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arXiv:cond-mat/0204528 · Physical Review A

Free expansion of a Bose-Einstein condensate in a one-dimensional optical lattice

O. Morsch, Matteo Cristiani, Jörg Helge Müller, D. Ciampini, E. Arimondo

Published Aug 8, 2002• 52 citations
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Abstract

We have experimentally investigated the free expansion of a Bose-Einstein condensate in an array of two-dimensional traps created by a one-dimensional optical lattice. If the condensate held in a magnetic trap is loaded adiabatically into the lattice, the increase in chemical potential due to the additional periodic potential is reflected in the expansion of the condensate after switching off the magnetic trap. We have calculated the chemical potential from measurements of the transverse expansion of the condensate as a function of the lattice parameters.

DOI
10.1103/physreva.66.021601

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We have experimentally investigated the free expansion of a Bose-Einstein condensate in an array of two-dimensional traps created by a one-dimensional optical lattice. If the condensate held in a magnetic trap is loaded adiabatically into the lattice, the increase in chemical potential due to the additional periodic potential is reflected in the expansion of the condensate after switching off the magnetic trap. We have calculated the chemical potential from measurements of the transverse expansion of the condensate as a function of the lattice parameters.
We report experimental results on the dynamics and phase evolution of Bose-Einstein condensates in 1D optical lattices. The dynamical behaviour is studied by adiabatically loading the condensate into the lattice and subsequently switching off the magnetic trap. In this case, the condensate is free to expand inside the periodic structure of the optical lattice. The phase evolution of the condensate, on the other hand, can be studied by non-adiabatically switching on the periodic potential. We observe decays and revivals of the interference pattern after a time-of-flight.
We investigate the phase diffusion of a Bose–Einstein condensate (BEC) confined in the combined potential of a magnetic trap and a one-dimensional optical lattice. We show that the phase diffusion of the condensate in the whole optical lattice is evident and can be measured from the interference pattern of expanding subcondensates after the optical lattice is switched off. The maximum density of the interference pattern decreases significantly due to the mixing of the phase diffusion that appears in different subcondensates. This suggests a way to detect experimentally the notable phase diffusion of BECs.
Summary form only given. Since the experimental realization of Bose-Einstein condensation in the magnetically trapped quantum atomic gases, there have now been an enormous quantity of theory devoted to the properties of the trapped Bose-Einstein condensates (BEC). Motivated by the existing experiments, the bulk of the theoretical work has assumed a harmonic trap. Although recently a few papers have considered the consequences of exposing a BEC to a periodic optical potential, BEC confined in an optical lattice is still a new topic in this area. In the work, we develop theory to study the stationary and propagating properties of a Bose-Einstein condensate in an optical lattice. Instead of using an infinite optical lattice, we study the realistic case where the BEC is formed in a finite trapping potential and then is exposed to an infinite periodic potential created by off-resonance multiple laser beams.
We derive closed analytical expressions for the order parameter $\ensuremath{\Phi}(x)$ and for the chemical potential $\ensuremath{\mu}$ of a Bose-Einstein condensate loaded into a harmonically confined, one-dimensional optical lattice for sufficiently weak, repulsive, or attractive interaction and not too strong laser intensities. Our results are compared to exact numerical calculations in order to map out the range of validity of the perturbative analytical approach. We identify parameter values where the optical lattice compensates the interaction-induced nonlinearity, such that the condensate ground state coincides with a simple, single-particle harmonic-oscillator wave function.
Different experiments with Bose-Einstein rubidium condensates are presented in order to evidence the impact of condensate samples for the research in quantum optics and quantum physics. Measurements of the condensate free expansion, of the geometric forces acting on the condensate trapped into a time-orbiting-potential triaxial magnetic trap, of the acceleration of the condensate through a one-dimensional, off-resonant optical lattices and finally of the photoionization of the rubidium atoms composing the condensate are presented.