Session H5: Quench Dynamics and Cold Atoms Out of Equilibrium

Collapse and revival of the Fermi sea in a Bose-Fermi mixture

The collapse and revival of quantum fields is one of the most pristine forms of coherent quantum dynamics far from equilibrium. Until now, it has only been observed in the dynamical evolution of bosonic systems. We report on the first observation of the boson mediated collapse and revival of the Fermi sea in a Bose-Fermi mixture. Specifically, we present a simple model which captures the experimental observations shown in the talk titled \emph{Observation of Collapse and Revival Dynamics in the Fermionic Component of a Lattice Bose-Fermi Mixture} by Sebastian Will. Our theoretical analysis shows why the results are robust to the presence of harmonic traps during the loading or the time evolution phase. It also makes apparent that the fermionic dynamics is independent of whether the bosonic component consists of a coherent state or localized Fock states with random occupation numbers. Because of the robustness of the experimental results, we argue that this kind of collapse and revival experiment can be used to accurately characterize interactions between bosons and fermions in a lattice.   

Quench Dynamics of the Bose Condensate

Unlike the extensively explored unitary Fermi gases, very few studies have been conducted with a strongly interacting Bose gas. The experimental difficulty lies with the high three-body recombination rate, which scales as $n^2a^4$ for $a$ less than the atom-atom average separation. Recently, the JILA group achieved a quasi steady unitary state for timescales smaller than the atom loss timescale by ramping the magnetic field instantly close to a Feshbach resonance. We apply a renormalized mean field theory, in which the two body interaction depends on the interparticle distance near unitarity, to study the unitary Bose gas. This renormalization has predicted some convincing results for the Fermi gas [2]. We solve the time dependent Gross-Pitaevskii equation to understand the non-equilibrium dynamics of this degenerate Bose gas. We will also discuss the oscillations induced by a quantum quench [3].\\[4pt] [1] P. Makotyn, C. E. Klauss, D. L. Goldberger, E. A. Cornell and D. S. Jin, Nat. Phys. 10, 116 (2014)\\[0pt] [2] J. von Stecher, C. H. Greene, Phys. Rev. A 75,22716 (2007)\\[0pt] [3] C-L Hung, V. Gurarie and C. Chin, Science 341,1213 (2013)   

A large-N expansion based theoretical framework for modeling cold atoms in and out of equilibrium

The large-N expansion is a scheme for rearranging Feynman diagrams. Although this technique can be applied to cold atoms with contact interactions, for single-component ultra-cold bosons the leading-order large-N expansion does not reproduce Bogoliubov dispersion in the Bose-Einstein condensation (BEC) phase. However, we prove that the correct vacuum leads to a dispersion resembling Bogoliubov dispersion. Moreover, we have developed a theory, which includes the normal as well as the anomalous Green's functions. This theory, named leading-order auxiliary field theory, is gapless, conserving, and has a second-order phase transition. We also generalize it to describe a two-component Bose gas above its BEC transition temperature. The mixture to phase-separation transition is shown to survive at high temperature in this model without any BEC. Furthermore, the same theoretical framework can be applied to ultra-cold fermions and we found that the BCS-Leggett theory of BCS-BEC crossover can be derived as the leading-order theory from this framework. Importantly, our theoretical framework can be generalized to include time dependence so interesting dynamics in cold atoms could be investigated in a coherent fashion.   

Dynamics of atoms in bilayer optical lattices, and adiabatic state preparation

We study theoretically the dynamics of ultracold quantum gases trapped in optical lattices consisting of two layers (which can each either be one-dimensional or two-dimensional). Considering both bosons and fermions, we propose schemes for adiabatic state preparation of low-entropy states, making use of a separately tunable interlayer coupling, energy offset between the layers and repulsive interactions. In this context it is possible, for example, to use one layer as an entropy reservoir, which can be used to remove entropy from the other layer, before being decoupled from it. For the case of two coupled one-dimensional layers, we calculate the time-dependent dynamics exactly using the time-dependent density matrix renormalization group techniques. This allows us to identify parameter regimes where entropy transfer between layers occurs, and the emergence of characteristic many-body correlations in the low-entropy layer can be observed. This process is especially effective when the desired state in the low-entropy layer is gapped, and these states can be used as a starting point also for other adiabatic preparation protocols, including the realisation of metastable excited states.   

Higher band dynamics of few-body bosonic ensembles in multiwell potentials

The higher band dynamics of few-body bosonic ensembles is numerically investigated, via the numerically exact Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons (ML-MCTDHB). Initially the bosons are prepared in a superfluid-like state, with spatial correlations between different site, and then a quench of the contact interaction strength is applied to trigger the system out of equilibrium. The quench induced dynamics show rich phenomena, and various dynamical modes are identified, including the inter-well density-wave-like tunneling, the intrawell breathing, the intrawell dipolar oscillation, and the delocalized transport. The higher-band dipolar oscillation can also couple to other dynamical modes, and such coupling gives rise to a new type of avoided crossing in the spectrum of the dipolar oscillation. The higher band dynamics obtained by ML-MCTDHB is beyond the single-band Bose-Hubbard model, and illustrates the rich new physics in the strong interaction regime.   

New Dynamical Scaling Universality for Quantum Networks Across Adiabatic Quantum Phase Transitions

We reveal universal dynamical scaling behavior across adiabatic quantum phase transitions in networks ranging from traditional spatial systems (Ising model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our findings, which lie beyond traditional critical exponent analysis and adiabatic perturbation approximations, are applicable even where excitations have not yet stabilized and, hence, provide a time-resolved understanding of quantum phase transitions encompassing a wide range of adiabatic regimes. We show explicitly that even though two systems may traditionally belong to the same universality class, they can have very different adiabatic evolutions. This implies that more stringent conditions need to be imposed than at present, both for quantum simulations where one system is used to simulate the other and for adiabatic quantum computing schemes.   

Post-quench dynamics of long-range interacting systems

Lieb-Robinson bounds provide a rigorous underpinning to the common intuition that short-range interacting quantum systems should obey some notion of locality. These bounds have recently been extended to encompass systems with long-range (power-law) interactions [1], however such generalizations no longer enforce locality, allowing instead for correlations that grow with an arbitrarily large velocity. We demonstrate that this behavior arises from unnecessarily pessimistic assumptions used in deriving Lieb-Robinson bounds for long-range interacting systems, and emphasize that, on very general physical grounds, such a divergent velocity is unlikely and perhaps even impossible. We will explicitly demonstrate the mathematical origin of this apparently divergent velocity in the bound, and explain the reason why it does not necessarily exist in the true dynamics, by appealing to the simple and experimentally relevant example of an interacting XY chain. \\[4pt] [1] M. Hastings and T. Koma, Comm. Math. Phys. 265, 781 (2006).   

Universal Features of the Nonequilibrium Dynamics of Many-Body Quantum Systems

We describe the nonequilibrium dynamics of isolated quantum systems with two-body interactions. In these systems, the energy shell is a Gaussian of width $\sigma$ and it gives the maximum possible spreading of the energy distribution of any initial state. When the distribution achieves this shape, the fidelity decay is Gaussian until saturation. This establishes a lower bound for the fidelity decay in realistic systems. We find excellent agreement between our numerics and the analytical expression for the fidelity. We also provide the general conditions under which the short-time dynamics of few-body observables is controlled by $\sigma$. The analyses are developed for systems, initial states, and observables accessible to experiments with cold atoms in optical lattices.