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arXiv:0812.3767 · Physical Review A

Cold atoms in double-well optical lattices

Vyacheslav I. Yukalov, Elizaveta P. Yukalova

Published Dec 17, 2008• 26 citations
arXivHTMLPDF

Abstract

Cold atoms, loaded into an optical lattice with double-well sites, are considered. Pseudospin representation for an effective Hamiltonian is derived. The system in equilibrium displays two phases, ordered and disordered. The second-order phase transition between the phases can be driven either by temperature or by changing the system parameters. Collective pseudospin excitations have a gap disappearing at the phase-transition point. Dynamics of atoms is studied when they are loaded into the lattice in an initially nonequilibrium state. It is shown that the temporal evolution of atoms, contrary to their equilibrium thermodynamics, cannot be described in the mean-field approximation, since it results in a structurally unstable dynamical system, but a more accurate description is necessary taking into account attenuation effects.

DOI
10.1103/physreva.78.063610

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Cold atoms, loaded into an optical lattice with double-well sites, are considered. Pseudospin representation for an effective Hamiltonian is derived. The system in equilibrium displays two phases, ordered and disordered. The second-order phase transition between the phases can be driven either by temperature or by changing the system parameters. Collective pseudospin excitations have a gap disappearing at the phase-transition point. Dynamics of atoms is studied when they are loaded into the lattice in an initially nonequilibrium state. It is shown that the temporal evolution of atoms, contrary to their equilibrium thermodynamics, cannot be described in the mean-field approximation, since it results in a structurally unstable dynamical system, but a more accurate description is necessary taking into account attenuation effects.
We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.
Abstract We investigated the transport properties of cold atoms in a one-dimensional optical lattice under distance selective dissipation and external driving. We analyze how tunneling, on-site interaction, dissipation and external driving affect the transport of cold atoms. We used mean-field theory and the classical phase space method to explain the dynamics of the system. In order to analyze the transport effect of cold atoms, we calculate the relative density of atoms on each site and the standard deviation of relative density. The manipulation transport of cold atoms can be achieved through a step function like interaction in theory. In particular, we study the transport of cold atoms in the double-well with external driving. The steady states of the system are analytically derived.
Bose-Einstein condensates (BECs) in an optical lattice driven out of equilibrium and the subsequent dynamics are investigated in the limit of weak atom-atom interactions both within the classical mean-field approximation and by incorporating an approximate model for quantum fluctuations. A prediction of pulsating dynamical instability in which atoms periodically collect together and subsequently disperse back into the initial homogeneous state is made. This instability is a unique feature of this Hamiltonian system characterized by a single unstable mode and can be considered as a remnant of the integrability of the non-integrable system. A phase-space model has been employed to incorporate the quantum fluctuations within the truncated Wigner approximation. It is observed that the quasiperiodic behavior of the pulsating dynamics persists in the individual stochastic realizations that represent the typical experimental outcomes, but the effect of quantum fluctuations is manifested in the ensemble averages of various properties of the system. Quantum effects are increasingly prominent and the revivals of the ensemble averages of the wave function become progressively weaker when the effective interaction strength is increased. Motivated by these predictions, we apply similar methods to two-component BECs. Within the mean-field model we demonstrate a spontaneous emergence of a vector soliton like structure, a bound pair of a soliton and an anti-soliton, from the homogeneous imbalanced mixture of two BEC species. This is a feature that uniquely combines phase separation, pulsating instability, and formation of a dark-bright soliton pair when the parameters involved are tuned properly. ^
Double-well optical lattice in an insulating state is considered. The influence of atomic vibrations and mesoscopic disorder on the properties of the lattice are studied. Vibrations lead to the renormalization of atomic interactions. The occurrence of mesoscopic disorder results in the appearance of first-order phase transitions between the states with different levels of atomic imbalance. The existence of a nonuniform external potential, such as trapping potential, essentially changes the lattice properties, suppressing the disorder fraction and rising the transition temperature.
Double-well optical lattice in an insulating state is considered. The influence of atomic vibrations and mesoscopic disorder on the properties of the lattice are studied. Vibrations lead to the renormalization of atomic interactions. The occurrence of mesoscopic disorder results in the appearance of first-order phase transitions between the states with different levels of atomic imbalance. The existence of a nonuniform external potential, such as trapping potential, essentially changes the lattice properties, suppressing the disorder fraction and rising the transition temperature.