. In this talk, an introduction to the basics of pseudomode theory will be given, together with developments on reservoir memory [2,3] and entanglement in such reservoir structures [4].

[1] Decay of an atom coupled strongly to a reservoir, B.M. Garraway, Phys. Rev. A 55, 4636 (1997).
[2] Pseudomodes as an effective description of memory: Non-Markovian dynamics of two-state systems in structured reservoirs, L. Mazzola, S. Maniscalco, J. Piilo, K.-A. Suominen, and B.M. Garraway, Phys. Rev. A. 80, 012104 (2009).
[3] An application of quantum Darwinism to a structured environment, G. Pleasance and B.M. Garraway, in preparation (2017).
[4] Generation of entanglement density within a reservoir, C. Lazarou, B.M. Garraway, J. Piilo, and S. Maniscalco, J. Phys. B 44, 065505 (2011).
 

Information driven quantum dot heat engines

In this talk, we discuss some novel heat-engine functionalities using quantum dots [1-3] from a quantum transport perspective. We discuss quantum dot heat engines [1] driven by classical information via a hyperfine coupled quantum dot set up and present the unique characteristics that relate to information driven heat engines. Moving on to quantum information processing and heat engines, we employ a Lindblad approach [2] to a triple quantum dot system connected to collinear leads in order to demonstrate heat engine functionality that can generate quantum information in an ancillary system.

References:
[1] S. Datta, ArXiv: 0704:1623, (2007).
[2] B. Muralidharan and M. Grifoni, Phys. Rev. B, 88, 045402, (2013).
[3] B. De and B. Muralidharan, Phys. Rev. B, 94, 165416, (2016).
 

Non-equilibrium statistical physics for small quantum systems: Transport, fluctuations and Engineered devices

I will talk about two different aspects of nonequilibrium statistical physics:

1. Engineered light-matter open quantum systems and microscopic principles for giant photon amplification.
2. A brief overview of quantum transport including universal fluctuation relations and effect of electron-phonon interaction on charge transport.

    

Bosonization-debosonization and the nonequilibrium Kondo problem

After critically reexamining in the previous talk the Bosonization- deBosonization (BdB) procedure for systems including ‘boundaries’ and subsequently introducing a Consistent BdB procedure to address shortcomings that were found in transport calculations [1], we turn our attention to the physics of quantum dots. Under the right conditions, such dots can attain the Kondo regime in which tunneling conduction is possible at low temperatures despite the Coulomb blockade. We study this physics by focusing on the two-lead Kondo model [2]. The bosonization formalism can be used to access a solvable limit of this model known as its Toulouse point. I shall show that a consistent BdB procedure yields a modified set of physical results that are in better agreement with the phenomenology of the problem. Besides its general experimental relevance, the Toulouse limit of the two-lead Kondo model is a key theoretical prototype of a strongly correlated system away from equilibrium but nevertheless admitting a closed solution.

References:
[1] Nayana Shah and C. J. Bolech, Phys. Rev. B 93, 085440 (2016).
[2] C. J. Bolech and Nayana Shah, Phys. Rev. B 93, 085441 (2016).
 

(Non) equilibrium dynamics: a (broken) symmetry

It is fascinating that most many-body systems, if unperturbed, tend to relax towards thermal equilibrium dynamics. I will discuss a recent result showing that quantum equilibrium dynamics can be elevated to the rank of a universal (model-independent) symmetry of Keldysh field theories. This fundamental symmetry imposes strong constraints on the equilibrium correlation functions. But more importantly, this allows to study non- equilibrium dynamics as symmetry-breaking processes, providing important clues on the so-far poorly understood production of entropy in quantum mechanical systems.
 

Non-Markovian dynamics of a qubit due to single-photon scattering in a waveguide

We investigate the open dynamics of a local qubit due to scattering of a single photon in a waveguide. By adapting techniques of waveguide quantum electrodynamics to the study of scattering time evolution in combination with tools of open quantum systems theory, we work out the general features of the qubit's dynamical map and assess in a rigorous way its non-Markovian nature. Two fundamental sources of non-Markovianity are shown: the finite width of the photon wavepacket and the presence of a hard-wall boundary condition.

Reference: Y.-L. L. Fang, F. Ciccarello, and H. Baranger, to appear on arXiv (2017).
 

Exponential improvement in photon storage fidelities using subradiance and ``selective radiance'' in atomic arrays

A central goal within quantum optics is to realize efficient, controlled interactions between photons and atomic media. A fundamental limit in nearly all applications based on such systems arises from spontaneous emission, in which photons are absorbed by atoms and then re-scattered into undesired channels. In typical theoretical treatments of atomic ensembles, it is assumed that this re-scattering occurs independently, and at a rate given by a single isolated atom, which in turn gives rise to standard limits of fidelity in applications such as quantum memories for light or photonic quantum gates. However, this assumption can in fact be dramatically violated. In particular, it has long been known that spontaneous emission of a collective atomic excitation can be significantly suppressed through strong interference in emission between atoms. While this concept of ``subradiance" is not new, thus far the techniques to exploit the effect have not been well-understood. Here, we provide a comprehensive treatment of this problem. First, we show that in ordered atomic arrays in free space, subradiant states acquire an elegant interpretation in terms of optical modes that are guided by the array, which only emit due to scattering from the ends of the finite system. We also go beyond the typically studied regime of a single atomic excitation, and elucidate the properties of subradiant states in the many-excitation limit. Finally, we introduce the new concept of ``selective radiance." Whereas subradiant states experience a reduced coupling to all optical modes, selectively radiant states are tailored to simultaneously radiate efficiently into a desired channel while scattering into undesired channels is suppressed, thus enabling an enhanced atom-light interface. We show that these states naturally appear in chains of atoms coupled to nanophotonic structures, and we analyze the performance of photon storage exploiting such states. We find numerically that selectively radiant states allow for a photon storage error that scales exponentially better with number of atoms than previously known bounds.
 

An efficient method to study light propagation through nonlinear quantum media

I discuss a generalization of the quantum Langevin equations approach to study nonlinear light propagation through one-dimensional interacting open quantum lattice models. A matrix product operator description is developed to write and solve a large set of quantum Langevin equations of lattice operators obtained after integrating out the light fields. I talk an application of our method to a Heisenberg spin-1/2 chain with nearest-neighbor coupling. The transient and steady-state transport properties of an incoming monochromatic laser light are calculated for this model. I show how the local features of the spin chain and the chain length dependence of light transport coefficient behave with an increasing power of the incident light.
 

Emergence of singularities from decoherence in a Josephson junction

I will discuss the emergence of singularities during the quantum-to- classical transition by analyzing the decoherence of a many-particle wave function in the vicinity of a classical caustic. In particular, a Josephson junction can be made by coupling two Bose-Einstein condensates; when the coupling is turned on suddenly the Gross-Pitaevskii mean-field theory, which describes a classical field, predicts that caustics (containing fold and cusp catastrophes) will form in the number-difference probability distribution. The caustics are singular and thus represent a failure of the classical theory, but are well-behaved in the many-body theory where atom number is quantized. However, if the system is additionally subjected to a weak continuous measurement the quantum state decoheres and classicality and hence the singularity are restored, potentially leading to a paradox.
 

Spin Qubits

These lectures will provide an introduction to the theory of spin qubits in quantum dots and defects. We will cover spin 1/2, singlet-triplet, and exchange-only qubits, as well as hybrid quantum systems consisting of spins in combination with an electromagnetic cavity. Various methods for quantum control and quantum gate operation in these systems will be discussed. Spin qubits will also be treated as an open system in contact with their electromagnetic and solid-state environment, and the interplay between spin and valley degrees of freedom in valley-degenerate materials such as carbon and silicon will be covered.
 

Divergence-free Circuit Quantum Electrodynamics

Any quantum-confined electronic system coupled to the electromagnetic continuum is subject to radiative decay and renormalization of its energy levels. When inside a cavity, these quantities can be strongly modified with respect to their values in vacuum. In the planar circuit quantum electrodynamics architecture the radiative decay rate of a Josephson Junction qubit is strongly influenced by far off-resonant modes. A multimode calculation including all cavity modes however leads to divergences unless a cutoff is imposed. It has so far not been identified what the source of divergence is, or whether the divergence is a fundamental issue. I will show that unless gauge invariance is respected, any attempt at the calculation of circuit QED quantities is bound to diverge. I will then discuss a theoretical and computational framework based on a Heisenberg-Langevin approach to the calculation of a finite spontaneous emission rate and the Lamb shift, that is free of cutoff.

Photon Correlations in Waveguide QED: Rectification and Next-(Next-)Photon Statistics

Strong photon correlations are produced when even a few resonant emitters (qubits) are coupled to a photonic waveguide. These correlations result from the inelastic scattering caused by the nonlinearity of the emitters. I shall discuss two of our recent results in this area. First, we find that rectification is inherently connected to the inelastic scattering. Rectification occurs when two detuned qubits are coupled to the waveguide, and is enhanced when the detuning of the qubit frequencies is matched by a detuning of their separation from a half wavelength. We show that this condition corresponds to maximizing the inelastic scattering by driving a nearly dark pole in the system. Second, we investigate the "next-photon" and "next-next-photon" statistics in the case of one or two qubits coupled to the waveguide. These provide a more accurate characterization of photon bunching and anti-bunching than the customary g2(0). The calculation is carried out in the Markovian approximation using quantum jump methods, using a jump operator that corresponds to single photon detection by taking into account photon interference effects. I close by commenting on changes in photon correlations in the non-Markovian regime.
 

Quantum fluids of light in semiconductor microcavities

Semiconductor microcavities appear today as a new platform for the study of quantum fluids of light. They enable confining both light and electronic excitations (excitons) in very small volumes. The resulting strong light-matter coupling gives rise to hybrid light-matter quasi-particles named cavity polaritons. Polaritons propagate like photons but strongly interact with their environment via their matter part: they are fluids of light and show fascinating properties such as superfluidity or nucleation of quantized vortices. Finally patterning microcavities at the micron scale allows the engineering of polariton band structure and emulation of a wide variety of interesting Hamiltonians. The goal of this pedagogical lecture is to give an introductory overview of this very rapidly evolving research field.

In the first part, basic linear properties of cavity polaritons will be introduced. Light matter strong coupling regime, formation of hybrid light matter quasi particle will be explained together with experimental techniques to excite and probe these new quasi- particles. Effective mass, group velocity, pseudo-spin and band structure engineering will be addressed. We will then discuss how it is possible to trigger polariton condensation in a semiconductor microcavity, and manipulate polariton condensates in photonic circuits.

The second lecture will be devoted to polariton non-linearity. One of its spectacular manifestations is superfluidity and the disappearance of any scattering when a quantum fluid of light passes an obstacle. Topological excitations such as quantized vortices and solitons can also be generated in the wake of a defect. Another interesting manifestation of polariton Kerr nonlinearity is bistability: several experiments making use of such effect will be discussed.

In the last lecture, we will illustrate by several examples how polariton lattices allow emulating various Hamiltonians with distinct physical properties: quasi-crystal with fractal energy spectrum, 1D lattices with topological edge states or 2D honeycomb lattices emulating Dirac physics.
 

Lecture 1: Introduction to quantum dots
Lecture 2: Cavity-coupled spin qubits
Lecture 3: Photoemission, masing, and strong-coupling in cavity-coupled charge qubits

Three pedagogical lectures will be given, starting with a basic description of quantum dot physics and ending with recently published results from cavity-coupled double quantum dots. Lecture 1: quantum dots, single electron charging, double quantum dot charge stability diagrams, and the double dot as a charge qubit. Lecture 2: Hybrid quantum devices, charge- cavity coupling and readout, spin state control and readout. Lecture 3: An emphasis on non-equilibrium physics in cavity-coupled double dots.Photoemission and masing driven by single electron tunneling. Floquet – Sisyphus pumping of a single electron. Coherent coupling of a single charge to a single photon.
 

Mapping repulsive to attractive interaction in driven-dissipative quantum systems

Repulsive and attractive interactions usually lead to very different physics. Striking exceptions exist in the dynamics of driven-dissipative quantum systems. For the example of a photonic Bose-Hubbard dimer, I will show that one can establish a one-to-one mapping relating the cases of onsite repulsion and attraction. This mapping is, in fact, valid for an entire class of Markovian open quantum systems with time-reversal invariant Hamiltonian and physically meaningful inverse-sign Hamiltonian. To underline the broad applicability of the mapping, I will illustrate the one- to-one correspondence between the nonequilibrium dynamics in a geometrically frustrated spin lattice and that in a non-frustrated partner lattice.
 

Optimal efficiency and power: universality, cooperative effects, and examples

Carnot's seminal work has helped establishing the second law of thermodynamics. The upper bound efficiency, Carnot efficiency, however is usually far away from the maximum efficiency that can be realized in a realistic thermodynamic machine. We discuss some universal properties of optimal efficiency and power that are found only recently. A cooperative effect is emphasized and related to current state-of-art quantum and classical engines. Several examples are given.
 

Singular quench dynamics of a Bloch state

We report some nonsmooth dynamics of a Bloch state in a one- dimensional tight binding model with the periodic boundary condition. After a sudden change of the potential of an arbitrary site, quantities like the survival probability of the particle in the initial Bloch state show cusps periodically, with the period being the Heisenberg time associated with the energy spectrum. This phenomenon is a nonperturbative counterpart of the nonsmooth dynamics observed previously (Zhang J. M. and Haque M., arXiv:1404.4280) in a periodically driven tight binding model. Underlying the cusps is a Luttinger-like exactly solvable model, which consists of equally spaced levels extending from $-\infty$ to $+\infty$ , between which two arbitrary levels are coupled to each other by the same strength. Besides the momentum space, we have also studied the same scenario in the real space. The observation is that the probability density at an arbitrary site jumps indefinitely between plateaus.

[1] J. M. Zhang and H. T. Yang, Sudden jumps and plateaus in the quench dynamics of a Bloch state, EPL 116, 10008 (2016).
[2] J. M. Zhang and H. T. Yang, Cusps in the quench dynamics of a Bloch state, EPL 114, 60001 (2016).
[3] J. M. Zhang and Y. Liu, Fermi's golden rule: its derivation and breakdown by an ideal model, Eur. J. Phys. 37, 065406 (2016).
 

An ion in a sea of ultracold neutral atoms

In recent years several groups on an international scale have set up experiments where single laser-cooled trapped ions are immersed into a cloud of ultracold neutral atoms. One important motivation for this hybrid combination of cold neutral and charged particles is to study an open quantum system at a very high level of control. As an example, the ion can be viewed as an impurity that couples to an atomic bath via the relatively long range 1/r4 polarization potential. The interaction is predicted to lead to the formation of a polaron which can for the first time reach the strong coupling regime. Another example for interesting future research is to study transport in quantum gases by using the ion as a local probe. As a third example, decoherence phenomena in a bath can be investigated by measuring the decay of superposition states of the ion due to elastic and inelastic collisions with the neutral atom. I will give a brief overview over some of the activities of our own group and several other research groups in the field. This will include a discussion of challenges that occurred in the meantime, apparent roadblocks and possible work arounds.
 

Quantum Many-Body Physics with Multimode Cavity QED

By placing cold atoms in multimode optical cavities, one can engineer classes of Hamiltonians and forms of dissipation that enable one to access novel states of non-equilibrium matter. This experimental system combines quantum optics and ultracold atomic physics with the quantum many-body physics traditionally explored in condensed matter physics. In this talk, I will discuss the possibilities that arise from this system. In particular, I will discuss the experiments [1,2] where such a system has been realised, and how these have been used to demonstrate the potential of multimode cavity QED to engineer interactions with controllable range. Based on these experimental capabilities, I will then discuss our theoretical work beginning to exploit the potential offered by these experiments. I will discuss how a multimode cavity can be used to engineer a synthetic gauge field, in such a way that the synthetic field responds to the state of the atoms. Using this, we have shown how one may realise a Meissner- like effect for ultracold atoms[3].
If time allows, I will then discuss aspects of how a Hopfield associative memory can be realised in such a system [4], and discuss our recent work developing the microscopic theory of this behaviour. 

[This work has been done in collaboration with K. Ballantine (University of St Andrews), V. Vaidya, Y. Guo, A. Kollar, J. Cotler, S. Ganguili and B. Lev (Stanford).]

[1] A. J. Kollar, A. T. Papageorge, K. Baumann, M. A. Armen, and B. L. Lev, New J. Phys. 17, 043012 (2015).
[2] A. J. Kollar, A. T. Papageorge, V. D. Vaidya, Y. Guo, J. Keeling, and B. L. Lev, Nat. Commun. 8 14386 (2017)
[3] K. E. Ballantine, B. L. Lev, and J. Keeling, Phys. Rev. Lett. 118, 045302 (2017).
[4] S. Gopalakrishnan, B. L. Lev, and P. M. Goldbart, Phys. Rev. Lett. 107, 277201 (2011).
 

Probing the thermodynamics of quantum measurement with superconducting qubits.

The extension of thermodynamics into the realm of quantum mechanics, where quantum fluctuations dominate and systems need not occupy definite states, poses unique challenges. Superconducting quantum circuits offer exquisite control over the environment of simple quantum systems allowing the exploration of thermodynamics at the quantum level through measurement and feedback control. We use a superconducting transmon qubit that is resonantly coupled to a waveguide cavity as an effectively one-dimensional quantum emitter. By driving the emitter and detecting the fluorescence with a near-quantum-limited Josephson parametric amplifier, we track the evolution of the quantum state and characterize the work and heat along single quantum trajectories. By using quantum feedback control to compensate for heat exchanged with the emitter's environment we are able to extract the work statistics associated with the quantum evolution and examine fundamental fluctuation theorems in non-equilibrium thermodynamics.
 

Work extraction in heat engines: quantum versus classical

Heat engine is one of crucial topics to develop nonequilibrium thermodynamics. Reently quantum effects in thermodynamic operations attract much attention. Recent experiments demonstarted that even atomic scale heat engine is possible. In this talk, we consider a problem as to how to extract the quantum work. We derive a trade-off relation and will point out several problems.
 

Entanglement generation and dynamic phase transition in periodically driven integrable models.

In this talk, we shall discuss the generation of entanglement entropy S of a closed quantum system driven periodically with frequency w and for n drive cycles. We show that such a drive may be used to generate states for which the scaling of S lies between an area and a volume law. We provide a qualitative criterion for the change in nature of S which constitutes a generalization of Hastings' theorem to driven integrable systems. We also find that S and any correlation function of such a driven system decay to their steady state values as (w/n)^[(d+2)/2] for fast and (w/n)^[d/2] for slow drives; these two dynamical phases are separated by a transition associated with the change in topology of the spectrum of the system's Floquet Hamiltonian. We show that these dynamical phases show re- entrant behavior as a function of w for d = 1 (and a class of d = 2) models, provide a detailed phase diagram of the system, and discuss experiments which can test our theory.
 

Generic dynamical features of quenched interacting quantum systems

We study numerically and analytically the quench dynamics of isolated many-body quantum systems out of equilibrium. Using full random matrices from the Gaussian orthogonal ensemble, we obtain analytical expressions for the evolution of the survival probability, density imbalance, and out-of-time-ordered correlator. They are compared with numerical results for a one-dimensional disordered model with two-body interactions and shown to bound the decay rate of this realistic system.
Power-law decays are seen at intermediate times and overshoots beyond infinite time averages occur at long times when the system exhibits level repulsion. The fact that these features are shared by both the random matrix and the realistic disordered model indicates that they are generic to nonintegrable interacting quantum systems out of equilibrium.
 

Skyrmion spin texture in inversion symmetric magnets

Stable topological excitations such as domain walls, vortices are ubiquitous in condensed matter systems and are responsible for many emergent phenomena. Recently a new mesoscopic spin texture called skyrmion with radius about 10 ~100 nm was discovered experimentally in the chiral magnets without the inversion symmetry. The skyrmions can also be stabilized in heterostructures, where the inversion symmetry is broken at the interface. The Dzyaloshinskii-Moriya interaction is responsible for the stabilization of skyrmions in these systems. Skyrmions form a triangular lattice. In metallic magnets, skyrmions can be driven by a spin polarized current. Remarkably, the threshold current density to drive the skyrmions into motion is only about 100 A/cm 2 , which is 4-5 order of magnitudes weaker than that for magnetic domain walls. The high mobility, topological protected stability, compact size of skyrmions make them extremely promising for applications in spintronics, such as memory. In this talk, first I will attempt to summarize the experiments and to present an overview on skyrmions. Then I will talk about our recent work on skyrmion stabilization in inversion- symmetric magnets. Because of the additional symmetry, skyrmions in the inversion-symmetric magnets possess interesting properties, which can be exploited for device applications. I will discuss about the novel properties of skyrmions in inversion-symmetric magnets in comparison to those in chiral magnets.
 

An open quantum system generalization of a 1D quasiperiodic system with a single-particle mobility edge

TBA
 

Dissipative Quantum Phase Transitions in Interacting Light-Matter Systems

Developments in quantum engineering have brought forth the possibility of studying emergent collective phenomena in hybrid systems of interacting matter and light. These platforms, which are intrinsically open and dissipative, allow to probe fundamental many-body physics in uncharted territories. In this talk I will focus on dissipative quantum phase transitions, arising from the interplay between coherent dynamics and coupling to an environment. I will start from a paradigmatic light-matter phase transition, the Dicke superradiance, and discuss how non-Markovian bath correlations qualitatively change its physics, pointing out a connection with the Caldeira-Legget/spin-boson phase transition much studied in a condensed matter context. In the second part of the talk I will focus on the physics of coupled circuit QED lattices with Kerr non-linearity under incoherent drive and dissipation, describe protocols to stabilize driven Mott insulators of photons and their dissipative and dynamical transition toward nonequilibrium superfluids.
 

Dissipation as a resource for stabilizing quantum states with superconducting qubits

Recent advances in quantum-limited amplification have opened doors to high-fidelity non-demolition measurement of superconducting qubits and have already led to successful experiments on closed-loop control of such systems. However, the finite bandwidth of the amplification procedure, together with the time-consuming data acquisition and post-treatment of the output signal, lead to important latency in the feedback procedure.
Alternatively, the reservoir (dissipation) engineering circumvent the necessity of a real-time data acquisition, signal processing and feedback calculation. Coupling the quantum system to be stabilized to a strongly dissipative ancillary quantum system allows us to evacuate the entropy of the main system through the dissipation of the ancillary one. I will overview some theoretical proposals as well as the related experiments through the past few years illustrating the power of such autonomous feedback schemes for stabilizing highly non-classical states as well as for quantum error correction.
 

Quantum manifolds of steady states in driven, dissipative superconducting circuits

TBA
 

Out-of-equilibrium tunnel junction paradox and a new consistent bosonization-debsosonization framework

Bosonization has been widely used for tackling strongly correlated systems in low dimensions and is used as a theoretical method of choice for a large class of problems. It is also one of the few non-perturbative approaches that can be extended to study systems and devices out of equilibrium. In this talk we shall critically reexamine the Bosonization- deBosonization (BdB) procedure for systems including junctions and impurities. By focusing on the case of a tunneling junction out of equilibrium, we will be able to see that the conventional approach to BdB gives results that are not physically consistent while according to conventional wisdom they should match exactly with those obtained via a direct calculation that does not involve a transformation from fermionic to bosonic fields and back. I will then present the new Consistent BdB framework that we have recently developed in order to resolve this non- equilibrium transport paradox and argue that our modified framework should be widely applicable [1]. These ideas can be readily used to address more complicated scenarios of immediate experimental relevance [2], as will be highlighted in a follow-up presentation.

References:
[1] Nayana Shah and C. J. Bolech, Phys. Rev. B 93, 085440 (2016).
[2] C. J. Bolech and Nayana Shah, Phys. Rev. B 93, 085441 (2016).
 

Circuit-QED based spectroscopies of quantum impurities

Quantum impurity problems describe a localized quantum system with a few degrees of freedom (the impurity), that is non-perturbatively coupled to a large system (the bath). These impurities can exist in many different forms in solid-state materials and nanostructures, such as charged [1] or magnetic impurities [2], while the bath is typically constituted by a Fermi sea. However, understanding the quantum dynamics and the entanglement properties of these many-body electronic systems remains a tremendous challenge, both experimentally and theoretically.

The main underlying reason to this complexity lies in the presence of entanglement between the impurity and many modes of the bath that extend on a wide energy range, which prevents a brute force diagonalization of the full problem. In addition, in metallic devices such as artificial quantum dots, it has proved difficult experimentally to resolve or address electronic bath modes individually, due to internal losses of metallic islands.

I will present a unique architecture based on superconducting circuits to tackle this challenging problem. It offers two main advantages: first, it allows to reach the multi-mode ultra-strong coupling regime allowing to build a strong hybridization between the quantum system and its bath; second, high quality factors of superconducting circuits enable to monitor spectroscopically the qubit and its bath at the same time.

Our approach consists in coupling a superconducting artificial atom (namely a transmon qubit) to a meta-material made of thousands of SQUIDs [3,4,5]. The latter sustains many photonic modes and shows characteristic impedance close to the quantum of resistance. We succeeded in performing the full spectroscopy of the impurity plus bath system, which revealed strong hybridization of the transmon qubit with as many as ten modes of the bath. In this coupling regime, the common techniques used in circuit-QED (rotating wave approximation, exact diagonalization...) break down. To describe quantitatively our experimental data, we had to borrow a tool usually reserved to strongly interacting systems: the Self-Consistent Harmonic Approximation [6]. In the future, we plan to use this circuit to perform non-linear quantum optics experiments with a many-body system [4,7].

[1] P. W. Anderson, Phys. Rev. Lett. 18, 1049 (1967)
[2] J. Kondo, Prog. Theor. Phys. 32, 37 (1964).
[3] K. Le Hur, Phys. Rev. B 85, 140506(R) (2012).
[4] M. Goldstein et al., Phys. Rev. Lett. 110, 017002 (2013).
[5] I. Snyman and S. Florens, Phys. Rev. B 92, 085131 (2015).
[6] T. Giamarchi, ``Quantum physics in one dimension'' (Oxford 2003).
[7] N. Gheeraert et al., in preparation.
 

Magnetic resonance at the quantum limit and beyond

The detection and characterization of paramagnetic species by electron-spin resonance (ESR) spectroscopy has numerous applications in chemistry, biology, and materials science [1]. Most ESR spectrometers rely on the inductive detection of the small microwave signals emitted by the spins during their Larmor precession into a microwave resonator in which they are embedded. Using the tools offered by circuit Quantum Electrodynamics (QED), namely high quality factor superconducting micro-resonators and Josephson parametric amplifiers that operate at the quantum limit when cooled at 20mK [2], we investigate magnetic resonance in a new regime where the quantum nature of the microwave field plays a role and the spin sensitivity is correspondingly enhanced. We report an increase of the sensitivity of inductively detected ESR by 4 orders of magnitude over the state-of-the-art, enabling the detection of 1700 Bismuth donor spins in silicon with a signal-to-noise ratio of 1 in a single echo [3]. We also demonstrate that the energy relaxation time of the spins is limited by spontaneous emission of microwave photons into the measurement line via the resonator [4], which opens the way to on-demand spin initialization via the Purcell effect. Finally, we show that the sensitivity can be enhanced beyond the quantum limit by using quantum squeezed states of the microwave field [5].

[1] A. Schweiger and G. Jeschke, Principles of Pulse Electron Magnetic Resonance (Oxford University Press, 2001)
[2] X. Zhou et al., Physical Review B 89, 214517 (2014)
[3] A. Bienfait et al., Nature Nanotechnology 11(3), 253-257 (2015)
[4] A. Bienfait et al., Nature 531, 74 (2016)
[5] A. Bienfait et al., arxiv :1610.03329

Cooperative Effects in Closely Packed Quantum Emitters with Collective Dephasing

In a closely packed ensemble of quantum emitters, cooperative effects are typically suppressed due to the dephasing induced by the dipole-dipole interactions. Here, we show that by adding sufficiently strong collective dephasing cooperative effects can be restored. In particular, we show that the dipole force on a closely packed ensemble of strongly driven two-level quantum emitters, which collectively dephase, is enhanced in comparison to the dipole force on an independent non-interacting ensemble. Our results are relevant to solid state systems with embedded quantum emitters such as colour centers in diamond and superconducting qubits in microwave cavities and waveguides.

Generating resonating valence bond states through Dicke subradiance

Dicke's seminal 1954 paper introduced the notion of ‘superradiance’ in a system of spins coupled to a common photon mode. Certain quantum states of the spins dominate the radiation process so that the spins radiate coherently. Dicke's original thought experiment has recently been recreated in the lab using cavity-QED setups with two spins. I will explore extending this experiment to N spins and show that the radiation process naturally gives rise to entangled states. This suggests a new experimental tool to create multi-particle entanglement in the lab. In particular, a null- observation (non-observation of emitted photon) can be used to collapse the wavefunction onto a dark state. Remarkably, this dark state has resonating valence bond character. We show that the probability of collapse onto RVB state scales as N-1, making it possible to generate entangled states of more than 20 spins.

Reference: R. Ganesh, L. Theerthagiri and G. Baskaran, arXiv:1609.04853.
 

Keldysh Field Theory for Open Quantum Systems: Localization and Quantum Effects

We use an effective action formalism based on Keldysh field theory to study bosonic open quantum systems interacting with bosonic baths. For a non-interacting bosonic chain coupled to independent baths at each lattice sites, we find that a linear variation of the temperature of the baths with distance leads to an exponential decay of both particle and energy current. This holds even when the baths induce long range memory effects in the system. For an interacting system, using loop expansions together with Martin-Siggia-Rose formalism, we find that in addition to a dissipative and a classical noise term, we generate a multiplicative noise and a "quantum" noise in the system. The "quantum" noise is a random source term with non-classical distribution functions, and can be related to Wigner's quasiprobability distribution. Using renormalization group arguments, we show that in the coarse grained limit, there is a universal quasiprobability distribution characterized by a single parameter and find the analytic form of the distribution function.
 

Broadband parametric amplifiers for quantum measurements

Josephson parametric amplifiers (JPAs) have become a crucial component of superconducting qubit measurement circuitry, enabling recent studies of quantum jumps, generation and detection of squeezed microwave field, quantum feedback, real-time tracking of qubit state evolution, quantum error detection, and more. In this talk, I will describe the operation of a simple parametric amplifier design which is based on a single Josephson junction shunted by a capacitor to form a non-linear oscillator. The intrinsic Kerr non-linearity of this device enables parametric amplification by pumping the oscillator with a suitable drive tone and allows one to obtain near quantum limited noise performance for a typical gain of about 20 dB. The bandwidth of such devices are usually governed by the standard gain-bandwidth product and typical devices have 10 – 50 MHz of bandwidth. I will describe a technique which requires a simple modification of the embedding circuit to enhance the bandwidth beyond the standard gain-bandwidth product without affecting the noise performance of the device. I will present results on such a device where we obtained 640 MHz of bandwidth with 20 dB gain and near quantum limited noise performance [1]. I will finally conclude by discussing further extensions to this idea and adapting it to other parametric amplifier designs like the Josephson Parametric Converter.
 

Periodically Driven Array of Single Rydberg Atoms

We discuss the excitation dynamics in an array of single Rydberg atoms driven by a frequency modulated light field. The latter introduces an effective time-dependent Rabi coupling in a rotating frame, which leads to unprecedented dynamics in the presence of Rydberg-Rydberg interactions. In particular, the Rydberg blockade may exist even if the interaction strengths are significantly small compared to the single atom Rabi frequency; anti-blockade appears at large interactions with high excitation probabilities and state dependent population trapping. Finally, as an application to modulated driving, we characterize the freezing or localization dynamics of an excitation in an extended driven setup.
 

Interacting Quantum Systems in Hybrid Traps

Hybrid traps allow the accumulation of multiple quantum particles, which are different in their nature, to be put together so that the interactions between them can be studied precisely. Specifically, these can be ions, atoms, molecules and light. In such experiments, some combinations of these particles are trapped with overlap to study the interaction of interest. The different systems that we would like to trap interact with the electromagnetic field in very different ways, and this requires each class of object to be trapped with a different mechanism. Enabling the various mechanisms to function so that everything is confined to a tiny volume in space is a daunting technical challenge. In the first part of the talk I shall illustrate how these challenges are overcome in our experiment at RRI.

The trapped dilute gas systems are also simultaneously prepared in specific quantum states and typically the idea is to cool the systems to such temperatures so that the natural linewidths of these sets the limit of the energy uncertainty. Another objective is that the interactions are not dominated by the kinetic energy of the interacting particles. In this situation, the evolution of the typically state prepared systems on interaction will express itself in the change of motional or internal states of the interacting systems. The challenge then becomes how to detect these.

At RRI, we have been performing experiments with the above objectives for a while now and I shall discuss some of our experiments on these topics. These explorations have led to the understanding of several phenomena, which is often at variance with expectations. Some significant results shall be presented. I shall conclude by outlining strategies that we would pursue so that we are in a position to attack a wide range of possible problems related to open quantum systems.
 

Quantum gases with tunable interactions and non-perturbative measurements

I shall discuss about the new Sodium-Potassium quantum gas mixture experiment we are developing at Raman Research Institute, Bangalore. The goal of this experiment is to investigate quantum many body physics employing long-range anisotropic interactions between heteronuclear molecules with tunable electric dipole-dipole interactions. Using laser cooling and trapping and evaporative cooling techniques, we propose to achieve simultaneous quantum degenerate samples of neutral Sodium and Potassium atomic clouds. Thereafter, using an interspecies magnetic Feshbach resonance, weakly bound molecules will be created. Two-photon Raman adiabatic passage from this “Feshbach molecular” state to absolute ground state will be employed to prepare ultra-cold cloud of Sodium- Potassium molecules. This molecular cloud trapped in an optical lattice potential can afterwards be manipulated in presence of an external electric field to investigate various ground state solutions of the extended Hubbard model by direct imaging.

I shall also discuss about our ongoing experiments on spin fluctuations in a thermal vapor using the probe beam polarization fluctuation measurements. We observe polarization fluctuations in a far detuned probe laser which passes through a thermal vapor in presence of an orthogonal magnetic field revealing intrinsic spin fluctuations in the system. This technique is an example of non-perturbative measurement of dynamical structure factor and has promising applications in many other similar systems such as ultra-cold quantum gases. This spin noise spectroscopy technique will eventually be used as a non-perturbative detection technique for measurements on quantum degenerate gases.
 

Nonlinear optical spectroscopy of molecules with quantum light and in microcavitites

Nonlinear optical signals induced by quantized light fields and entangled photon pairs are presented. Different signals, and photon counting setups are discussed and illustrated for molecular model systems. Conventional nonlinear spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. An intuitive diagrammatic approach is presented for calculating ultrafast spectroscopy signals induced by quantum light, focusing on applications involving entangled photons with nonclassical bandwidth properties—known as “time-energy entanglement.” Nonlinear optical signals induced by quantized light fields are expressed using time-ordered multipoint correlation functions of superoperators in the joint field plus matter phase space. These are distinct from Glauber’s photon counting formalism which uses normally ordered products of ordinary operators in the field space. One notable advantage for spectroscopy applications is that entangled-photon pairs are not subjected to the classical Fourier limitations on the joint temporal and spectral resolution. Properties of entangled-photon pairs relevant to their spectroscopic applications will be surveyed. Different optical signals, and photon counting setups are discussed and illustrated for molecular model systems. Crossings of electronic potential surfaces in nuclear configuration space, known as conical intersections, determine the rates and outcomes of virtually all photochemical molecular processes. Strong coupling of molecules to the quantum vacuum field of micro cavities can modify the potential energy surfaces thereby manipulating the photophysical and photochemical reaction pathways. The photonic vacuum state of a localized cavity mode can be strongly mixed with the molecular degrees of freedom to create hybrid field-matter states known as polaritons. Simulations of the avoided crossing of sodium iodide and sodium fluoride in a cavity which incorporate the quantized cavity field into the nuclear wave packet dynamics will be presented. We show how the branching ratio between the covalent and ionic dissociation channels can be strongly manipulated by the optical cavity. New imaging techniques based on x-ray diffraction from electronic coherence in conical intersections will be presented.
 

References:

1. Markus Kowalewski, Kochise Bennett, and Shaul Mukamel. "Cavity femtochemistry; Manipulating nonadiabatic dynamics at avoided crossings", J. Phys. Chem. Lett ,2016, 7, 2050-2054
2. Konstantin E. Dorfman, Frank Schlawin, and Shaul Mukamel. "Nonlinear optical signals and spectroscopy with quantum light", Rev. Mod. Phys. 88, 045008 (2016) arXiv:1605.06746v1
3. Kochise Bennett, Markus Kowalewski, and Shaul Mukamel. "Novel Photochemistry of Molecular Polaritons in Optical Cavities", Faraday Discussions, 2016, 194, 259-282. DOI: 10.1039/C6FD00095A

    

Rydberg aggregates in ultracold gases

Rydberg Atoms in highly excited electronic states with n=30-100 are recent additions to the versatile toolkit of ultracold atomic physics. When resonant dipole dipole interactions involving two atomic states are at play, these furnish interesting model system for e.g. energy transport (static Rydberg atom assemblies) or multi-Born-Oppenheimer surface motion (moving atoms). We will discuss the interplay of this kind of dynamics with the host cold gas, in which Rydberg excitations are typically embedded. We show how the cold gas can allow continuous observation of the atomic motion or excitation transport, in turn leading to controllable decoherence. Thus the system of Rydberg aggregates embedded in cold gases furnishes a versatile quantum simulation platform for open quantum systems.

[1] S. Wüster and J.M. Rost arxiv:1707.04099 (2017).
[2] D. Schönleber et al. PRL 114 123005 (2015).
[3] H. Schempp et al. PRL 115, 093002 (2015).
[4] S. Wüster, PRL 119 013001 (2017).

Ultrathin optical fibers for neutral cold atom probing and manipulation

A subwavelength diameter optical nanofibre (ONF) has a large fraction of its guided light mode as an evanescent field, which extends radially beyond the surface of the fibre, see Fig. 1. Resonant and off-resonant interactions of this light field with surrounding cold atoms can lead to interesting phenomena, such as the observation of ultralow power nonlinear effects [1,2]. Our work follows two strands. In the first, we explore the formation and behaviour of neutral Rydberg atoms near ONFs. Rydberg atoms have a high dipole moment and a long lifetime, enabling the study of dipole-induced interactions. The combination of Rydberg atoms with an ONF could be a unique testbed for the study of surface-induced interactions on atomic dipoles in the submicron range or for fibre-mediated quantum networks. The second strand of research involves studying nanofibre-aided multiphoton atomic transitions and effects such as EIT and 4WM. Here, we exploit some of the properties of higher order fibre modes such as a stronger evanescent field around the fiber waist [3], the coupling of the orbital and spin angular momentum of light [4], and novel atom trapping geometries [5].
 

References:
[1] R. Kumar, V. Gokhroo, K. Deasy and S. Nic Chormaic, Phys. Rev. A, vol. 91, p. 053842 (2015)
[2] R. Kumar, V. Gokhroo and S. Nic Chormaic, New. J. Phys., vol. 17, p. 123012 (2015)
[3] R. Kumar, V. Gokhroo, K. Deasy, A. Maimaiti, M. C. Frawley, C. Phelan and S. Nic Chormaic, New J. Phys. vol. 17, p. 013026 (2015)
[4] F. Le Kien, T. Busch, V. G. Truong and S. Nic Chormaic, arxiv.org/abs/1703.00109 (2017) [5] C. Phelan, T. Hennessy and T. Busch, Opt. Exp., vol. 21, p. 27093 (2013)
 

Correlations and entanglement of microwave photons emitted in a cascade decay

We use a three-level artificial atom in the ladder configuration as a source of microwave photons of different frequency. Our artificial atom is a transmon-type superconducting circuit, driven at the two-photon transition between ground and second-excited state. The transmon is embedded into a single-pole, double-throw switch [1] that selectively routes different-frequency photons into different spatial modes. We characterize the decay process for both continuous-wave and pulsed excitation. When the source is driven continuously, power cross-correlations between the two modes exhibit a crossover between strong antibunching and superbunching, typical of cascade decay, and an oscillatory pattern as the drive strength becomes comparable to the radiative decay rate. Using pulsed excitation, we prepare an arbitrary superposition of the ground and second-excited state, and monitor the spontaneous emission of the source in real time. This scheme allows us to deterministically produce entangled photon pairs, as demonstrated by nonvanishing phase correlations and more generally by joint state tomography of the two itinerant photonic modes. [2]
 

References:
[1] M. Pechal, J.C. Besse, M. Mondal, M. Oppliger, S. Gasparinetti, and A. Wallraff, Phys. Rev. Appl. 6, 024009 (2016).
[2] S. Gasparinetti, M. Pechal, J.C. Besse, M. Mondal, C. Eichler, and A. Wallraff, submitted.
 

Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System

One of the central goals in the study of quantum chaos is to establish a correspondence principle between classical chaos and quantum dynamics. Due to the singular nature of the \hbar→ 0 limit, it has been a long-standing problem to recover key fingerprints of classical chaos such as the Lyapunov exponent starting from a microscopic quantum calculation. It was recently proposed that the out-of-time-ordered four-point correlator (OTOC) might serve as a useful characteristic of quantum-chaotic behavior because, in the semi-classical limit, its rate of exponential growth resembles the classical Lyapunov exponent. In this talk, I will present OTOC as a tool to unify the classical, quantum chaotic and weak localization regime for the quantum kicked rotor model--a textbook model of quantum chaos. Through OTOC, I will demonstrate how chaos develops in the quantum chaotic regime and is subsequently destroyed by the quantum interference effects that result in dynamical localization. We also make a quantitative comparison between the growth rate of OTOC and the classical Lyapunov exponent.
 

Thermalization in closed quantum many-body systems I: Basic notions, integrable systems
Thermalization in closed quantum many-body systems II: Non-integrable systems
Reversibility and irreversibility in closed quantum many-body systems

This set of pedagogical lectures will give an introduction to the topic of thermalization in closed quantum many-body systems.

Lecture I:

• Key experiments in closed quantum many-body systems
• Possible definitions of thermalization
• Integrable vs. non-integrable systems
• Thermalization dynamics to the generalized Gibbs ensemble (GGE) in integrable systems

Lecture II:

• Thermalization dynamics in non-integrable systems
• Eigenstate thermalization hypothesis (ETH)
• Prethermalization
• Hydrodynamic tails
• Outlook of important questions for future research

Lecture III:

• Reversibility vs. irreversibility in classical physics
• Experiments in closed quantum many-body systems
• Possible definitions of irreversibility (echo decay, out-of-time-order correlators, scrambling)
• Results and outlook

   

Robust low energy Andreev bound states and quantized transport in semiconductor-superconductor heterostructures

Andreev bound states (ABS) are a generic low-energy feature in semiconductor-superconductor heterostructures. I will talk about how partially unfolded Andreev bound states – ABS whose component Majorana bound states (MBS) are only weakly overlapping -- represent a generic low-energy feature that emerges in non-homogeneous semiconductor nanowires coupled to superconductors in the presence of a Zeeman field. The emergence of these low-energy modes is not correlated with any topological quantum phase transition. Increasing the length scale of the potential inhomogeneity leads to a continuous evolution from strongly overlapping MBSs, which can be viewed as “regular” ABSs that cross zero energy, to spatially separated weakly overlapping MBSs, which can be regarded as robust ABSs that have nearly zero energy in a significant range of parameters and generate signatures similar to the non- degenerate zero-energy Majorana zero modes (MZMs) that emerge in the topological superconducting phase. I will discuss why the only way to distinguish topological MZMs from robust low energy ABSs in the topologically-trivial regime of SM-SC heterostructure wire involves correlating the dI/dV spectra from both ends of the wire, a task which has so far not been performed.
 

Mesoscopic quantum electrodynamics: from atomic-like physics to condensed matter

In this lecture, I will describe how mesoscopic circuits embedded in microwave cavities can be used to study light-matter interaction in novel situations. After introducing the basic tools for the microscopic description of light matter interaction in these systems, I will focus on two important topics: the coupling of a double quantum dot to microwave photons in a quantum information perspective and the use of the microwave cavity for ultra-sensitive compressibility measurements in a condensed matter perspective. I will show at the end of the lecture how these ideas can be generalized in more complex systems.
 

Prolonging coherence times by bath engineering

Quantum systems lose coherence upon interaction with the environment and tend towards classical states. Quantum coherence is known to exponentially decay in time so that macroscopic quantum superpositions are generally unsustainable. We show that, slower than exponential decay of coherences is experimentally realized in an atom-optics kicked rotor system subjected to nonstationary Lévy noise in the applied kick sequence. The slower coherence decay manifests in the form of quantum subdiffusion that can be controlled through the Lévy exponent.
 

Currents in strongly coupled molecular junctions

In recent years, the electron conduction through a single molecular junction has attracted a lot of research interest due to its fundamental interest in exploring quantum effects and its applications in miniaturization of electronic components (molecular electronics). The idea of molecular electronics is to control the electronic current by manipulating the physical and chemical properties of the molecule. There are several theoretical methods to calculate conductance of molecular junctions. Some are (semi) perturbaive while others are not. Among various formulations to compute conductance of molecular junctions, quantum master equation (QME) method [1], which is (semi) perturbative, and nonequilibrium Greens’ function (NEGF) approach [2], which is nonperturbative, are the two most successful formulations. The QME has a simple kinetic structure which makes it very useful in understanding the time-dependent processes in molecular junctions. On the other hand, the NEGF method, although in principle exact, is more involved and is generally used to study steady-state properties. In this talk, I shall present some recent results [3,4] using NEGF and show that within QME formulation some essential physics is lost which leads to completely different results.
 

[1] H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2002).
[2] H. Haug and A. P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, Berlin, 1995).
[3] H. K. Yadalam and U. Harbola, Phys. Rev. B 93, 035312 (2016). [4] H. K. Yadalam and U. Harbola, Phys. Rev. B 94, 115424 (2016).

Control of light-matter interaction in two-dimensional Van der Waals materials

Two-dimensional (2D) Van der Waals materials have emerged as a very attractive class of optoelectronic material due to the unprecedented strength in its interaction with light. In this talk I will discuss approaches to enhance the strength of this interaction even further using microcavities, and metmaterials. I will first discuss the formation of strongly coupled exciton- photon quasiparticles (microcavity polaritons) at room temperature [1] and the valley polarization properties of these polaritons [2] in the 2D transition metal dichacogenide systems.
Following this I will discuss the broadband enhancement of spontaneous emission from these 2D materials using hyperbolic metamaterials [3].
Finally, I will also briefly discuss our recent work on room temperature single photon emission from hexagonal boron nitride [4] and the prospects of developing robust quantum emitters using them.

[1] Strong light-matter coupling in two-dimensional atomic crystals, X. Liu, et al., Nature Photonics 9, 30 (2015).
[2] Optical control of room temperature valley polaritons, Z. Sun, et al. In Press, Nature Photonics (2017).
[3] Broadband Enhancement of Spontaneous Emission in Two- Dimensional Semiconductors Using Photonic Hypercrystals, T. Galfsky, et al. Nano Lett. 16, 4940 (2015).
[3] Photoinduced modification of single photon emitters in hexagonal boron nitride, Z. Shotan, H. Jayakumar, C. R. Considine et al. ACS Photonics 3, 2490 (2016).

Transport and fractality in boundary-driven (quasi)disordered chains​

In this talk we report on the response of (quasi)disordered spin-chains at high temperature to boundary driving through reservoirs at its ends. In the strongly interacting regime, we unveil a rich dynamical phase diagram that displays a panoply of transport properties as an interplay between interaction and disorder strengths: localized, ballistic, superdiffusive, diffusive, and subdiffusive. These effects occur well away from the many-body localization critical point, and whilst the system is still deep in the ergodic phase. Similar anomalous transport is shown to occur in the quasidisordered system at criticality even without interactions; in addition, the nonequilibrium steady state here exhibits spatial fractality in many of its expectation values, opening an alternative route to experimentally probe a system's fractal properties in contrast to measuring quantum wavefunctions.