Session J3: Nonlinear Dynamics and Out-of-equilibrium Trapped Gases

Merging of independent condensates: disentangling the Kibble-Zurek mechanism

An important step in the study of out-of-equilibrium physics is the Kibble-Zurek theory which describes a system after a quench through a second-order phase transition. This was studied in our group with a temperature quench across the normal-to-superfluid phase transition in an annular trap geometry, inducing the formation of supercurrents. Their magnitude and direction were detected by measuring spiral patterns resulting from the interference of the ring-shaped condensate with a central reference disk. According to the KZ mechanism domains of phase are created during the quench, with a characteristic size depending of its duration. In our case this results in a stochastic formation of supercurrents depending on the relative phases of the domains. As a next step of this study, we now design ourselves the patches thanks to our tunable trapping potential. We control both the number of condensates to be merged (from one to twelve) and their merging time. We report an increase of the vorticity in the ring for an increased number of patches compatible with a random phase model. We further investigate the time required by the phase to homogenize between two condensates.   

Spontaneous Generation and Evolution of Defects in a Quenched Bose Gas

We provide a detailed numerical analysis of the Trento experiments with quenched Bose-Einstein condensates in an elongated harmonic trap (Donadello et al., PRA 94, 023628 (2016)) where defects in the order parameter are spontaneously generated by the Kibble-Zurek mechanism. Using the stochastic projected Gross-Pitaevskii equation, and by quenching both temperature and chemical potential, we are able to capture both the early-time phase transition dynamics and the observed long-term coarse-graining evolution, reproducing the experimentally-observed condensate growth dynamics, and long-term defect evolution. The emerging picture sheds light into how the initial thermal state passes through a transient “turbulent” state of many highly-excited vortical structures, before settling into a few interacting long-lived solitonic vortices. By numerically tracking the number of spontaneously-formed defects during and after the quench, we quantify the dependence of vortex number, vortex linelength and coherence length on quench rate, also demonstrating the observed breakdown of Kibble-Zurek scaling for fast quenches, arising as a result of coarse-graining dynamics prior to experimental measurements.   

Quenches from finite-temperature ultracold matter

Although interaction quenches are known to drive interesting dynamics, much prior work has focused on quenches initiated from states that are near the ground state. In contrast, experiments in ultracold matter - from fermionic atoms in optical lattices to dipolar molecules - are often outside this regime, necessitating the study of quenches from higher temperature states. Although in equilibrium, high temperatures are usually associated with trivial, structureless states, driving such states out of equilibrium can lead to rich behavior. For example, we have recently shown that starting from a hot, uncorrelated state of fermions in an optical lattice and evolving it in time leads to substantial intricately-structured correlations between sites - even without interactions during the dynamics. Because including interactions challenges existing theoretical methods (both numerical and analytic) we are developing tools that exploit the nature of the high-temperature initial conditions to calculate these dynamics. We will describe and analyze the accuracy of one such method, a dynamic numerical linked cluster expansion, and its applications to spin systems relevant to cold atoms.   

Non-equilibrium phase transitions in a driven-dissipative system of interacting bosons

Atomic, molecular, and optical systems provide unique opportunities to study simple models of driven-dissipative many-body quantum systems. Typically, one is interested in the resultant steady state, but the non-equilibrium nature of the physics involved presents several problems in understanding its behavior theoretically. Recently, it has been shown that in many of these models, it is possible to map the steady-state phase transitions onto classical equilibrium phase transitions. In the language of Keldysh field theory, this relation typically only becomes apparent after integrating out massive fields near the critical point, leaving behind a single massless field undergoing near-equilibrium dynamics. In this talk, we study a driven-dissipative XXZ bosonic model and discover critical points at which two fields become gapless. Each critical point separates three different possible phases: a uniform phase, an anti-ferromagnetic phase, and a limit cycle phase. Furthermore, a description in terms of an equilibrium phase transition does not seem possible, so the associated phase transitions appear to be inherently non-equilibrium.   

Collective many-body bounce in the breathing-mode oscillations of a finite-temperature Tonks-Girardeau gas.

We analyse the breathing-mode oscillations of a harmonically quenched Tonks-Giradeau (TG) gas using an exact finite-temperature dynamical theory. We predict a striking collective manifestation of impenetrability---a collective many-body bounce effect. The effect, while being invisible in the evolution of the \emph{in situ} density profile of the gas, can be revealed through a nontrivial periodic narrowing of its momentum distribution, taking place at twice the rate of the fundamental breathing-mode frequency of oscillations of the density profile. We identify physical regimes for observing the many-body bounce and construct the respective nonequilibrium phase diagram as a function of the quench strength and the initial equilibrium temperature of the gas. We also develop a finite-temperature hydrodynamic theory of the TG gas, wherein the many-body bounce is explained by an increased thermodynamic pressure during the isentropic compression cycle, which acts as a potential barrier for the particles to bounce off.   

Exploring collective spin dynamics in a weakly interacting gas of fermions

Strongly correlated states are often associated with strongly interacting regimes. However, weak interactions can also lead to strong correlations, given sufficiently long coherent interaction times. Ultracold atomic Fermi gases, with precisely controllable parameters, offer a versatile platform to investigate the emergence of collective behavior in out-of-equilibrium settings. Here we present observations of non-trivial collective behavior that emerges in the spin dynamics of a gas of $^{40}$K atoms in the weakly interacting regime. Starting with a spin-polarized gas, we study collective spin dynamics in a Ramsey sequence, both with and without a spin-reversal pulse. We observe large oscillations with life times up to 100 milliseconds. In contrast to demagnetization in the strongly interacting regime, there are multiple revivals. Experimental results are compared to a fully quantum model that maps motional trap states with s-wave scattering onto a spin chain with long-range interactions. The broader impact of this study is an improved understanding of magnetic correlations driven by the exchange interactions between itinerant spins.   

Spin diffusion of ultracold 87Rb in inhomogeneous spin-dependent potentials

We study the effect of an inhomogeneous differential potential on the relaxation dynamics of spin structures in ultracold $^{87}$Rb near degeneracy. In a homogeneous differential potential, the diffusion of spin inhomogeneities has been shown to exhibit instabilities that interconvert longitudinal and transverse spin. These instabilities couple transverse and longitudinal spin dynamics and lead to large-scale coherent spin fluctuations. However, the addition of a spatially inhomogeneous spin-dependent potential is predicted to suppress this instability and decouple the spin dynamics. We present progress towards observing this phenomenon by measuring the diffusion of a longitudinal domain wall in the presence of an optically-created inhomogeneous differential potential. We observe trapping of a transverse spin wave within the domain wall and a separation of timescales for transverse and longitudinal spin relaxation, indicative of anisotropic spin diffusion. We also study the role of coherence in these dynamics.   

Faster than Exponential Decay of Out-of-Time-Ordered Correlators

In studies of nonequilibrium quantum dynamics, several attempts have been made to connect the exponential decay rate of the Loschmidt echo and the survival probability with the classical Lyapunov exponent. The same idea has been recently extended to the out-of-time-ordered four-point correlator (OTOC). We show that the OTOC, just like the survival probability, may in fact show faster than exponential decays. This occurs not only for chaotic many-body quantum systems with level repulsion, but also for integrable models.   

Parametric Cooling of Ultracold Atoms

An oscillator is characterized by a restoring force which determines the natural frequency at which oscillations occur. The amplitude and phase-noise of these oscillations can be amplified or squeezed by modulating the magnitude of this force (e.g. the stiffness of the spring) at twice the natural frequency. This is parametric excitation; a long-studied phenomena in both the classical and quantum regimes. Parametric cooling, or the parametric squeezing of thermo-mechanical noise in oscillators has been studied in micro-mechanical oscillators [1] and trapped ions [2]. We study parametric cooling in ultracold atoms. This method shows a modest reduction of the variance of atomic momenta, and can be easily employed with pre-existing controls in many experiments. Parametric cooling is comparable to delta-kicked cooling [3], sharing similar limitations. We expect this cooling to find utility in microgravity experiments where the experiment duration is limited by atomic free expansion. [1] D. Rugar and P. Gr\"{u}tter, Phys. Rev. Lett., 67:699 (1991) [2] V. Natarajan, et al., Phys. Rev. Lett., 74:2855(1995) [3] H. Ammann, N. Christensen, Phys. Rev. Lett., 78:2088 (1997) T. Kovachy, et al., Phys. Rev. Lett., 114:143004 (2015)