Session H24: Non-Equilibrium Physics in AMO Systems II

Phonon excitations in a one dimensional Bose gas

Cold atomic gases provide a powerful tool to investigate quantum many-body systems [1]. Phonons, which are low-energy collective excitations for one dimensional superfluids, play a major role in the relaxation dynamics of such systems. It has been shown that mechanisms of phonon dephasing and rephasing generate, respectively, losses and recurrences of coherence in a quantum isolated system, and that the long time behavior of the system itself is determined by the spectrum of the phononic modes [2]. In our experiment we are able to excite and detect phonon modes individually and to monitor them over time.
Our system consists in a 1D BEC of ⁸⁷Rb atoms confined in a box trap, which provides a dispersion relation where the phonon energies are commensurate. We implement a shaking process that modulates the box walls symmetrically at a fixed frequency. The density profile of the cloud can be obtained via absorption imaging at different times. Doing so, we are able to investigate, within a reasonably broad range of frequencies, the growth of the lower symmetric modes when the system is excited, and their subsequent evolution and damping after the end of the shaking.

[1] Schweigler et al., Nature 545, 323 (2017)
[2] Rauer et al., Science 360, 307 (2018)   

Exact strong-ETH violating eigenstates and quasiparticle descriptions of many-body scar states in the Rydberg-blockaded atom chain

A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a period-2 charge density wave initial state (Z2 state), and theoretical works identified a set of many-body ``scar states'' in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at infinite temperature that can be represented exactly as matrix product states with finite bond dimension, for both periodic boundary conditions (two exact E = 0 states) and open boundary conditions (two E = 0 states and one each E = ± √2). This discovery explicitly demonstrates violation of strong eigenstate thermalization hypothesis in this model. These states show signatures of translational symmetry breaking with period-2 bond-centered pattern, despite being in 1d at infinite temperature. We show that the whole tower of Z2 many-body scar states can be excellently approximated as single or multiple ``quasiparticle excitations" on top of our exact E = 0 states, and propose a quasiparticle explanation of the strong oscillations observed in experiments. We also discuss the possibility of similar construction for Z3 many-body scar states relevant for quench with period-3 CDW initial state.   

Observation of Non-Gaussian Statistics and Levy Flights in Nitrogen Vacancy Centers

A nitrogen-vacancy center can be used as a probe of the interacting
13C nuclear spins in a diamond crystal. Under the right
conditions, its behavior can be described as a random walk with step sizes
drawn from a distribution without a well-defined mean or standard deviation.
Its behavior is then described by Levy statistics, providing an opportunity
to study Levy statistics in a well understood system.   

Detection of quantum phases via out-of-time-order correlators

We elucidate the relation between out-of-time-order correlators (OTOCs) and phase transitions via analytically studying the OTOC dynamics both in non-degenerate and degenerate spectra. Our method indicates that for a wide variety of quantum phase transitions, OTOCs can directly characterize various quantum phases as well as their symmetry breaking patterns. Key ingredients about how to utilize OTOC to detect and characterize a quantum phase transition are presented. We further discuss how our method could be useful to understand the dynamical features of the OTOCs.   

Beyond Bose Fireworks: Stimulated Emission of Exotic Shaken Condensates

Periodic modulation of the two-body interaction in a Bose condensate has led to the interesting observation of “Bose fireworks” [Nature 551, 356–359 (2017)]; these were later shown to be well captured by our time-dependent Gross-Pitaevskii simulations [arXiv:1807.08781]. The promise of these experiments is that this stimulated emission may, through the process of parametric amplification, make it possible to unravel the structure (i.e., wavefunction amplitude and phase) of an unknown condensate. We seek to fulfill this promise by presenting numerical simulations of analogous fireworks patterns in more complex systems. We consider single and multiple imprinted vortices (giving rise to "chiral jets") as well as more exotic states. Using the far-field jets to reveal the character of the initial condensate is reminiscent of established procedures in particle physics and we address how this expertise can be exploited.   

Dynamical critical behavior of long-range spin models

Long range interacting spin models exhibit a variety of order-to-disorder phase transitions. We consider prototypical long-range spins models, and investigate dynamical properties of the order parameter as well as entanglement after a sudden quench in the Hamiltonian. The quench dynamics is studied through a combination of exact numerics and analytical calculations. We show that, depending on the nature of quench, different dynamical critical behavior arises. Specifically, we identify regimes when the stationary state at long times exhibits a non-thermal scaling behavior, and describe the signatures in the entanglement. Our results are amenable to realization in experiments with trapped-ion experiments where long-range interactions naturally arise.   

Floquet resonances from integrability: Spin polarization in a driven central spin model

Adiabatically varying the driving frequency of a periodically driven many-body quantum system can induce controlled transitions between resonant eigenstates of the time-averaged Hamiltonian, corresponding to adiabatic transitions in the Floquet spectrum and presenting a general tool in quantum many-body control. Using the central spin model as an application, we show how such controlled driving processes can lead to a polarization-based decoupling of the central spin from its decoherence-inducing environment at resonance. While it is generally impossible to obtain the exact Floquet Hamiltonian in driven interacting systems, we exploit the integrability of the central spin model to show how techniques from quantum quenches can be used to explicitly construct the Floquet Hamiltonian in a restricted many-body basis and model Floquet resonances.   

Floquet-Induced Superfluidity with Periodically Modulated Interactions of Two-Species Hardcore Bosons in a One-dimensional Optical Lattice

We consider two species of hard-core bosons in a one-dimensional optical lattice with periodically modulated repulsive interactions. Using Floquet theory the periodic can be mapped to an effective Hamiltonian for high frequencies, which is described by a static interaction and hopping parameters that depend on the local densities. In particular, if the density difference of one species is non-zero on neighboring sites, the effective hopping of the other species is reduced and can even take on negative values. Using a combination of analytic calculations and different numerical simulations we establish the full quantum phase diagram for half-integer filling for this system. The density-dependent reduction of hopping drives a quantum phase transition into a superfluid phase. For negative hopping a previously unknown state is found, where one species induces a gauge phase of the other species, which leads to a new superfluid phase. The corresponding experimental signatures in time-of-flight experiments are calculated and show characteristic signatures of the different phases.   

Analysis of weakly-driven multi-emitter cQED systems

In this work, we show that a weakly driven multi-emitter cQED system can be analyzed by approximating the driving coherent state with a single- and two-photon Fock state, and using the Scattering matrix formalism to analyze the response of this system to these Fock states. This is a significantly more computationally feasible approach than the master equation formalism, allowing the analysis of multi-emitter systems with ~50 emitters. We use this approach to analyze the transmission and second order correlations induced in the incident coherent state by the multi-emitter system. In particular, we show that for identical emitters, increasing the number of emitters does not improve the polaritonic photon blockade. Moreover, we analyze the impact of inhomogeneous broadening on the second order correlation function of the light emitted by the multi-emitter system with large number of emitters, and analyze the emergence and behaviour of subradiant photon blockade in such multi-emitter systems.   

The Density Matrix Renormalization Group for Periodically Driven Many-Body Systems

Driving a quantum system periodically in time can profoundly alter its long-time dynamics and trigger exotic quantum states of matter. We propose a new DMRG method which directly deals with the Fourier components of the eigenstates of a periodically driven system using Floquet theory. With this new method we can go beyond effective Hamiltonians and take into account higher Floquet modes. Numerical results are presented for the isotropic Heisenberg antiferromagnetic spin-1/2 chain under both local (edge) and global driving for energies, spin-spin correlation and temporal fluctuations. As the frequency is lowered, the spin system enters into a Floquet regime with a coherent exciations of a large number of Floquet modes, which shows characteristic quantum correlations that cannot be described by any effective static model.
  

Effective Cross Section Enhancement from Embedded Atomic Lattice Impurities

Atoms arranged in a two-dimensional lattice strongly interact with light via collective excitations. Such lattices can be supplemented with impurity atoms which couple to the collective array modes and permit the manipulation of emission properties. In particular, the combination of strong array-light coupling and large impurity atom non-linearity enable highly nonlinear responses to collminated, far-field radiation. We explore the effective enhancement of impurity cross section which results from this coupling in a variety of lattice potentials and parameter regimes. Higher-order photon correlations are calculated and pertinet extensions, such as long-lived photon bound states and multi-impurity systems, are discussed.   

Scrambling dynamics across a thermalization-localization quantum phase transition

We study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with sub-ballistic operator spreading. The critical disorder strength for the ballistic to sub-ballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, at the eigenstate localization transition, the operator dynamics changes from a power-law behaviour to logarithmic, which is hard to detect from our numerics. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.   

Quantum Brownian motion in a quasiperiodic potential

We study the behavior of a quantum particle in one dimension subject to Ohmic dissipation, moving in a bichromatic quasiperiodic potential. The bath is described by the Caldeira-Leggett model; absent the potentials, the particle-bath system resolves the Langevin equation in the classical limit. In a single-period potential, the particle undergoes a zero-temperature localization-delocalization transition as dissipation strength is decreased. We show that the delocalized phase is absent in the quasiperiodic case, even when the deviation from periodicity is infinitesimal. Using the renormalization group, we determine how the crossover time to the localized phase depends on the dissipation strength and incommensurability of the two frequencies, and from this, extract a localization length. Finally, we show that a similar problem can be realized as the strong-coupling limit of a mobile impurity moving in a periodic optical lattice and immersed in a one-dimensional Fermi or Bose gas.   

Memories of Initial States in the Dynamics of Disordered Systems

We consider the dynamics of a one dimensional closed disordered system of non-interacting bosons/fermions which is initialized to a Fock state with a pattern of 0 and 1 particles on alternating sites. We show that in the long time limit, the imbalance between the densities in the two sublattices reach a finite value in the localized phase given by, I(∞) = Tanh ( 1/ 2 ξ), where ξ is the localization length. For a chain with random potential disorder, the imbalance is finite for any disorder, whereas for the Aubrey Andre model, it shows a localization-delocalization transition. For a modified Aubrey Andre model, the imbalance as a function of the disorder shows a kink when the mobility edge first appears. We find that in this case, I(∞) = ∑_i Tanh [ 1/ 2 ξⁱ], where ξⁱ is the localization length corresponding to each of the three bands in the model. Our work relates experimentally measureable non-equilibrium quantities in these systems to the localization length and hence shows a new method for extracting the localization length in these systems.