Session G4: Non-equilibrium Dynamics I

Topological Analysis of an Atomic Quantum Pumping System

We examine a system consisting of two reservoirs of particles connected by a channel. In the channel are two oscillating repulsive potential-energy barriers. It is now known that such a system can transport particles from one reservoir to the other, even when the chemical potentials in the reservoirs are equal. We use computations and the theory of chaotic transport -- an iterated map of the phase plane -- to study this system. Transport is described by passage around or through a heteroclinic tangle. Topological properties of the tangle are described using a generalization of Homotopic Lobe Dynamics (HLD). This theory uses a symbolic algebra to characterize topological properties of the tangle, and predicts some properties of high iterates of the map (long-time behavior) from properties of low iterates (short-time behavior). We compare these predicted properties with direct computation of trajectories. We find that HLD accurately predicts all transport properties forced by the initial topological structure of the tangle. In addition, we also find transport properties not predicted by the initial topology.   

A test of Kibble-Zurek theory using spinor Bose-Einstein condensates

We investigate the predictions of Kibble-Zurek phenomena in the vicinity of a quantum phase transition in the sodium spinor Bose-Einstein condensates. Close to a phase transition, the relaxation time of a system diverges and the system ceases to be adiabatic. Kibble-Zurek phenomena exploits this critical slowing down of the system to predict the rate of formation of defects, as they form when a freeze-out occurs during a linear quench. This freeze-out is predicted to take place when relaxation time becomes comparable to the time left for the system to reach the phase transition.In our earlier work we have observed a quantum phase transition in a spinor Bose-Einstein condensate.\footnote{E. M. Bookjans, A. Vinit, and C. Raman, Phys. Rev. Lett. 107, 195306 (2011).} We test the predictions of the Kibble-Zurek theory by performing linear quenches at varying rates across the phase transition and quantifying the number of defects seeded in the process. This can also be used to predict the critical exponents of the phase transition.   

Quench Dynamics in the Presence of a Bath

Feshbach resonance are now widely used to tune the interaction strength in cold atoms. This allows one to experimentally study the out-of-equilibrium dynamics of a quench associated with instantaneously changing the strength of the interactions between fermionic and bosonic atoms. Previous theoretical studies based on standard time dependent Bogoliubov or BCS theory (for bosons and fermions) have not included the presence of a thermal bath. This bath is essential for ultimate equilibration. In this talk we show how to include the bath following a Leggett-Caldeira type approach. We point out some of the important differences in the quench dynamics between bosonic and fermionic superfluids.   

Interplay of spontaneous emissions and thermalization of cold bosons in optical lattices

We study the non-equilibrium dynamics of cold bosons in an optical lattice, in the presence of spontaneous emission events from incoherent light scattering. Computing the dynamics described by the many-body master equation, we characterize the behaviour of both intra- and inter-band excitations, and identify to what extent excitations can be thermalized by the system, and on which timescales this occurs. Comparing simple observables, we find regimes with weak interactions and intra-band excitations in which the system relaxes rapidly to values described by a thermal distribution. Conversely, we find that for inter-band excitations or in regimes of stronger interactions that thermalization of simple observables such as the kinetic energy does not occur on typical experimental timescales. As well as providing an experimentally realizable case study for thermalization in these system, these results have important implications for the characterization of heating and decoherence in optical lattice experiments.   

State preparation and non-equilibrium dynamics in bilayer Bose-Hubbard systems

We study the ground states and non-equilibrium dynamics of ultra-cold Bose gases in bilayer optical lattice systems with separately tunable interlayer coupling, energy offset between the layers and repulsive interactions. The case of two coupled one-dimensional chains is treated in a numerically exact manner using the adaptive time-dependent density matrix renormalization group which allows us to study the change of offset and interlayer coupling in real time. We identify parameter regimes where the ground state of the coupled system in the limit of small interlayer coupling consists of a Mott insulator in one layer and a superfluid state in the other layer can serve as an entropy reservoir. We then investigate time-dependent dynamics in this system, studying entropy transfer between layers as we change the layer offset energy and coupling strength. In addition to applications as a preparation scheme for fully interacting Mott-insulator states, feasible with available experimental techniques, the investigated protocols could be easily adapted to also allow for a controlled preparation of highly excited states.   

Dissipative phase transitions in anisotropic spin models

We study anisotropic Heisenberg spin chains with dissipation similar to spontaneous emission. We examine the steady state due to the balance of coherent interaction and dissipation. As the XYZ components of the interaction change, the system undergoes a phase transition from a paramagnetic phase to a ferromagnetic or antiferromagnetic phase. We show that the ferromagnetic and antiferromagnetic phases exist only when the interaction is sufficiently anisotropic. We study quantum fluctuations (squeezing) and spatial correlations in the different phases of the system. Experimental implementations include trapped ions and atoms in optical lattices interacting via Rydberg blockade.   

Quantum interference-induced stability of repulsively bound pairs of excitations

Since the observation in optical lattices of bound pairs of atoms that can exist even in the presence of repulsive interactions, several works have been dedicated to their formation, dynamics and relaxation. Here we discuss the dynamics of two types of bound pairs. One corresponds to doubly occupied sites in one-dimensional Bose-Hubbard systems, the so-called doublons. The other is pairs of neighboring excited spins in anisotropic Heisenberg spin-1/2 chains. We investigate the possibility of decay of the bound pairs due to resonant scattering by a defect or due to collisions of the pairs. We show that the amplitudes of the corresponding transitions are very small. This is the result of destructive quantum interference and explains the stability of the bound pairs.   

Structure formation in immiscible two--species Bose--Einstein condensates in perturbed harmonic traps

We investigate the mean--field equilibrium solutions for a trapped two--species $^{87}$Rb--$^{133}$Cs immiscible Bose--Einstein condensate, and show that the density profiles observed in a recent Bose-Einstein experiment (D. J. McCarron \emph{et al.} Phys. Rev. A 84, 011603 (2011)), which include ball and shell formations and axially/radially separated states, can be reproduced when accounting for weak linear perturbations. We also demonstrate the importance of the coupled growth of the two condensates by a simple finite temperature model which reveals such structures to be generally metastable in the presence of dissipation, with our findings confirmed by the more accurate Stochastic Projected Gross--Pitaevskii equation.