In this work we analyze the simultaneous emergence of diffusive energy transport and local thermalization in a nonequilibrium one-dimensional quantum system, as a result of integrability breaking. Specifically, we discuss the local properties of the
steady state induced by thermal boundary driving in a XXZ spin chain with staggered magnetic field. By means of efficient large-scale matrix product simulations of the equation of motion of the system, we calculate its steady state in the long-time limit.We start by discussing the energy transport supported by the system, finding it to be ballistic in the integrable limit and diffusive when the staggered field is finite. Subsequently, we examine the reduced density operators of neighboring sites and find that for large systems they are well approximated by local thermal states of the underlying Hamiltonian in the nonintegrable regime, even for weak staggered fields. In the integrable limit, on the other hand, this behavior is lost, and the identification of local temperatures is no longer possible. Our results agree with the intuitive connection between energy diffusion and thermalization.
We adapt the time-evolving block decimation (TEBD) algorithm, originally devised to simulate the dynamics of 1D quantum systems, to simulate the time-evolution of non-equilibrium stochastic systems. We describe this method in detail; a systems probab
ility distribution is represented by a matrix product state (MPS) of finite dimension and then its time-evolution is efficiently simulated by repeatedly updating and approximately re-factorizing this representation. We examine the use of MPS as an approximation method, looking at parallels between the interpretations of applying it to quantum state vectors and probability distributions. In the context of stochastic systems we consider two types of factorization for use in the TEBD algorithm: non-negative matrix factorization (NMF), which ensures that the approximate probability distribution is manifestly non-negative, and the singular value decomposition (SVD). Comparing these factorizations we find the accuracy of the SVD to be substantially greater than current NMF algorithms. We then apply TEBD to simulate the totally asymmetric simple exclusion process (TASEP) for systems of up to hundreds of lattice sites in size. Using exact analytic results for the TASEP steady state, we find that TEBD reproduces this state such that the error in calculating expectation values can be made negligible, even when severely compressing the description of the system by restricting the dimension of the MPS to be very small. Out of the steady state we show for specific observables that expectation values converge as the dimension of the MPS is increased to a moderate size.
We investigate the dynamics of Rydberg electrons excited from the ground state of ultracold atoms trapped in an optical lattice. We first consider a lattice comprising an array of double-well potentials, where each double well is occupied by two ultr
acold atoms. We demonstrate the existence of molecular states with equilibrium distances of the order of experimentally attainable inter-well spacings and binding energies of the order of 10^3 GHz. We also consider the situation whereby ground-state atoms trapped in an optical lattice are collectively excited to Rydberg levels, such that the charge-density distributions of neighbouring atoms overlap. We compute the hopping rate and interaction matrix elements between highly-excited electrons separated by distances comparable to typical lattice spacings. Such systems have tunable interaction parameters and a temperature ~10^{-4} times smaller than the Fermi temperature, making them potentially attractive for the study and simulation of strongly correlated electronic systems.
We observe a sudden breakdown of the transport of a strongly repulsive Bose-Einstein condensate through a shallow optical lattice of finite width. We are able to attribute this behavior to the development of a self-trapped state by using accurate num
erical methods and an analytical description in terms of nonlinear Bloch waves. The dependence of the breakdown on the lattice depth and the interaction strength is investigated. We show that it is possible to prohibit the self-trapping by applying a constant offset potential to the lattice region. Furthermore, we observe the disappearance of the self-trapped state after a finite time as a result of the revived expansion of the condensate through the lattice. This revived expansion is due to the finite width of the lattice.
We study the interaction-induced localization -- the so-called self-trapping -- of a neutral impurity atom immersed in a homogeneous Bose-Einstein condensate (BEC). Based on a Hartree description of the BEC we show that -- unlike repulsive impurities
-- attractive impurities have a singular ground state in 3d and shrink to a point-like state in 2d as the coupling approaches a critical value. Moreover, we find that the density of the BEC increases markedly in the vicinity of attractive impurities in 1d and 2d, which strongly enhances inelastic collisions between atoms in the BEC. These collisions result in a loss of BEC atoms and possibly of the localized impurity itself.
We analyze the outcome of a Mott insulator to superfluid transition for a two-component Bose gas with two atoms per site in an optical lattice in the limit of slow ramping down the lattice potential. This manipulation of the initial Mott insulating s
tate transforms local correlations between hyperfine states of atom pairs into multiparticle correlations extending over the whole system. We show how to create macroscopic twin Fock states in this way an that, in general, the obtained superfluid states are highly depleted even for initial ground Mott insulator states.
