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arXiv:1706.09148 · Physical Review A

Bose-Hubbard lattice as a controllable environment for open quantum systems

F. Cosco, Massimo Borrelli, Juan José Mendoza-Arenas, Francesco Plastina, Dieter Jaksch, Sabrina Maniscalco

Published Apr 9, 2018• 20 citations
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Abstract

We investigate the open dynamics of an atomic impurity embedded in a one-dimensional Bose-Hubbard lattice. We derive the reduced evolution equation for the impurity and show that the Bose-Hubbard lattice behaves as a tunable engineered environment allowing one to simulate both Markovian and non-Markovian dynamics in a controlled and experimentally realizable way. We demonstrate that the presence or absence of memory effects is a signature of the nature of the excitations induced by the impurity, being delocalized or localized in the two limiting cases of a superfluid and Mott insulator, respectively. Furthermore, our findings show how the excitations supported in the two phases can be characterized as information carriers.

DOI
10.1103/physreva.97.040101

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•Aug 1, 2012•1 citation
We investigate the open dynamics of an atomic impurity embedded in a one-dimensional Bose-Hubbard lattice. We derive the reduced evolution equation for the impurity and show that the Bose-Hubbard lattice behaves as a tunable engineered environment allowing one to simulate both Markovian and non-Markovian dynamics in a controlled and experimentally realizable way. We demonstrate that the presence or absence of memory effects is a signature of the nature of the excitations induced by the impurity, being delocalized or localized in the two limiting cases of a superfluid and Mott insulator, respectively. Furthermore, our findings show how the excitations supported in the two phases can be characterized as information carriers.
We study quantum information flow in a model comprised of a trapped impurity qubit immersed in a Bose-Einstein-condensed reservoir. We demonstrate how information flux between the qubit and the condensate can be manipulated by engineering the ultracold reservoir within experimentally realistic limits. We show that this system undergoes a transition from Markovian to non-Markovian dynamics, which can be controlled by changing key parameters such as the condensate scattering length. In this way, one can realize a quantum simulator of both Markovian and non-Markovian open quantum systems, the latter ones being characterized by a reverse flow of information from the background gas (reservoir) to the impurity (system).
Abstract We study the dynamics of a two-level impurity embedded in a two-dimensional Bose–Hubbard (BH) model at zero temperature from an open quantum system perspective. Results for the decoherence across the whole phase diagram are presented, with a focus on the critical region close to the transition between superfluid and Mott insulator. In particular we show how the decoherence and the deviation from a Markovian behaviour are sensitive to whether the transition is crossed at commensurate or incommensurate densities. The role of the spectrum of the BH environment and its non-Gaussian statistics, beyond the standard independent boson model, is highlighted. Our analysis resorts on a recently developed method (2020 Phys. Rev. Res. 2 033276) – closely related to slave boson approaches – that enables us to capture the correlations across the whole phase diagram. This semi-analytical method provides us with a deep insight into the physics of the spin decoherence in the superfluid and Mott phases as well as close to the phase transitions.
The Bose-Hubbard model is the simplest model of interacting bosons on a lattice. It has recently been the focus of much attention due to the realization of this model with cold atoms in an optical lattice. The ability to tune parameters in the Hamiltonian as a function of time in cold atom systems has opened up the possibility of studying out-of-equilibrium dynamics, including crossing the quantum critical region of the model in a controlled way. In this paper, I give a brief introduction to the Bose Hubbard model, and its experimental realization and then give an account of theoretical and experimental efforts to understand out-of-equilibrium dynamics in this model, focusing on quantum quenches, both instantaneous and of finite duration. I discuss slow dynamics that have been observed theoretically and experimentally for some quenches from the superfluid phase to the Mott insulating phase and the picture of two timescales, one for fast local equilibration and another for slow global equilibration, that appears to characterize this situation. I also discuss the theoretical and experimental observation of the Lieb-Robinson bounds for a variety of quenches and the Kibble-Zurek mechanism in quenches from the Mott insulator to superfluid. I conclude with a discussion of open questions and future directions.
The dynamics and non-Markovianity of an atomic impurity qubit (AIQ) immersed in a structured environment is explored where the AIQ is driven by a two-dimensional field and the environment is a quasi-two-dimensional dipolar Bose-Einstein condensate (dBEC). We derive a non-Markovian master equation for the AIQ with initial correlation between the qubit and the dBEC, which contains all the influences of the non-Markovian environment on the atomic impurity qubit. Analyzing the spectrum density for the AIQ-dBEC coupled system and solving the dynamics of the qubit, we find that the atomic impurity qubit can be partially stabilized in its excited state by controlling the xxx-direction field with the yyy-direction field fixed. Our analysis reveals that it is the formation of the system-environment bound state that results in such a suppressed dissipation. The present paper is helpful for understanding the effect of the structured and modulated environment and enriches the dynamics of an open system.
We investigate a system of fermions trapped in a quasiperiodic potential from an open quantum system theory perspective, designing a protocol in which an impurity atom (a two-level system) is coupled to a trapped fermionic cloud described by the noninteracting Aubry-Andr\'e model. The Fermi system is prepared in a charge-density-wave state before it starts its relaxation. In this work we focus our attention on the time evolution of the impurity in such an out-of-equilibrium environment and study whether the induced dynamics can be classified as Markovian or non-Markovian. We find how the localized phase of the Aubry-Andr\'e model displays evidence of strong and stable memory effects and can be considered as a controllable and robust non-Markovian environment.
Quantum degenerate atomic gases offer a unique platform for the exploration of a wide variety of interacting many-body systems in a pristine environment, based on a set of powerful tools for the coherent control of the atoms' internal and external degrees of freedom. Here, we present experimental studies of strongly interacting bosonic mixtures in one-dimensional (1D) systems, in which the mobilities of the two species are independently controlled with a state-selective optical lattice. In a first experiment, we freeze out the tunneling of one species from a binary mixture, and study the formation of ``quantum emulsion'' states, where immobile atoms serve as a static, random disorder for a more mobile species. We investigate the 1D superfluid-to-insulator transition in the presence of this disorder, and make comparisons to the effects of quasi-disorder from an incommensurate optical lattice. We observe enhanced localization in the more random potential, highlighting the important role of correlations in disordered systems. Through a combined measurement of transport, localization, and excitation spectra, we are able to obtain strong evidence for observation of a disordered, insulating quantum phase, the 1D Bose glass. In a second experiment, we introduce a new experimental technique for the characterization of ultracold gases held in optical lattices. In analogy to neutron diffraction from solids, we use atomic de Broglie waves to non-destructively probe the spatial structure of 1D Mott insulators through elastic Bragg diffraction, and to probe inelastic band-structure excitations of more weakly interacting 1D Bose gases. Furthermore, we use the diffraction of matter waves to detect the formation of forced-antiferromagnetic ordering in a crystalline atomic spin mixture. Lastly, we study the dynamical response of matter waves to a periodically pulsed, incommensurate optical lattice, a situation that realizes a system of two coupled kicked quantum rotors. We observe that the coupling induces a suppression of energy growth at quantum resonances, and a localization-to-delocalization transition in momentum space for off-resonant driving. Our observations confirm a long-standing theoretical prediction for the two-rotor system, and illustrate how classical behavior can emerge from the evolution of a simple quantum system. | 193 pages