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arXiv:1109.6045 · Physical Review A

Phase coherence and fragmentation of two-component Bose-Einstein condensates loaded in state-dependent optical lattices

Hyunoo Shim, Thomas H. Bergeman

Published Oct 17, 2016• 3 citations
arXivHTMLPDF

Abstract

A binary mixture of interacting Bose-Einstein condensates (BEC) in the presence of fragmentation-driving external lattice potentials forms two interdependent mean-field lattices made of each component. These effective mean-field lattices, like ordinary optical lattices, can induce additional fragmentation and phase coherence loss of BECs between lattice sites. In this study, we consider the nonequilibrium dynamics of two hyperfine states of one-dimensional Bose-Einstein condensates, subjected to state-dependent optical lattices. Our numerical calculations using the truncated Wigner approximation (TWA) show that phase coherence in a mixture of two-component BECs can be lost not just by optical lattices, but by mean-field lattices gradually formed by other components, and we reveal that such an effect of internal mean-field lattices, however, is limited, contrary to external optical lattices, in regard to phase decoherence.

DOI
10.1103/physreva.94.043631

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A binary mixture of interacting Bose-Einstein condensates (BEC) in the presence of fragmentation-driving external lattice potentials forms two interdependent mean-field lattices made of each component. These effective mean-field lattices, like ordinary optical lattices, can induce additional fragmentation and phase coherence loss of BECs between lattice sites. In this study, we consider the nonequilibrium dynamics of two hyperfine states of one-dimensional Bose-Einstein condensates, subjected to state-dependent optical lattices. Our numerical calculations using the truncated Wigner approximation (TWA) show that phase coherence in a mixture of two-component BECs can be lost not just by optical lattices, but by mean-field lattices gradually formed by other components, and we reveal that such an effect of internal mean-field lattices, however, is limited, contrary to external optical lattices, in regard to phase decoherence.
Phase coherence and localization of Bose-Einstein Condensates (BEC) in optical lattices is a notable property that is changing under the superfluid-Mott insulator phase transition. For a single-component BEC, long-range phase coherence across lattice wells is lost as the lattice height is sufficiently increased. Phase coherences of two-component overlapping mixture of BECs, however, are nontrivial because of the interspecies interaction between components, affecting localization of condensates. For such cases, the BECs form two interdependent mean-field lattices made of each component in addition to optical lattices. We prepare initial BEC clouds as a collection of small Bogoliubov quasiparticles added to classical mean-fields, and obtain the dynamics under phase space representations, where the density operators are projected onto phase space. Among various phase space representations, we focus on a Truncated Wigner Approximation (TWA) and a positive P representation, and we construct a hybrid model to combine them. Since a high volume of numerical integration is required for sufficient convergence from ensembles, we construct efficient numerical methods to reduce the sample variance. We demonstrate time evolution of phase coherence of one-component and two-component BECs in state-dependent optical lattices. For one-component BECs, we show that phase coherence loss depends on lattice heights. In the cycling process of lattice height changes, we investigate nonadiabatic effects depending on initial ramp-up speeds. The hybrid model compared with the TWA exhibits temporal fluctuations in coherence and sudden phase diffusion at the end of ramp-up of a lattice. For two-component BECs, we consider that the two wavefunctions are localized at periodic potential wells whose positions differ by a half-period between the two. Dependence on population imbalance between two components becomes another factor on coherence loss. We show that under gradual loading of an optical lattice effective only to first component, loss of phase coherence of first atoms is enhanced and that of second atoms is weakened as the fraction of second atoms is increased in the mixture. We also demonstrate effects of localizing mean-field lattices on coherence loss under various lattice heights.
We consider dynamics of a two-component Bose–Einstein condensate, where the components correspond to different hyperfine states of the same sort of atoms. External microwave radiation leads to resonant transitions between the states. The condensate is loaded into the optical lattice. We invoke the tight-binding approximation and examine the interplay of spatial and internal dynamics of the mixture. We show that internal dynamics qualitatively depends on the intra-component interaction strength and the phase configuration of the initial state. We focus attention on two intriguing phenomena occurring at certain values of the parameters. The first phenomenon is the spontaneous synchronization of Rabi oscillations running inside neighboring lattice sites. The other one is demixing of the condensate with formation of immiscible solitons at sufficiently strong nonlinearity. Demixing is preceded by the transient regime with highly irregular behavior of the mixture.
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. ^
We study the splitting of a harmonically trapped atomic Bose-Einstein condensate when we continuously turn up an optical lattice (or a double-well) potential. As the lattice height is increased, quantum fluctuations of atoms are enhanced. The resulting nonequilibrium dynamics of the fragmentation process of the condensate, the loss of the phase coherence of atoms along the lattice, and the reduced atom number fluctuations in individual lattice sites are stochastically studied within the truncated Wigner approximation. We perform a detailed study of the effects of temperature and lattice height on atom dynamics, and investigate the validity of the classical Gross-Pitaevskii equation in optical lattices. We find the atom number squeezing to saturate in deep lattices due to nonadiabaticity in turning up of the lattice potential that is challenging to avoid in experiments when the occupation number of the lattice sites is large, making it difficult to produce strongly number squeezed (or the Mott insulator) states with large filling factors. We also investigate some general numerical properties of the truncated Wigner approximation.
We study the phase coherence property of Bose−Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza–Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.
We theoretically study the loading of a two-species Bose–Einstein condensate to an optical lattice in a tightly confined one-dimensional trap. Due to quantum fluctuations, the relative inter- and intra-species phase coherence between the atoms and the on-site atom number fluctuations are reduced in the miscible regime. For the immiscible case the fluctuations are enhanced and the atoms form metastable interleaved spatially separated domains where the domain length and its fluctuations are affected by quantum fluctuations.