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Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & Astronomy

Critical temperature and condensed fraction of Bose-Einstein condensation in optical lattices

Yu Xue

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Critical temperature and condensate fraction of Bose-Einstein condensation in the optical lattice are studied.The results show that the critical temperature in optical lattices can be characterized with an equivalent critical temperature in a single lattice,which provide a fast evaluation of critical temperature and condensate fraction of Bose-Einstein condensation confined with pure optical trap.Critical temperature can be estimated with an equivalent critical temperature.It is predicted that critical temperature is proportional to q in q number lattices for superfluid state and should be equal to that in a single lattic for Mott insulate state.Required potential depth or Rabi frequency and maximum atom number in the lattices both for superfluid state and Mott state are presented based on views of thermal mechanical statistics.

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Critical temperature and condensate fraction of Bose-Einstein condensation in the optical lattice are studied.The results show that the critical temperature in optical lattices can be characterized with an equivalent critical temperature in a single lattice,which provide a fast evaluation of critical temperature and condensate fraction of Bose-Einstein condensation confined with pure optical trap.Critical temperature can be estimated with an equivalent critical temperature.It is predicted that critical temperature is proportional to q in q number lattices for superfluid state and should be equal to that in a single lattic for Mott insulate state.Required potential depth or Rabi frequency and maximum atom number in the lattices both for superfluid state and Mott state are presented based on views of thermal mechanical statistics.
Bose–Einstein condensation in a finite one-dimensional atomic Bose gas trapped in an optical lattice is studied within Bogoliubov’s approximation and then beyond this approximation, within the static fluctuation approximation. A Bose–Hubbard model is used to construct the Hamiltonian of the system. The effect of the potential strength on the condensate fraction is explored at different temperatures; so is the effect of temperature on this fraction at different potential strengths. The role of the number of lattice points (the size effect) at constant number density (the filling factor) is examined; so is the effect of the number density on the condensate fraction. The results obtained are compared to other published results wherever possible.
We evaluate the Bose-Einstein condensate density and the superfluid fraction of bosons in a periodic external potential using path-integral Monte Carlo methods. The periodic lattice consists of a cubic cell containing a potential well that is replicated along one dimension using periodic boundary conditions. The aim is to describe bosons in a one-dimensional optical lattice or helium confined in a periodic porous medium. The one-body density matrix is evaluated and diagonalized numerically to obtain the single boson natural orbitals and the occupation of these orbitals. The condensate fraction is obtained as the fraction of bosons in the orbital that has the highest occupation. The superfluid density is obtained from the winding number. From the condensate orbital and superfluid fraction, we investigate (1) the impact of the periodic external potential on the spatial distribution of the condensate, and (2) the correlation of localizing the condensate into separated parts and the loss of superflow along the lattice. For high-density systems, as the well depth increases, the condensate becomes depleted in the wells and confined to the plateaus between successive wells, as in pores between necks in a porous medium. For low-density systems, as the well depth increases the BEC is localized at the center of the wells (tight binding) and depleted between the wells. In both cases, the localization of the condensate suppresses superflow leading to a superfluid-insulator crossover. The impact of the external potential on the temperature dependence of the superfluidity is also investigated. The external potential suppresses the superfluid fraction at all temperatures, with a superfluid fraction significantly less than one at low temperature. The addition of an external potential does not, however, significantly reduce the transition temperature.
In this paper we develop an analytic expression for the critical temperature for a gas of ideal bosons in a combined harmonic lattice potential, relevant to current experiments using optical lattices. We give corrections to the critical temperature arising from effective mass modifications of the low energy spectrum, finite size effects, and excited band states. We compute the critical temperature using numerical methods and compare to our analytic result. We study condensation in an optical lattice over a wide parameter regime and demonstrate that the critical temperature can be increased or reduced relative to the purely harmonic case by adjusting the harmonic trap frequency. We show that a simple numerical procedure based on a piecewise analytic density of states provides an accurate prediction for the critical temperature.
Bose–Einstein condensates (BEC) of sodium atoms are transferred into one-dimensional (1D) optical lattice potentials, formed by two laser beams with a wavelength of 1064 nm, in a shallow optical trap. The phase coherence of the condensate in the lattice potential is studied by changing the lattice depth. A qualitative change in behavior of the BEC is observed at a lattice depth of ∼ 13.7 E r, where the quantum gas undergoes a transition from a superfluid state to a state that lacks well-to-well phase coherence.
87Rb Bose Einstein Condensate in 3D optical lattice was studied in the regime of weak interaction(the superfluid phase) and strong interaction(the Mott insulating phase). The stability of superfluid currents was studied using a moving optical lattice. The critical momentum for stable superfluid current varies from 0.5 recoil momentum (shallow lattice) to 0 (the Mott insulator) as the system reaches the Mott insulator transition. The phase diagram for the disappearance of superfluidity was studied as a function of momentum and lattice depth. Our phase diagram boundary ex-trapolates to the critical lattice depth for the superfluid-to-MI transition. When a one-dimensional gas was loaded into a moving optical lattice a sudden broadening of the transition between stable and unstable phases was observed. A new auxiliary vacuum chamber, which is called the science chamber, was de-signed and installed to improve optical lattice experimental performance and imaging resolution power. Atoms are transported from the main chamber to the science cham-ber. By further evaporation cooling, BECs with N- 2-3 x 104 atoms are produced
Bose-Einstein condensation (BEC) in cold gases can be turned on and off by an external potential, such as that presented by an optical lattice. We present a model of this phenomenon which we are able to analyze rigorously. The system is a hard core lattice gas at half of the maximum density and the optical lattice is modeled by a periodic potential of strength $\ensuremath{\lambda}$. For small $\ensuremath{\lambda}$ and temperature, BEC is proved to occur, while at large $\ensuremath{\lambda}$ or temperature there is no BEC. At large $\ensuremath{\lambda}$ the low-temperature states are in a Mott insulator phase with a characteristic gap that is absent in the BEC phase. The interparticle interaction is essential for this transition, which occurs even in the ground state. Surprisingly, the condensation is always into the p=0\mathbf{p}=\mathbf{0}p=0 mode in this model, although the density itself has the periodicity of the imposed potential.