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arXiv:1804.06147 · Physical Review A

Adiabaticity when raising a uniform three-dimensional optical lattice in a bimodal Bose-Einstein condensate

Dariusz Kajtoch, Emilia Witkowska, Alice Sinatra

Published Aug 17, 2018• 4 citations
arXivHTMLPDF

Abstract

Using the time-dependent Bogoliubov approach, we study adiabaticity for a two-component Bose-Einstein condensate in a three-dimensional time-dependent optical lattice with unit filling, in the superfluid and weakly interacting regime. We show that raising the lattice potential height can couple the ground state of the Bogoliubov Hamiltonian to excited states with two quasiparticles of opposite quasimomenta. In the symmetric case for interactions and density in the two components these represent sound waves where the two components oscillate out of phase. We find an analytic expression for the adiabatic time, its dependence on the fraction of atoms in each component, and its scaling with the system size.

DOI
10.1103/physreva.98.023621

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Using the time-dependent Bogoliubov approach, we study adiabaticity for a two-component Bose-Einstein condensate in a three-dimensional time-dependent optical lattice with unit filling, in the superfluid and weakly interacting regime. We show that raising the lattice potential height can couple the ground state of the Bogoliubov Hamiltonian to excited states with two quasiparticles of opposite quasimomenta. In the symmetric case for interactions and density in the two components these represent sound waves where the two components oscillate out of phase. We find an analytic expression for the adiabatic time, its dependence on the fraction of atoms in each component, and its scaling with the system size.
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 investigate a model of a two-component Bose-Einstein condensate residing in an optical lattice. Within a Bogoliubov approach at the mean-field level, we derive exact analytical expressions for the excitation spectrum of the two-component condensate when taking into account hopping and interactions between arbitrary sites. Our results thus constitute a basis for works that seek to clarify the effects of higher-order interactions in the system. We investigate the excitation spectrum and the two branches of superfluid velocity in more detail for two limiting cases of particular relevance. Moreover, we relate the hopping and interaction parameters in the effective Bose-Hubbard model to microscopic parameters in the system, such as the laser light wavelength and atomic masses of the components in the condensate. These results are then used to calculate analytically and numerically the drag coefficient between the components of the condensate. We find that the drag is most effective close to the symmetric case of equal masses between the components, regardless of the strength of the intercomponent interaction and the lattice well depth.
We investigate a Bose-Einstein condensate (BEC) trapped in a two-dimensional optical lattice in the presence of weak disorder within the framework of the Bogoliubov theory. In particular, we analyze the combined effects of disorder and an optical lattice on quantum fluctuations and superfluid density of the BEC system. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the lattice still induces a characteristic three-dimensional (3D) to one-dimensional crossover in the behavior of quantum fluctuations, despite the presence of weak disorder. Furthermore, we use the linear response theory to calculate the normal fluid density of the condensate induced by disorder. Our results in the 3D regime show that the combined presence of disorder and lattice induce a normal fluid density that asymptotically approaches 4/3 of the corresponding condensate depletion. Conditions for possible experimental realization of our scenario are also proposed.
We investigate a model of a two-component Bose-Einstein condensate residing on an optical lattice. Within a Bogolioubov-approach at the mean-field level, we derive exact analytical expressions for the excitation spectrum of the two-component condensate when taking into account hopping and interactions between arbitrary sites. Our results thus constitute a basis for works that seek to clarify the effects of higher-order interactions in the system. We investigate the excitation spectrum and the two branches of superfluid velocity in more detail for two limiting cases of particular relevance. Moreover, we relate the hopping and interaction parameters in the effective Bose-Hubbard model to microscopic parameters in the system, such as the laserlight wavelength and atomic masses of the components in the condensate. These results are then used to calculate analytically and numerically the drag coefficient between the components of the condensate. We find that the drag is most effective close to the symmetric case of equal masses between the components, regardless of the strength of the intercomponent interaction and the lattice well depth.
The speed of sound of a Bose-Einstein condensate in an optical lattice is studied both analytically and numerically in all spatial three dimensions. Our investigation shows that the sound speed depends strongly on the strength of the lattice. In the one-dimensional case, the speed of sound falls monotonically with increasing lattice strength. The dependence on lattice strength becomes much richer in two and three dimensions. In the two-dimensional case, when the interaction is weak, the sound speed first increases and then decreases as the lattice strength increases. For the three-dimensional lattice, the sound speed can even oscillate with the lattice strength. These rich behaviors can be understood in terms of compressibility and effective mass. Our analytical results in the limit of weak lattices also offer an interesting perspective to help with our understanding: they show that the lattice component perpendicular to the sound propagation increases the sound speed while the lattice component parallel to the propagation decreases the sound speed. The various dependences of the sound speed on the lattice strength are the result of this competition.