Many-body Landau–Zener dynamics in coupled one-dimensional Bose liquids

Abstract

The Landau-Zener model of a quantum mechanical two-level system driven with a linearly time dependent detuning has served over decades as a textbook paradigm of quantum dynamics. In their seminal work [L. D. Landau, Physik. Z. Sowjet. 2, 46 (1932); C. Zener, Proc. Royal Soc. London 137, 696 (1932)], Landau and Zener derived a non-perturbative prediction for the transition probability between two states, which often serves as a reference point for the analysis of more complex systems. A particularly intriguing question is whether that framework can be extended to describe many-body quantum dynamics. Here we report an experimental and theoretical study of a system of ultracold atoms, offering a direct many-body generalization of the Landau-Zener problem.In a system of pairwise tunnel-coupled 1D Bose liquids we show how tuning the correlations of the 1D gases, the tunnel coupling between the tubes and the inter-tube interactions strongly modify the original Landau-Zener picture. The results are explained using a mean-field description of the inter-tube condensate wave-function, coupled to the low-energy phonons of the 1D Bose liquid. arXiv:1003.4956v1 [cond-mat.quant-gas]

Linear quantum quench in the Heisenberg XXZ chain: Time-dependent Luttinger-model description of a lattice system

“…Linear quenches occuring over a finite time can interpolate between the more familiar limits of an instantaneous quench and an adiabatic sweep. Very recently, a few experiments have examined the response of many-body experiments to such finitetime quenches [5,6]. It is thus of vital current interest to address the dynamics under linear sweeps of system parameters such as interaction strength.…”

Phase diagram of Landau-Zener phenomena in coupled one-dimensional Bose quantum fluids

“…To proceed, we will consider the experimental realization reported in Ref. [3] where the transfer of particles in x and z directions is studied in what it is called the ground-state and inverse sweeps, the former accounting for a sweep starting from the ground state, namely, where all the particles initiate in the bottom well with lower energy, and the latter where the initially filled sites are the ones with higher energy. This scheme leads us to answer several questions, on one side those related to the stationary properties, such as, the energy spectrum, and on the other side, aspects related to the dynamical behavior of the atomic population in the wells.…”

“…Starting from the Bose-Hubbard Hamiltonian of an optical lattice [3], one can write down the Hamiltonian of atoms in the two-well chain as,…”

“…In addition, since the number of particles per lattice sites in the actual experiments is not too large, it is possible to perform accurate numerical simulations of the system. Such a analysis gives rise to a richer spectrum with respect to the single dimer considered in [3].…”

“…As it is well known [1,2], the transition probability between the two energy states is the well known LZ formula P LZ = exp(−2πJ 2 / α) written in terms of the tunnelling-coupling parameter J and the time-dependent detunning ∆ = αt, accounting for the probability that a particle initially in the bottom well at t = −∞ reaches at t = ∞ the opposite well. Recent experiments have demonstrated the many body generalization of the LZ phenomena by loading an ultracold Bose gas into a pair of coupled one-dimensional chains where a controllable inter-chain sweep leads to the observation of both, avoided crossings and breakdown of adiabatic inter-chain transfer [3].…”