Session J4: Non-Equilibrium Dynamics with Quantum Gases

Non Equilibrium Quantum Criticality: an intuitive approach

Since their discovery in 1976, equilibrium quantum critical points have attracted continuous interest, due to their universality (i.e. the independence from the microscopic details of the systems). In two recent papers [1,2] we have extended these concepts to non-equilibrium systems, by studying the universal properties of quantum systems driven by time-dependent noise. We were able to demonstrated that [1] they can show a new class of non-equilibrium quantum criticality, and [2] small perturbations around the critical point lead to new physical phenomena, such as the spontaneous generation of an effective temperature and an effective dissipation. To this end, we developed a real-time renormalization group (RG) in the Keldysh path-integral formalism, which may however appear cryptic to the non-experts. In this talk, I will show how the main conclusions of the RG approach can be understood by simpler arguments based on circuit theory and fluctuation-dissipation relations. \\[4pt] [1] E.G. Dalla Torre, et al. ``Quantum critical states and phase transitions in the presence of non-equilibrium noise,'' Nature Physics 6, 806 (2010) \\[0pt] [2] E.G. Dalla Torre, et al. ``Dynamics and universality in noise driven dissipative systems,'' arXiv: 1110.3678 (2011)   

Dynamics of noise correlations of ultracold bosons in an optical lattice

We study second order correlations of ultracold bosons in an optical lattice for superfluid and Mott insulating phases. Starting with a superfluid ground state, a sudden increase in the lattice depth projects it into a non-equilibrium state. We examine the subsequent dynamics of the system - analyzing noise correlations of the atomic cloud after time-of-flight expansion. We also investigate the effects of three and higher-body interactions on noise correlations in deep lattices.   

Stability of Counterflow Superfluidity

We examine the stability of the counterflow superfluid state in two component mixtures of ultracold atoms in optical lattices. Using a Gutzwiller mean-field approach, we find a sharp boundary separating stable counterflow from a dynamically unstable regime. As the inter-component interaction strength increases, the critical counterflow rate drops, falling to zero when interactions are strong enough to induce phase separation of the two components. Going beyond mean-field theory, we compute the decay rate of counterflow within the stable regime due to phase slips. The results agree well with numerically exact simulations and are calculated in a regime of parameters relevant to current experiments on mixtures of ultracold alkali atoms.   

Fermion Dynamics from Gross-Pitaevskii--like Equations

The dynamics of condensed fermions (i.e. the Unitary Fermi Gas) play a key role in understanding a range of physical systems, from dynamics in rotating traps of cold atoms, to explaining pulsar glitches in neutron stars. Density functional theory (\textsc{dft}) provides a powerful tool for modeling these dynamics, but unfortunately, simulating even a few vortices requires the use of leadership class computing. This talk will address the efficacy of using modified Gross-Pitaevskii (\textsc{gp}) like equations to model the dynamics of Fermi systems. These \textsc{gp}-like equations are significantly easier to solve, yet still capture much of the relevant physics. We shall advocate an approach of using fermionic \textsc{dft} to adjust the form of the modified \textsc{gp}-like equations, and then using the latter to model more complicated phenomena beyond the capability of the fermionic \textsc{dft}. The dynamics of vortices pinned on defects will serve as an example.   

Expansion of Bose-Hubbard Mott insulators in optical lattices

We present a study of the expansion of bosonic Mott insulators in the presence of an optical lattice after switching off a confining potential. We use the Gutzwiller mean-field approximation and consider two different setups. In the first one, the expansion is restricted to one dimension. We show that this leads to the emergence of two condensates with well-defined momenta, and argue that such a construct can be used to create atom lasers in optical lattices. In the second setup, we study Mott insulators that are allowed to expand in all directions in the lattice. In this case, a simple condensate is seen to develop within the mean-field approximation. However, its constituent bosons are found to populate many nonzero momentum modes. An analytic understanding of both phenomena in terms of the exact dispersion relation in the hard-core limit is presented.   

Protection of dissipative quantum state preparation by interlacing the control with dynamical decoupling pulses

Various dissipative processes have recently be exploited for preparing quantum state with multipartite entanglement between many qubits. Most such schemes are applicable only to an ensemble of identical qubits, and inhomogeneous broadening will reduce the state preparation fidelity. Here we show that by interlacing the dynamical decoupling pulse sequence with the dissipative state preparation control, the errors resulting from the inhomogeneous broadening can be suppressed up to certain order of the pulse interval and the desired entangled states can be prepared with high fidelity. We give two examples where sequence of pi pulses interlaced with dissipative control realize high fidelity preparation of cluster states and many-body singlets of atomic qubits.   

Periodically and almost periodically driven quantum system

When a quantum system is driven periodically in time it can display dynamical localization, i.e its energy grows extremely slowly and may saturate at a value smaller than the infinite temperature limit. We show that by making the period of the perturbation longer this phenomenom is destroyed and the energy of the system grows quickly and saturates at the infinite temperature limit. We argue that this process is related to the breaking down of a particular form of perturbation theory (in the duration in of driving) and can be interpreted as a transition from a local to a long-range effective Hamiltonian. We discuss how robust our findings are against small aperiodicity in the driving. We finally discuss how realize this interesting non-equilibrium physics in cold atom experiments.   

Cold bosons in noisy optical lattices

Cold atoms in optical lattices open the possibility to experimentally study strongly interacting many-body quantum systems with controllable parameters. A key challenge to prepare interesting quantum states in these systems is to achieve sufficiently low temperatures. At these temperatures a deep theoretical understanding of possible heating processes and how they affect the characteristics of the quantum state becomes essential. In every realistic experiment there exist many sources of noise that cause phase and amplitude fluctuations in the standing laser waves that form the optical lattice potential. This classical noise can lead to heating and a significant change of the quantum state. We study the stochastic many-body non-equilibrium dynamics of bosons in an optical lattice and determine how the state changes depending on the characteristics of the noise. We do this by solving time-dependent stochastic many-body Schr\"odinger equations, both analytically and numerically.   

Many-body Landau-Zener Transition in Cold Atom Double Well Optical Lattices

Ultra-cold atoms in optical lattices provide an ideal platform for exploring many-body physics of a large system arising from the coupling among a series of small identical systems whose few-body dynamics are exactly solvable. Using Landau-Zener (LZ) transition of bosonic atoms in double well optical lattices as an experimentally realizable model, we investigate such few to many body route by exploring the relation and difference between the few-body (in one double well) and many-body (in double well lattice) non-equilibrium dynamics of cold atoms in optical lattices. We find the many-body coupling between double wells greatly enhances the LZ transition probability, while keeping the main features of the few-body dynamics. Various experimental signatures of the many-body LZ transition, including atom density, momentum distribution, and density-density correlation, are obtained.   

Quasi steady-states, spin statistics, and interaction-induced transport of ultra-cold atoms in 1D optical lattices

We consider several non-equilibrium scenarios where ultra-cold atoms are initially loaded into the ground state of a 1D optical lattice. The system is then set out of equilibrium either by inducing a density imbalance or by imposing time-dependent inhomogeneous interactions. To monitor the dynamics, we have implemented the micro-canonical approach to transport [1] which has been previously used to study electron dynamics in nanoscale systems. We have found that by removing particles on the right half of the lattice, fermions form a quasi steady-state current, which can be observed as a plateau in the current as a function of time. In contrast, the bosonic current oscillates and decays to zero in the thermodynamic limit [2]. The difference appears in uniform lattices as well as lattices with a harmonic trap. Further, when light-induced interactions are applied to half of the lattice, we have found, using a Hartree-Fock approximation, a conducting-nonconducting transition in the fermionic case as the interaction increases. Our studies are relevant to recent experiments on transport of ultra-cold atoms and address fundamental issues in nanoscale electronic transport. \\[4pt] [1] Di Ventra and Todorov,J. Phys. Cond. Matt. 16, 8025 (2004).\\[0pt] [2] Chien, Zwolak, Di Ventra, arXiv: 1110.1646.   

Spin Caloritronics in Noncondensed Bose Gases

We consider coupled spin and heat transport in a two-component, atomic Bose gas in the noncondensed state. We find that the transport coefficients show a temperature dependence reflecting the bosonic enhancement of scattering, and discuss experimental signatures of the spin-heat coupling in spin accumulation and total dissipation. Inside the critical region of Bose-Einstein condensation, we find anomalous behavior of the transport coefficients, and in particular, an enhancement for the spin caloritronics figure of merit that determines the thermodynamic efficiency of spin-heat conversion.   

Universal energy fluctuations in thermally isolated driven systems

When an isolated system is brought in contact with a heat bath, its final energy is random and follows the Gibbs distribution--this finding is a cornerstone of statistical physics. The system's energy can also be changed by performing non-adiabatic work using a cyclic process. Almost nothing is known about the resulting energy distribution in this set-up, which is in particular relevant to recent experimental progress in cold atoms, ion traps, superconducting qubits and other systems. Here we show that when the non-adiabatic process consists of many repeated cyclic processes, the resulting energy distribution is universal and different from the Gibbs ensemble. We predict the existence of two qualitatively different regimes with a continuous second-order-like transition between them. We illustrate our approach by performing explicit calculations for both interacting and non-interacting systems.   

Lie-algebraic Approach to Dynamics of Closed Quantum Systems and Quantum-to-Classical Correspondence

I will briefly review our recent work on a Lie-algebraic approach to various non-equilibrium quantum-mechanical problems, which has been motivated by continuous experimental advances in the field of cold atoms. First, I will discuss non-equilibrium driven dynamics of a generic closed quantum system. It will be emphasized that mathematically a non-equilibrium Hamiltonian represents a trajectory in a Lie algebra, while the evolution operator is a trajectory in a Lie group generated by the underlying algebra via exponentiation. This turns out to be a constructive statement that establishes, in particular, the fact that classical and quantum unitary evolutions are two sides of the same coin determined uniquely by the same dynamic generators in the group. An equation for these generators - dubbed dual Schr{\"o}dinger-Bloch equation - will be derived and analyzed for a few of specific examples. This non-linear equation allows one to construct new exact non-linear solutions to quantum-dynamical systems. An experimentally-relevant example of a family of exact solutions to the many-body Landau-Zener problem will be presented. One practical application of the latter result includes dynamical means to optimize molecular production rate following a quench across the Feshbach resonance.   

Visibility of the Amplitude (Higgs) Mode in Condensed Matter and Cold Atomic Systems

The amplitude mode is a ubiquitous collective excitation in condensed matter systems with broken continuous symmetry. It is expected in antiferromagnets, short coherence length superconductors, charge density waves, and lattice Bose condensates. Its detection is a valuable test of the corresponding field theory, and its mass gap measures the proximity to a quantum critical point. However, since the amplitude mode can decay into low energy Goldstone modes, its experimental visibility has been questioned. Here we show that the visibility depends on the symmetry of the measured susceptibility. We discuss various experimental setups for measuring the scalar susceptibility. We show that the optical conductivity of the O(2) theory (relativistic superfluid) displays a threshold behavior at the Higgs mass.