Session D02: Nonequilibrium Dynamics in Ultracold Matter

Quantum Cherenkov Transition in Bose Polaron Systems

We study the behavior of a finite-momentum impurity immersed in a weakly interacting Bose-Einstein condensate (BEC) of ultra-cold atoms near an interspecies Feshbach resonance. Using the time-dependent variational approach and a non-Gaussian transformation, we study both ground state properties and quench dynamics of the system after a sudden immersion of the impurity into the BEC. While in the subsonic regime dynamics corresponds to relaxation into the quasiparticle state, in the supersonic regime we observe rapid emission of Cherenkov phonons. This phenomenon manifests in several ways during real-time dynamics of the system and showcases a rich interplay between polaronic physics and Cherenkov physics. We see qualitatively different long-time behavior of average impurity speed and Loschimdt echo depending on the impurity-boson interaction strength. Aspects of the discussed dynamical behavior can be probed in experimental protocols.   

Tuning of Scattering Resonances by Time-Periodic Driving

Scattering by a short-range inter-particle potential with time-periodic modulation is investigated with Floquet theory without assuming any high frequency approximations. For a harmonic drive it turns out that strong resonances occur, which allow versatile tuning of the s-wave scattering length and the resonance width by adjusting frequency and driving amplitude. Our approach leads to a simple description of the effect in terms of a generalized Fano-Anderson model, which in turn identifies the physical origin and leads to an analytic quantitative description of the resonances. Results for general experimental situations of magnetic and optical driving using two coupled channels and including higher harmonics are discussed.   

Quench dynamics of two-component dipolar Fermions in a Quasiperiodic potential

Motivated by the recent experiments in fermionic polar gases, we study the quenched
dynamics of two-component dipolar fermions, in the presence and absence of a
quasiperiodic potential. We investigate the localization of the charge and spin degree of
freedom separately, by probing local and global dynamical observables [1]. To study non-
equilibrium dynamics, we start with two different product states, doublons and a Neel
state. We calculate the long time dynamics of the fermionic Hamiltonian using exact-
diagonalization and matrix-product-state formalisms. In the case of doublons, we
demonstrate the transition from delocalized to localized MBL phase.
In the case of Neel state, by introducing strong enough disorder,
we show that the localization of the spin degree of freedom is also possible along with the
charge degree of freedom when on-site and long-range interaction couplings are equal in
strength. Our predictions for localizations of both charge and spin degrees of freedom should be
observed in experiments with fermionic dipolar atoms subject to a quasiperiodic potential.
[1] B. Pandey, E. Dagotto, and S. K. Pati, in preparation.
  

Enabling ultrastrong-coupling phenomena with single-drive Jaynes--Cummings models

We propose the effective simulation of light-matter ultrastrong-coupling phenomena with strong-coupling systems. Recent theory and experiments have shown that the single-atom quantum Rabi model can be simulated by the Jaynes-Cummings model with two additional classical drives. Here, we show that quantum nonlinear optical phenomena, relying on the counter-rotating terms of the quantum Rabi model, can be implemented by the Jaynes-Cummings and Tavis-Cummings models with only a single classical drive. We analyze three examples (one atom exciting two photons, frequency conversion, and one photon exciting two atoms) and show that they could be demonstrated with several currently available experimental quantum-optics systems, including superconducting circuits and trapped ions.   

Dynamics of the decay of dark solitons in superfluid Fermi gases

Dark solitons are solitary matter waves which retain their shape while propagating at a constant velocity. They emerge in a wide variety of physical systems, including ultracold atomic gases. In superfluid Bose gases, dark solitons have been observed to decay into quantized vortices through the so-called snake instability mechanism. Recent experiments in superfluid Fermi gases have also interpreted soliton decay via this mechanism. However, using both numerical simulations and a perturbative analysis based on a low-energy effective field theory, we show that there is a qualitative difference between soliton decay in the BEC- and BCS-regimes of superfluid Fermi gases.
In the BEC-regime, the characteristic snaking deformations of the soliton plane are induced by fluctuations of the amplitude of the order parameter, while in the BCS-limit, fluctuations of the phase destroy the soliton core through the formation of local Josephson currents, without the occurrence of a snaking pattern. The difference between both mechanisms should be experimentally observable, providing an incentive to consider both past and future experiments from a new perspective.   

Operator complexity of adiabatic gauge potential

Recently, there has been great interest in studying the growth rates of operator complexity and out-of-time-order correlators in many-body quantum systems. Here we characterize the complexity of the adiabatic gauge potential (AGP), which encodes the geometry of eigenstates when varying a control parameter in a Hamiltonian. For generic systems, the AGP is a highly non-local and entangled operator. We find that its Frobenius norm, which can be explicitly related to operator growth, shows remarkably different scaling with system size for integrable and non-integrable systems: polynomial versus exponential. Using the length of Pauli string operator as a measure of the AGP complexity, we compute operator weight distributions and the Shannon entropy to better understand the norm's system size scaling.   

Transport in a bosonic superfluid point contact

We discuss heat and particle transport of a weakly interacting, low temperature Bose-Einstein condensate in a quantum point contact. We show that the presence of gapless phonon modes in the condensate yields a contact resistance at zero temperature and a corresponding nonzero DC conductance. As a consequence, we predict zero thermopower and Lorenz number at zero temperature, a breakdown of the bosonic Wiedemann-Franz law. The consequences on heat and particle transport measurements in bosonic two-terminal setups should be readily observable in existing experiments.
  

Entanglement production by interaction quenches of quantum chaotic subsystems

The entanglement production in bipartite quantum systems is studied for initially unentangled product eigenstates of the subsystems, which are assumed to be quantum chaotic [1]. Based on a perturbative computation of the Schmidt eigenvalues of the reduced density matrix, explicit expressions for the time-dependence of entanglement entropies, including the von Neumann entropy, are given. An appropriate re-scaling of time and the entropies by their saturation values leads a universal curve, independent of the interaction. The extension to the non-perturbative regime is performed using a recursively embedded perturbation theory to produce the full transition and the saturation values. The analytical results are found to be in good agreement with numerical results for random matrix computations and a dynamical system given by a pair of coupled kicked rotors.

[1] Pulikkottil et al, arXiv: 1909.04733.   

The entanglement membrane in deterministic systems

In certain analytically-tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and related dynamical observables, reduces to an effective statistical mechanics of an ‘entanglement membrane’ in spacetime. These tractable systems involve an average over random local unitaries defining the dynamical evolution. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries. Our approach relies on introducing effective ‘pairing’ degrees of freedom in spacetime, inspired by the structure emerging in random unitary circuits. We also provide an efficient algorithm for determining the ‘line tension’ of the entanglement membrane in 1+1D models.   

Nonequilibrium dual-boson approach

We develop nonequilibrium auxiliary quantum master equation dual boson method (aux-DB),
and argue that it presents a convenient way to describe steady states of correlated impurity models
(such as single molecule optoelectronic devices) where electron and energy transport should be taken
into account. The aux-DB is shown to provide high accuracy with relatively low numerical cost.
Theoretical analysis is followed by illustrative simulations within generic two-level junction model,
where the new scheme is benchmarked against numerically exact results.   

Modeling Collective Emission in Cavities by Phase Space Trajectories

We model N electronic two-level systems (TLSs) coupled to a multimode cavity by sampling independent trajectories in Wiger phase space with a Meyer-Miller-Stock-Thoss (MMST) mapping Hamiltonian. We show that this approach can not only provide us an intuitive physical interpretation of quantum electrodynamics (i.e. sampling electronic and photonic zero-point energies in phase space represents radiative self-interaction and vacuum fluctuations respectively), but also correctly describe many intriguing collective emission phenomena, including spontaneous emission for an array of TLSs in the singly excited manifold, Dicke's superradiance and subradiance when all TLSs are excited, and even the quantum statistics for the delay time in superradiance. We also discuss possible further improvements of this approach.   

The role of integrability in speeding up collective spin polarization.

The central spin problem plays an important role in a variety of condensed matter systems, including quantum dots and nitrogen vacancy centers in diamond. We study an anisotropic central spin model with two classes of special eigenstates: bright and dark. We find these states to be robust against perturbations around two integrable points of the model. By driving of the central magnetic field, the structure of these eigenstates can be harnessed to access highly polarized many-body configurations. Using approximate shortcuts to adiabaticity, we develop a highly efficient and experimentally viable polarizing scheme.   

Quantum Weak Measurement Back-action Control On A Strongly Interacting BEC

The choice of weak measurement phase can affect the energy dynamics of a nonlinear quantum system. We report on progress towards controlling the measurement back-action on a strongly interacting Bose Einstein condensate (BEC) continuously monitored under phase-contrast imaging setup. We have derived the master equation using the fixed number state approximation. These have been reduced to a coupled set of differential equations of motions under Gaussian Approximation for the BEC. We use measurement phase dependent back-action in these equations for feed-back control. We discuss potential applications and experimental realizations.   

Unitary Subharmonic Response of Floquet Majorana Modes

Detection and manipulation of Majorana fermions are essential for creating a topological quantum computer. To this end, we show that unpaired Majorana modes in Floquet systems can directly be visualized using the phenomenon of unitary subharmonic response. Namely, starting from highly non-equilibrium initial states, the unpaired Majorana modes exhibit boundary oscillations that have twice the driving period, are localized, and have up to exponentially long lifetimes with respect to the system's parameters. While the lifetime is still limited in translationally invariant systems, we show how disorder can be engineered to stabilize the subharmonic response of Majorana modes. We also suggest a viable implementation in modern multiqubit systems, such as superconducting circuits and atomic systems.   

Real time dynamics of impurity and disorder scattering with interacting Fermion wave packets

Recent advances for ultra-cold gases allow the controlled scattering by disorder and localized impurities using moving interacting Fermion wave packets in a trap after a quick displacement in position. We analyze the damping and scattering behavior from large scale numerical t-DMRG simulations in 1D as a function of interaction, displacement and disorder strength in a regime where a comparison with our experiments is possible. Attractive interactions make the wave-packets more susceptible for both single impurities and disorder scattering, which leads to a significant larger damping and quicker breakdown of the oscillations. Repulsive interactions have a much smaller effect, but overall a reduction of scattering can be observed. The corresponding experiments for 3D scattering show maximum stability and minimal damping near the unitary point.