ICTS

We report the observation of long-lived Floquet prethermal discrete time crystalline (PDTC) order in a three-dimensional position-disordered lattice of interacting dipolar-coupled 13C nuclei in diamond at room temperature. We demonstrate a novel strategy of "two-frequency" driving, involving an interleaved application of slow and fast drives that simultaneously prethermalize the spins with an emergent quasi-conserved magnetization along the x-axis, while enabling continuous and highly resolved observation of their dynamic evolution when periodically kicked away from x. The PDTC order manifests itself in a robust period doubling response of this drive-induced quasi-conserved spin magnetization interchanging between x and -x; our experiments allow a unique means to study the formation and melting of PDTC order. We obtain movies of the time-crystalline response with a clarity and throughput orders of magnitude greater than previous experiments. Parametric control over the drive frequencies allows us to reach PDTC lifetimes up to 396 Floquet cycles which we measure in a single-shot experiment. Such rapid measurement enables detailed characterization of the entire PDTC phase diagram, rigidity and lifetime, informing on the role of prethermalization towards stabilizing the DTC response. The two-frequency drive approach represents the simplest generalization of DTCs to multi-frequency drives; it expands the toolkit for realizing and investigating long-lived non-equilibrium phases of matter stabilized by emergent quasi-conservation laws.

I'll talk about some recent work in line with the theme of this workshop. First, I’ll discuss the formation of shock fronts and current bounces predicted in a light-pulse-quench for helical edge states of a 2D topological insulator. Results obtain from chiral hydrodynamics with strong dissipation, mediated by the unusual one-particle Umklapp interaction that arises via Rashba spin-orbit coupling. Current switching could be observed in a patterned “THz antenna” device. Second, I’ll present results showing a strong enhancement of Cooper pairing in special 1D models with a wide spectrum of fractal wave functions (“spectrum-wide quantum criticality,” SWQC). Self-consistent BCS numerics in the quasiperiodic Aubry-Andre and power-law random-banded matrix models both exhibit a concomitant enhancement of superconductivity with a spectrum-wide Anderson metal-insulator transition. The pairing enhancement is attributed to the strong overlaps exhibited by fractal wave functions at the transition (Chalker scaling). In the past few years, we discovered robust SWQC in 2D continuum models of nodal quasiparticles that arise as surface states of bulk topological superconductors, as well as 2D d-wave superconductivity with quenched nematic randomness. Our 1D results suggest that the interplay of SWQC and strong interactions could play a role in high-Tc d-wave superconductivity. 

In this talk, I will explore the similarities and differences between the fluid dynamical equations that govern ocean waves and the "hydrodynamics" of Fractional Quantum Hall (FQH) fluids. The linearized edge dynamics of the FQH hydro reveals two chiral edge modes propagating in the same direction: a non-dispersing Kelvin mode (observed on coasts) and a dispersing chiral boson mode. The presence of two modes at the edge of a Laughlin state is somewhat perplexing because only one chiral mode is expected for these states.Contrary to what is discussed in literature, I will explain that the Kelvin mode is incompatible with the gauge anomaly and, thus, cannot be associated with the charge transport at the edge. However, the chiral boson mode is consistent with the anomaly-induced chiral edge dynamics. By invoking a fluid dynamical perspective, we can gain further insights into the non-linear dynamics of FQH edge.

In this talk, I will introduce the Periodically Refreshed Baths (PReB) scheme. Simulating non-Markovian dynamics of interacting quantum many-body systems strongly coupled to multiple baths at different temperatures and chemical potentials is a challenging and experimentally relevant problem. The PReB scheme allows for efficient tensor network based numerical simulation of such situations much beyond what is possible in most other techniques. Going further, one can extend the PReB scheme beyond just a numerical technique, to a dynamical process that can be potentially realized in experiments. We then explore the thermodynamics of the steady state of the PReB process. This leads to novel Periodically Refreshed Quantum Thermal Machines, which can interpolate between autonomous quantum thermal machines and those based on collisional or repeated interactions with single-site environments. These quantum thermal machines work on a single-stroke thermodynamic cycle where the working material is always out-of-equilibrium. They can have many counter-intuitive properties, which I will demonstrate via a simple example.

Refs: Phys. Rev. B 104, 045417 (2021),  Quantum 6, 801 (2022).

Quantum materials exhibit remarkable phenomena when driven by the strong fields in femtosecond pulses of light. Recent years have seen a surge of interest in using long-wavelength laser pulses to create photon-dressed Floquet-Bloch states. Much of this excitement is driven by the predictive power of Floquet theory, which has been used, for example, to correctly predict the formation of topological edge states in periodically-driven systems that exhibit no topological properties in equilibrium. Many of these proposals have been verified in quantum simulation settings, but are only just beginning to be explored in quantum materials.

In this talk, I will present results on the electrical transport properties of quantum materials driven by ultrafast pulses of mid-infrared light. In monolayer graphene, we observe an anomalous Hall effect induced by circularly polarized light in the absence of an applied magnetic field. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect a Floquet-engineered topological band structure. The results are a critical first step towards realizing and controlling light-induced topological edge states in quantum materials. I will also discuss our recent results on the Weyl semimetal MoTe2. We observe a rectified, circular dichroic photocurrent response that scales linearly (as opposed to quadratically) with the applied laser field, which is a predicted signature of a photocurrent response originating from the formation of Floquet-Bloch states.

Strong coupling between matter and quantized electromagnetic modes may offer yet another approach of controlling equilibrium phases or dynamics of quantum many-body systems. Recent developments have utilized cavity confinement to realize ultrastrong light-matter interaction in the absence of external driving, where conventional theoretical methods often fail. I will talk about how one can analyze strongly coupled quantum light-matter systems at arbitrary interaction strengths by using a simple unitary transformation. I discuss its application to construction of tight-binding Hamiltonians, cavity control of quantum phases, and dissipative quantum phase transition in resistively shunted Josephson junctions.

Firstly, I will present a generic and exact scaling form of the spectral form factor (SFF) in a many-body quantum chaotic system, deriving the so-called “bump-ramp-plateau” behaviour. Secondly, I will introduce and provide an analytical solution of a generalization of SFF for non-Hermitian matrices, called Dissipative SFF, which displays a "ramp-plateau" behaviour with quadratic ramp. Thirdly, I will provide evidences that non-Hermitian Ginibre ensemble behaviour generically emerge in many-body quantum chaotic systems, due to the presence of many-body interaction.

We will discuss the universal nature of measurement induced phase transitions (MIPTs) in random quantum circuits when the measurement profile follows a static profile. First, the measurement induced transition is shown to be unstable to static but spatially random perturbations and the transition flows off to an infinite randomness fixed point. Second, the nature of several distinct quasiperiodic profiles will be studied and non-Pisot structures will be used to tune between irrelevant and relevant perturbations at the MIPT. In the latter case, the transition flows to an infinite quasiperiodic fixed point where the entanglement scaling is dictated by the wandering exponent of the quasiperiodic profile. The nature of these transitions are computed using large scale Clifford simulations and will be shown to be well described by real space renormalization group calculations. 

In this talk, I show how a dynamical entanglement transition in a monitored quantum system is revealed by a local order parameter with the addition of feedback. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and uncontrolled phases as a function of the rate at which the control is applied. We show that such control transitions persist in open quantum systems where control is implemented with local measurements and unitary feedback. Starting from a simple classical model with a known control transition, we define a quantum model that exhibits a diffusive transition between a chaotic volume-law entangled phase and a disentangled controlled phase. Unlike other entanglement transitions in monitored quantum circuits, this transition can also be probed by correlation functions without resolving individual quantum trajectories. Building on this, we define a version of this model with classically simulable stabilizer circuits and show that not only does the entanglement transition separate from the control transition, but it returns to the universality class found for the 1+1D entanglement transition in hybrid stabilizer circuits.

In this talk we will consider two classes of periodically driven systems in one dimension. In the first case, we consider a spin-1/2 $XY$ model in a transverse field, where the field is driven periodically in time. The periodic driving can generate two kinds of modes, topological modes (for which the phases of the Floquet eigenvalues are 0 or $\pi$) and non-topological modes (for which the phases can be arbitrary), which are localized at the ends of a finite-sized system. We study the out-of-time-ordered correlators (OTOCs) of spin operators which are local ($\sigma^z$) or non-local ($\sigma^x$) in terms of Jordan-Wigner fermions. The OTOCs of non-local operators show pronounced scrambling and unscrambling of quantum information after reflections from the ends of the systems. Further, the OTOCs of both local and non-local operators can detect the presence of end modes which give rise to oscillations as a function of the stroboscopic time. Both kinds of OTOCs show that information propagates with a maximum velocity known as the Lieb-Robinson bound.

In the second case, we study a system of fermions where there is an on-site potential which varies periodically in space, and the strength of the potential is varied periodically in time. We find that system becomes dynamically localized for special values of the driving strength and frequency. The dynamical localization gives rise to an extreme limit of the Su-Schrieffer-Heeger model in which the nearest-neighbor hoppings are zero and non-zero alternately; as a result, there are an extensive number of conserved quantities. Further, if there are density-density interactions between particles on nearest-neighbor sites, the system effectively turns into the transverse field Ising model. We study the half-chain entanglement entropy versus the Floquet quasienergy and find that the large number of conserved quantities can give rise to a highly fragmented structure of the entanglement versus quasienergy plot. A study of the time evolution of the Loschmidt echo and some two-point correlation functions show long-time oscillations indicating that the system has anomalous thermalization behavior.

References: S. Sur and DS, arXiv:2210.15302,  S. Aditya and DS, arXiv:2305.06056.

We discuss recent developments in the stochastic approach to non-equilibrium quantum spin systems based on links between quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as averages over classical stochastic processes. We illustrate this approach for the quantum Ising model by extracting the Loschmidt amplitude and the magnetization dynamics from the numerical solution of stochastic differential equations. We demonstrate that the method is capable of handling integrable and non-integrable problems in a unified framework, including those in higher dimensions. We highlight the utility of trajectory-resolved Weiss fields for extending this approach, both in space and in time. 

Quantum supremacy is the ability for quantum computers/devices to efficiently solve a well-defined computational task that is guaranteed to be inefficient for classical computers. The most common task to realise quantum supremacy in near-term quantum devices is sampling from the output probability distribution, demonstrated with 53 superconducting qubits by Google[1]. Despite being able to outperform classical computers, sampling from a complex quantum system has very few direct useful applications. Early proposals for realizing quantum supremacy include boson sampling, random quantum circuits and 2D Ising models. We have managed to extend this family to include to driven many-body systems in analog quantum simulators settings.  The work is based on complexity theory arguments and supports earlier intuitions and heuristic claims, that is indeed computational hard to simulate complex quantum dynamics. Our result opens the path for a multitude of analog platforms to showcase and benchmark quantum supremacy, including cold atoms, ions and superconducting qubits. The connection was made via showing that sampling from the output distribution of thermalizing driven many-body systems is #P hard and the hardness is connected with the quantum phase matter is in. Recently, in collaboration with USTC China, an experiment has been performed where some of our predictions were checked in cold atom setup [3].
 

References

[1]    Frank  Arute, Kunal  Arya, […],  John  M.  Martinis,  Quantum  supremacy  using  a  programmable superconducting processor Nature, 574, 505-510 (2019)
[2]    J. Tangpanitanon, S. Thanasilp, M. A. Lemonde, N. Dangiam, D. G. Angelakis Quantum supremacy in driven quantum many-body systems, arxiv.org/2002.11946 (to appear in Quantum Science and Technology)
[3]    Yong-Guang Zheng et al, Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System, arXiv: arXiv:2210.08556

Interacting many-body systems subject to driving and dissipation can exhibit a wealth of complex phenomenon, even in the limit where the dynamics can be described by a Markovian, Lindblad master equation.  I will discuss how a subtle version of time-reversal symmetry relevant to open quantum systems (a kind of quantum detailed balance) can in some cases be exploited to allow exact analytic descriptions of such systems.  I will discuss applications to both a kind of driven-dissipative Bose Hubbard model, and a driven-dissipative transverse-field Ising model.

We propose a novel framework to characterize the thermalization of many-body dynamical systems close to integrable limits using the scaling properties of the full Lyapunov spectrum. We use a classical unitary map model to investigate macroscopic weakly nonintegrable dynamics beyond the limits set by the KAM regime. We perform our analysis in two fundamentally distinct long-range and short-range integrable limits which stem from the type of nonintegrable perturbations. Long-range limits result in a single parameter scaling of the Lyapunov spectrum, with the inverse largest Lyapunov exponent being the only diverging control parameter and the rescaled spectrum approaching an analytical function. Short-range limits result in a dramatic slowing down of thermalization which manifests through the rescaled Lyapunov spectrum approaching a non-analytic function. An additional diverging length scale controls the exponential suppression of all Lyapunov exponents relative to the largest one.

Optical properties of crystals involve the geometry and topology of Bloch wavefunctions in ways similar to the appearance of Berry curvature in the quantum Hall effect.   As a result, nonlinear optical properties can be intrinsic and even quantized in certain limits.  For periodic driving, Floquet theory offers a compact way to derive several important quantities.  We start by reviewing the basics of optical properties and show how linear optics in Weyl semimetals can be related to that in other metals, while in nonlinear optics there can be a unique quantization effect that may have already been observed experimentally in certain Weyl semimetals.  An active experimental direction in recent years is the use of pump pulses, or alternately current drives, that are chosen to modify the symmetry of a material.  For example, circularly polarized light provides a means to induce broken time-reversal symmetry in a non-magnetic material, while current drive breaks both time-reversal and inversion symmetries.  Examples discussed include current-induced linear optical effects in semimetals and superconductors, where they provide important probes of topological band structure and order parameter symmetry respectively.  We discuss the effects of interactions and how solids behave beyond perturbation theory in closing.

In this talk we will present preliminary results from a study considering the collective dissipative dynamics of two or more Harmonic oscillators interacting with a 1-D electromagnetic bath by exactly solving the dynamics numerically in various regimes of coupling strengths. While the weak coupling regime leads to expected results in agreement with the Markovian Lindblad master equations, we uncover interesting collective dynamics in the strong coupling regime.

Recently a hydrodynamic theory of integrable systems has been developed which makes it possible to understand non-equilibrium processes in such systems. I will discuss this theory in the context of a collection of Hard rods in one dimension which is one of the simple interacting integrable systems. In the second part of the talk, I will talk about what happens when the microscopic integrability is broken by trapping them inside a confining potential. Understanding non-equilibrium dynamics of trapped integrable systems has recently drawn a lot of interest. I will discuss chaos, ergodicity and thermalisation properties of trapped hard rods.

Caustics are the brightest regions of wave patterns and occur generically in nature as a result of natural focusing. Examples include rainbows, gravitational lensing, ships’ wakes, and tidal bores. Branched flow is a related effect where caustics evolve into well-defined branches or tubes of intensity that persist over many correlation lengths of a weakly random potential and are believed to explain phenomena ranging from electron propagation in semiconductors to tsunami focusing. In this talk I will present examples of this behaviour in a simple periodically and quasiperiodically driven system.