Session R6: Dynamics with Ultracold Atomic Gases I

Eigenstate distribution of observables in an integrable quantum system after a quench

A generic, non-integrable quantum system is expected to follow the eigenstate thermalization hypothesis (ETH): the expectation value of a few-body observable in an individual eigenstate which has energy close to the mean value is equal to the thermal expectation value of the the observable. For a system that follows the ETH, all eigenstates with significant weight in the diagonal distribution give identical values. We explore the conditions under which similar phenomena is expected to hold in integrable systems. We investigate quantum quenches in hard-core bosons in one-dimensional optical lattices. These systems can be efficiently simulated using the Jordan- Wigner mapping to free fermions and exact diagonalization of the single-particle states. We calculate the full energy spectrum as well as the density and momentum distribution functions in individual many- body eigenstates after the quench. The results of the diagonal ensemble are compared with thermal expectation values.   

Spontaneous creation of non-zero angular momentum modes in tunnel-coupled two-dimensional degenerate Bose Gases

We investigate the dynamics of two tunnel-coupled two-dimensional degenerate Bose gases. The reduced dimensionality of the clouds enables us to excite specific angular momentum modes by tuning the coupling strength, thereby creating striking patterns in the atom density profile. The extreme sensitivity of the system to the coupling and initial phase difference results in a rich variety of subsequent dynamics, including vortex production, complex oscillations in relative atom number and chiral symmetry breaking due to counter-rotation of the two clouds.   

Geometric study of optical billiards with cold atoms

We present experimental work exploring the qualitative and quantitative geometric properties of optical billiards with cold atoms. We load $^{87}$Rb atoms from a magneto-optical trap to a dynamic blue detuned dipole trap that confines the atoms to a plane. We first search for the signature associated with a topological transition from one globally connected region to two locally separated connected regions in a sand clock shape trap. We perform a similar study on a trap with the shape of a rhombus plus a line barrier in the middle. The collective motion of the atoms is the signature of an intermediate topological transition. We also quantify the degree of geometric symmetry breaking of a regular polygon by comparing the dynamics of cold atoms inside dipole traps with shapes of equilateral triangle, square and regular hexagon. Our results are compared with theoretical simulations that we also extend to three dimensions.   

Breakdown of macroscopic quantum self-trapping in coupled mesoscopic one dimensional Bose gases

Two coupled BECs with a large population imbalance exhibit macroscopic quantum self-trapping (MQST) if the ratio of interaction energy to tunneling energy is above a critical value. Here we investigate effect of quantum fluctuations on MQST. In particular, we analyze the dynamics of a system of two elongated Bose gases prepared with a large population imbalance, where due to the quasi one dimensional character of the gas we no longer have true long range order, and the effect of quantum fluctuations is much more important. We show that MQST is possible in this system, but even when it is achieved it is not always dynamically stable. Using this instability one can construct states with sharply peaked momentum distributions around characteristic momenta dependent on system parameters. Our other finding is the nonmonotonic oscillating dependence of the decay rate of the MQST on the length of the wires. We also address the interesting question of thermalization in this system and show that it occurs only in sufficiently long wires.   

Two-frequency population dynamics in a low-barrier double-well BEC

The dynamics of a a $^{87}$Rb Bose-Einstein condensate (BEC) are studied in a RF-dressed double-well. As we deform the trap from a single to a double well, we bias the system to prepare a population imbalance, $z$, between the wells. After suddenly removing the bias we observe population and phase dynamics. For $\mu \la V_b$, where $\mu$ is the chemical potential and $V_b$ the barrier height, we observe plasma oscillations in $z$ about $z = 0$, as predicted in the two-mode model of the Josephson junction. Additionally, we observe a second, higher frequency component in these oscillations. Through a comparison to three-dimensional GPE calculations, we find that the two-mode frequency dynamics are due to nonlinear mixing of the dipole mode with an octupole mode.   

Controlling spin dynamics in a one-dimensional quantum gas

Reducing the dimensionality of a system has dramatic consequences and leads to remarkable new physics. In this regard, quantum gases offer unique opportunities to address important open questions in quantum many-body physics, by allowing full control over all relevant parameters. We create coherent superpositions of both spin and motional degrees of freedom and probe spin dynamics of a one-dimensional (1D) Bose gas of $^{87}$Rb on an atom chip. We observe interaction-driven focusing of one spin component by mean field interaction with another component, directly related to the effective 1D interaction strength. We demonstrate experimental control over the 1D interaction strengths through state-selective radio-frequency dressing. The focusing behavior is altered by tuning the transverse trapping potential in a state-dependent way. This enables, for instance, access to the point of spin-independent interactions where exact quantum many-body solutions are available.   

Studies of 1D gases away from integrability

We have studied atoms in optical lattices to address the fundamental question of what is needed for a many-body quantum system to approach a thermal distribution. Specifically, we prepare Rb atoms in an array of 1D tubes formed by a 2D optical lattice in so-called quantum Newton's cradle states,\footnote{Kinoshita \textit{et. al}, ``A quantum Newton's Cradle,'' Nature \textbf{440}, 900 (2006)} and then observe their time evolution. When the lattice is very deep, we can only set lower limits on the collision-dependent evolution of the momentum distribution. When the lattice is shallow enough that some atoms can populate the second vibrational band after a two-body collision, we find that the system thermalizes at a rate proportional to the inter-tube tunneling rate. For intermediate lattice depths, we observe collision-dependent evolution, but to final momentum distributions that seem to retain a memory of the initial state. Such partial thermalization is reminiscent of classical physics described by the KAM theorem.   

Stochastic Quantum Gas Dynamics

We study the dynamics of weakly-interacting finite temperature Bose gases via the Stochastic Gross-Pitaevskii equation (SGPE). As a first step, we demonstrate [jointly with A. Negretti (Ulm, Germany) and C. Henkel (Potsdam, Germany)] that the SGPE provides a significantly better method for generating an equilibrium state than the number-conserving Bogoliubov method (except for low temperatures and small atom numbers). We then study [jointly with H. Nistazakis and D.J. Frantzeskakis (University of Athens, Greece), P.G.Kevrekidis (University of Massachusetts) and T.P. Horikis (University of Ioannina, Greece)] the dynamics of dark solitons in elongated finite temperature condensates. We demonstrate numerical shot-to-shot variations in soliton trajectories (S.P. Cockburn et al., arXiv:0909.1660.), finding individual long-lived trajectories as in experiments. In our simulations, these variations arise from fluctuations in the phase and density of the underlying medium. We provide a detailed statistical analysis, proposing regimes for the controlled experimental demonstration of this effect; we also discuss the extent to which simpler models can be used to mimic the features of ensemble-averaged stochastic trajectories.   

Many-body Landau-Zener dynamics in coupled 1D Bose liquids

Non-equilibrium dynamics attracted a lot of recent interest. The departure from standard statistical mechanics is studied in a large variety of systems, at the heart of which lies the very fundamental setup of two levels undergoing an anti-crossing, knowing as the famous Landau-Zener (LZ) problem. Non-interacting atoms in a double well with tunable energy difference provide a generic two-mode system to study the dynamics of a LZ sweep. We experimentally realize a generalized LZ problem in an array of pairwise coupled tubes with interacting ultracold $^{87}$Rb atoms in an optical superlattice potential. We investigate the impact of interactions and dimensionality on the sweep fidelity for sweeps in the ground state and in the excited state. The results show that interactions in the tubes improve the fidelity for sweeps in the ground state. For sweeps in the excited state we find relaxation of the system which can be explained in terms of one-dimensional low-energy excitations along the tubes, providing an intrinsic bath for thermalization.   

Dynamical localization of spin dynamics in a spin-1 Bose condensate via modulation of spin interaction

Spin mixing dynamics in a spin-1 Bose-Einstein condensate can be localized by a temporal modulation of spin exchange interaction, which is tunable via optical Feshbach resonance. Adopting techniques from coherent control, we demonstrate the localization/freezing of spin mixing dynamics, and the suppression of the intrinsic dynamic instability and spontaneous spin domain formation in a ferromagnetically interacting condensate of $^{87}$Rb atoms. Different control schemes are also discussed.