ICTS

Much has been learned about universal properties of the eigenstate entanglement entropy for one-dimensional lattice models, which is described by a Hermitian Hamiltonian. While very less of it has been understood for non-Hermitian systems. In this talk  I will discuss   a non-Hermitian, non-interacting model of fermions which is invariant under combined  PT transformation. Our models show a phase transition from PT unbroken phase to broken phase as we tune the hermiticity breaking parameter. Entanglement entropy of such systems can be defined in two different ways, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates which form a complete set of bi-orthonormal eigenstates. We demonstrate that the entanglement entropy of the ground state and also of the typical excited states show some unique features in both of these phases of the system. Most strikingly, entanglement entropy obtained taking a combination of both left and right eigenstates shows a divergence at the transition point. While in the PT-unbroken phase, the entanglement entropy obtained from only the right (or equivalently left) eigenstates shows identical behavior as of an equivalent Hermitian system which is connected to the non-Hermitian system by a similarity transformation.

In my talk I will discuss the dynamics of correlations in a paradigmatic setup to observe PT-symmetric physics: a pair of coupled oscillators, one subject to a gain one to a loss. Starting from a coherent state, quantum correlations (QCs) are created, despite the system being driven only incoherently, and can survive indefinitely. Both total and QCs exhibit different scalings of their long-time behavior in the PT-broken/unbroken phase and at the exceptional point (EP). In particular, PT symmetry breaking is accompanied by non-zero stationary QCs. This is analytically shown and quantitatively explained in terms of entropy balance. The EP in particular stands out as the most classical configuration, as classical correlations diverge while QCs vanish.

The discovery of two new orthogonal polynomials also known as Xm Exceptional Laguerre and Jacobi orthogonal polynomials leads to search a new family of exactly solvable (ES) real as well as PT symmetric complex potentials. These new potentials are the rational extension of the known ES conventional potentials. Some of the rationally extended real and PT symmetric complex potentials with their solutions in terms of these polynomials are discussed. Keywords: New orthogonal polynomial; Rationally extended potential, PT symmetric potential.
References: [1] D.Gomez-Ullate,N.Kamran,R.Milson,J.Math.Anal.Appl.359(2009)352.
[2] D.Gomez-Ullate,N.Kamran,R.Milson,J.Phys.A43(2010)434016.
[3] C.Quesne,J.Phys.A41(2008)392001.
[4] S.Odake,R.Sasaki,Phys.Lett.B684(2010)173; Phys.Lett.B679(2009)414;
[5] R.K.Yadav,A.Khare,B.P.Mandal,Ann.Phys.331(2013)313; Phys. Lett. B 723 433 (2013); Phys. Lett. A 379 (2015) 67.
[6] R. K. Yadav, N. Kumari, A. Khare and B. P. Mandal, Ann. Phys. 359 (2015) 46.
[7] N. Kumari, R. K. Yadav, A. Khare, B. Bagchi and B. P. Mandal, Ann. Phys.373 (2016) 163.
[8] R. K. Yadav, A. Khare, N. Kumari and B. P. Mandal, Ann. Phys.400 (2019) 189.

Scattering of low-energy waves has numerous applications in different areas of physics and engineering. This has motivated the development of a rigorous mathematical theory of low-energy scattering in one dimension. For exponentially decaying potentials this theory provides a rather elaborate scheme for computing the coefficients of the series expansion of the reflection and transmission amplitudes in powers of the wavenumber k. In this talk, we offer an alternative and much simpler approach to low-energy scattering that relies on the dynamical formulation of stationary scattering. This is an approach to potential scattering in which the transfer matrix is related to the time-evolution operator for a non-unitary two-level quantum system. The coefficients of the low-energy series for the scattering data depend on a pair of solutions of the zero-energy Schrödinger equation. We introduce a transfer matrix for the latter and relate it to the evolution operator for another non-unitary two-level system. Our approach applies to both real and complex scattering potentials. We use it to treat the low-energy potential scattering in the half-line and comment on its utility in the study of transmission of scalar waves through a traversable wormhole. 
References: 
1. A. Mostafazadeh, “Solving scattering problems in the half-line using methods developed for scattering in the full line,” Ann. Phys. (NY) 411, 167980 (2019); arXiv:1910.07382.
2. B. Azad, F. Loran, and A. Mostafazadeh, “Transmission of low-energy scalar waves through a traversable wormhole,” Eur. Phys. J. C 80, 197 (2020); arXiv:2010.15023.
3. F. Loran, and A. Mostafazadeh, “Dynamical formulation of low-energy scattering in one dimension,” preprint arXiv:2102.06084.

Non-Hermitian quantum theories have been applied in many other areas of physics. In this talk, I will review recent developments in the formulation of non-Hermitian quantum field theories, highlighting features that are unique compared to Hermitian theories. I will describe their second quantisation, their crucial discrete symmetries and how continuous symmetry properties are borne out, including Noether's theorem, the Goldstone theorem and the Englert-Brout-Higgs mechanism. As examples, I will describe non-Hermitian deformations of QED, the Higgs-Yukawa theory and flavour oscillations, illustrating the potential implications for the neutrino sector.  Together, these results pave the way for a systematic programme of non-Hermitian model building beyond the Standard Model of particle physics.

In non-Hermitian scattering problems the behavior of the transmission probability is very different from its Hermitian counterpart; it can exceed unity or even be divergent, since the non-Hermiticity can add or remove the probability to and from the scattering system. In the present paper, we consider the scattering problem of a PT-symmetric potential and find a counter-intuitive behavior. In the usual PT-symmetric non-Hermitian system, we would typically find stationary semi-Hermitian dynamics in a regime of weak non-Hermiticity but observe instability once the non-Hermiticity goes beyond an exceptional point. Here, in contrast, the behavior of the transmission probability is strongly non-Hermitian in the regime of weak non-Hermiticity with divergent peaks, while it is superficially Hermitian in the regime of strong non-Hermiticity, recovering the conventional Fabry-Perot-type peak structure. We show that the unitarity of the S-matrix is generally broken in both of the regimes, but is recovered in the limit of infinitely strong non-Hermiticity.
This talk is based on the following paper:
Ken Shobe, Keiichi Kuramoto, Ken-Ichiro Imura, Naomichi Hatano,
Non-Hermitian Fabry-Perot Resonances in a PT-symmetric system,
arXiv:2011.02097; submitted to Phys. Rev. Research

We review the first quantum detection problem, under repeated strong measurements. Focusing on the return problem and stroboscopic smapling, Grunbaum et al. showed that the mean return time, for a finite dimensional system is quantized, and equal to the number of distinct energy levels in the system provided that all have a finite over lap with the detected state. Close to critical sampling times, the variance of this time exhibits large fluctuations which we analyse. We show how similar effects are found in the Zeno limit for a non-Hermitian model, and for random sampling times. The effect is related to a topological invariant, and it implies that the mean return time, is insensitive to the sampling rate. For the transition problem, namely when the initial and final states are orthogonal, we find rich classes of behaviors.

We investigate Non-Hermitian quantum field theoretic model with $\iota g\phi^3$ interaction in 6 dimension. Such a model is PT-symmetric for the pseudo scalar field $\phi $. We analytically calculate the 2-loop $\beta$ function and analyse the system using renormalization group technique. Behavior of the system is studied near the different fixed points. Unlike $g\phi^3$ theory in 6 dimension $\iota g\phi^3$ theory develops a new non trivial fixed point which is energetically stable. Existence of new non-trivial UV fixed points is also shown for three and four loop $\beta $-functions.

We derive and study the Born and Markov approximated Redfield, local-Lindblad and the recently derived universal Lindblad quantum master equation, for open Heisenberg XXZ and XX spin chains coupled to multiple thermal reservoirs. In the equilibrium scenario, over a wide range of the intersite coupling parameter, we find that the Redfield and universal Lindblad approaches correctly predict the expected thermal steady-state, wheareas the local-Lindblad approach is inadequate. In the case of non-equilibrium baths at different chemical potential and/or temperature, Redfield predict a non-monotonic behaviour of current with the intersite coupling parameter, which is completely missed by local-Lindblad. For the XX chain with baths attached at the edge sites, we also derive closed-form analytical results for time dynamics of two-point correlation functions. We use these results to present an important flaw in the universal Lindblad approach, by showing that it does not obey the continuity equation for spin current. Finally, we find that the universal-Lindblad boundary current agrees with the Redfield current. Hence, we argue that the correct way to compute current in the universal-Lindblad approach is via boundary currents.

Ladder operators are used in quantum mechanics in several contexts, and are usually attached to suitable commutation or anti-commutation relations, as in the bosonic and in the fermionic cases. Since some years, raising and lowering operators not connected by the "standard" Dirac adjoint and acting on biorthogonal families have been considered, mainly in connection with non self-adjoint Hamiltonians. In this talk we discuss some recent results on these operators and on their connected bi-coherent states. The mathematical role of distribution theory in this analysis is discussed.

I will demonstrate how new integrable nonlocal systems in space and/or time can be constructed by exploiting certain parity transformations and/or time reversal transformations possibly combined with a complex conjugations. By employing Hirota’s direct method as well as Darboux-Crum transformations I will show how to construct explicit multi-soliton solutions for nonlocal versions of Hirota’s equation that exhibit new types of qualitative behaviour. I will exploit the gauge equivalence between these equations and an extended version of the continuous limit of the Heisenberg equation to show how nonlocality is implemented in those latter systems and an extended version of the Landau-Lifschitz equation. I conclude by discussing different types of non-Hermitian field theories that allow for the construction of well-defined Bogomolny-Prasad-Sommerfield (BPS) soliton solutions by imposing self-duality. I will argue that the reality of the energy of these solutions is due to the topological properties of the complex BPS solutions. These properties result in general from modified versions of antilinear CPT symmetries that relate self-dual and an anti-self-dual theories. The talk is based on joint work with Julia Cen, Francisco Correa and Takanobu Taira.

Exceptional points (EPs) are degeneracies of non-Hermitian Hamiltonians where both eigenvalues and corresponding eigenvectors coalesce. Over the past five years, EPs in open wavesystems with gain, loss, or both, have been intensely explored due to their topological properties and enhanced sensitivity. In this classical domain (the number of energy quanta is much larger than one), the non-unitary dynamics of a system are accurately described by an effective, non-Hermitian Hamiltonian. In contrast, the dynamics of a minimal quantum system, inevitably coupled to the environment, are described by a Lindblad equation for its density matrix. I will review the challenges for realizing a quantum system that undergoes the non-unitary, coherent time evolution generated by a non-Hermitian Hamiltonian, or more generally, parity-time symmetric quantum systems. I will then show how these challenges can be overcome in multiple platforms comprising ultracold atoms, integrated or table-top quantum photonics, and superconducting qubits. This work was done in collaboration with Le Luo group (Sun Yat-Sen University), Anthony Laing group (Bristol), and Kater Murch group (Wash U).

The quantum tunneling is one the earliest studied problems of quantum mechanics. However how much time does a particle takes to tunnel through a classically forbidden potential is still an open problem. In the year 1962, Hartman studied the problem of tunnelling time by using stationary phase method (SPM) and showed that the tunneling time is independent of thickness of classically opaque barrier for a sufficiently thick barrier. The saturation of tunnelling time with the thickness of the barrier for an opaque barrier is known as Hartman effect. This paradox is not yet resolved.

We investigated the effect of PT-symmetry in the tunnelling time as calculated by SPM. We find that for system respecting PT-symmetry, the tunneling time saturates with the thickness of the P T-symmetric barrier and thus shows the existence of Hartman effect. For the case when PT-symmetry is broken, the tunneling time depends upon the thickness of the barrier and Hartman effect is lost. It is also found that the Hartman effect from a real barrier is due to the limiting case of a layered PT-symmetric system. Thus it appears that PT-symmetry may be playing some role in the occurrence of Hartman effect. We also present results of two general theorems related to Hartman
effect in this talk.

The scattering of waves through disordered media is a paradigmatic phenomenon that has captured the interest of various communities of physics for quite some time now. Recently the problem of localization attracted renewed interest as research moved to two largely unexplored directions, namely the many body interactions, and the effect of non-Hermiticity. In this talk, we will try to answer some of the main questions that stem from the interplay of disorder and non-Hermiticity in scattering media and optical lattices, in the context of non-Hermitian photonics [1]. The first part of the talk will be devoted to a generalization of the concept of plane waves that is possible only in non-Hermitian media [2]. The experimental
observation of such constant-intensity (CI-waves) in the acoustic regime [3], as well as, their application to suppression of localization and unidirectional invisibility [4,5] will be presented. In the second part of the talk, we will examine the effect of uncorrelated complex disorder in optical waveguide lattices [6]. At the end, we will discuss recent results regarding pseudospectra of non-Hermitian matrices with higher order exceptional points. Connection of the above topics to non-
Hermitian random matrices will be also examined.

REFERENCES
[1] R. El-Ganainy, K.G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian Physics and PT-symmetry”, Nat. Phys. 14, 11 (2018).
[2] K.G. Makris, A. Brandstötter, P. Ambichl, Z.H. Musslimani, and S. Rotter, “Wave propagation through disordered media without backscattering and intensity variations”, Light Sci. Appl. 6, e17035 (2017).
[3] E. Rivet, A. Brandstötter, K.G. Makris, H. Lissek, S. Rotter, and R. Fleury, “Constant-pressure sound waves in non-Hermitian disordered media”, Nat. Phys. 14, 479 (2018).
[4] A. Brandstötter, K.G. Makris, and S. Rotter, “Scattering-free pulse propagation through invisible non-Hermitian media”, Phys. Rev. B 99, 115402 (2019).
[5] K.G. Makris, I. Kresic, A. Brandstötter, and S. Rotter, “Scattering-free channels of invisibility across non-Hermitian media”, Optica 7, 619 (2020).
[6] A. Tzortzakakis, K.G. Makris, and E. N. Economou, “Non-Hermitian disorder in two-dimensional optical lattices”, Phys. Rev. B 101, 014202 (2020).

In this work, we reveal the occurrence of higher-dimensional exceptional manifolds in the spectrum of a magnetized donor atom at the endpoint of a molecular chain. We demonstrate the presence of both an exceptional ring and an exceptional surface in the parameter space of an externally applied magnetic field, which reflect underlying symmetries in the model. We propose electron spin resonance (ESR) as a method to observe these exceptional manifolds in experiment. We emphasize that the exceptional manifolds arise in our system due to the influence of the microscopic degrees of freedom ascribed to the molecular chain. This is as opposed to treatments in which explicit non-Hermitian elements are introduced to represent macroscopic approximations over such degrees of freedom. [1] Yujin Dunham, Kazuki Kanki, Savannah Garmon, Gonzalo Ordonez, Satoshi Tanaka, arXiv:2012.14655

In this talk, I will discuss both coherent photonic and incoherent electron transport properties in voltage biased quantum dot circuit-QED systems. For the photonic part, I will discuss transmission spectroscopy, the photon amplification principle, and the statistics of emitted photons below and above the masing threshold. The impact of large scale systems on photon gain will also be discussed. In the last part of the talk, I will discuss the steady-state electron transport properties to better understand the intricate interplay between light and matter

Consider an experiment where a quantum particle is released from a box at time t=0 and a particle detector placed at some distance clicks as soon as the particle "arrives" at the detector. What is the time of arrival of the particle? This is the quantum first passage problem and this requires one to study the quasi-Zeno dynamics of a system whose unitary dynamics is punctuated by repeated projective measurements. We show that this dynamics can be described by a non-Hermitian Hamiltonian and discuss various physical consequences that can be extracted.

In practice the dynamics of any open quantum system is expected to deviate from the ideal unitary dynamics due to coupling with the environment. A minimal set up where a test of quantum mechanics can be performed is via study of bounds on temporal correlation functions, which are defined by dichotomic observables. It is well known that such standard measure of quantumness of the dynamics of a system are temporal analog of Bell's inequality, known as Leggett-Grag inequality (LGI) and is bounded above in quantum mechanics by value 1.5 (Luder’s bound) for a two level system, though the algebraic maximum is 3. The purpose of this presentation is to provide an exact proof that the upper bound on LGI for arbitrary time dependent Hermitian dynamics of a two level system is 1.5, which earlier has been proven for the static time independent Hermitian dynamics only. Furthermore, we provide an exact proof that a two level quantum system coupled to a Markovian bath, such that the reduced dynamics of the system can be represented in Kraus operator form, also exactly follows the same bound of 1.5. Moreover, since the Kraus operators define a dynamics which can be represented by a linear map, we show that introducing minimal non-linearltiy in such maps, which for example can be mimicked using non-Hermitian dynamics leads to violation of the quantum mechanical bound of 1.5. (communicated to Phys. Rev. A)

The concepts and tools from the theory of non-Hermitian quantum systems are used to investi- gate the dynamics of a quantum thermal machine. This approach allows us to characterize in full generality the analytical time-dependent dynamics of an autonomous quantum thermal machine, by solving a non-Hermitian Liouvillian for an arbitrary initial state. We show that the thermal machine features a number of exceptional points for experimentally realistic parameters. The signatures of a third-order exceptional point, both in the short and long-time regimes are demonstrated. As these points correspond to regimes of critical decay towards the steady state, in analogy with a critically damped oscillator, our work opens interesting possibilities for the precise control of the dynamics of quantum thermal machines.
Ref: Shishir Khandelwal, Nicolas Brunner and Géraldine Haack, arXiv:2101.11553.

In this talk, I will show that we can achieve the strong inhomogeneity regime with a change of the spin orbit interaction strength larger than the hopping energy between two localized electronic orbitals. This is achieved by the use of carbon nanotube double quantum dots coupled to two magnetically textured gates. We probe this system using a microwave cavity which allows us to sense the spin texture of the electronic states induced in the carbon nanotube.

Numerous recent works have suggested using open quantum systems as a way to implement fully quantum non-Hermitian dynamics. The quantum-mechanical steady states of such systems have now however been fully characterized. I’ll discuss recent theory work that attempts to fill this gap, focusing on the paradigmatic non-reciprocal Hatano-Nelson model. There are a number of surprises, including an unexpected dependence on particle statistics (fermions or bosons), and a sensitivity to boundary conditions that is non-trivially related to the non-Hermitian skin effect.

In the first part of the talk [1], we will discuss localization in cavity-QED arrays. We show that a careful engineering of drive, dissipation and Hamiltonian results in achieving indefinitely sustained self-trapping. We show that the intricate interplay between drive, dissipation, and light-matter interaction results in requiring an optimal window of drive strengths in order to achieve such non-trivial steady states. In the second part of the talk [2], we will discuss optimal protocols for efficient photon transfer in a cavity-QED network. This is executed through a stimulated Raman adiabatic passage scheme where time-varying inductive or capacitive couplings (with carefully chosen sweep rate) play a key role.
[1] A. Dey, M. Kulkarni, Phys. Rev. A 101, 043801 (2020)
[2] A. Dey, M. Kulkarni, Phys. Rev. Research 2, 042004, Rapid Communications (2020)

In recent times there has been much discussion of non-Hermitian quantum systems in the context of many body systems owing to the exotic manifestations like violation of Lieb-Robinson bound (PRL 124,136802 (2020)), non-Hermitian skin effect (PRL 121, 086803 (2018)), suppression of defect production in Kibbel-Zurek mechanism (Nature Comm. 10, 2254 (2019)) and correspondence between (d+1) dimensional gapped Hermitian systems and d-dimensional point-gapped non-Hermitian systems (PRL 123, 206404 (2019)). Hence a possibility of simulating such a system which will facilitate the direct observation of such phenomena could be of great importance. It is known that the dynamics of a single spin-1/2 PT-symmetric system can be simulated by conveniently embedding it into a subspace of a larger Hilbert space with unitary dynamics. In the context of many body physics, what would be the consequence of complexity of such ideas of embedding non-Hermitian many body systems in unknown. We show that such an embedding leads to non-trivial Hamiltonian which has complex interactions. We consider a simple example of N free PT-symmetric spin-1/2s to obtain the resulting many-body interacting Hamiltonian of N+1 spin-1/2s. We can visualize it as a strongly correlated central spin model with the additional spin-1/2 playing the role of central spin. We would show that due to the orthogonality catastrophe, even a vanishing small exchange field applied along the anisotropy axis of the central spin leads to a strong suppression of its decoherence arising from spin-flipping perturbations.

This talk would be based on the following paper: Anant V. Varma, and Sourin Das, Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model” arXiv:2012.13415 (communicated to Phys. Rev. B) .

Following a generic approach that leads to Bogomolny-Prasad-Sommerfield (BPS) soliton solutions by imposing self-duality, we investigate two different types of non-Hermitian field theories. First, we construct exact ‘t Hooft-Polyakov monopole in the non-Hermitian model with local SU(2) and modified antilinear CPT symmetry, giving rise to a finite and real monopole mass that saturate the lower energy bound. Next, we consider the complex extended sine-Gordon model, where we establish explicitly that the energies are the same as those in an equivalent pair of a non-Hermitian and Hermitian theory obtained from a pseudo-Hermitian approach by means of a Dyson map. We argue that the reality of the energy is due to the modified versions of antilinear CPT symmetries that relate self-dual and anti-self-dual theories. Based on: 1) A. Fring and T. Taira, ’t Hooft-Polyakov monopoles in non-Hermitian quantum field theory, Phys. Lett. B 807, 135583 (2020). 2) A. Fring and T. Taira, Complex BPS solitons with real energies from duality, arXiv:2007.15425, accepted for publication in J. Phys. A: Math. and Theor. (2020).