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Physical Review A

Ground-state properties of a Bose-Einstein condensate tuned by a far-off-resonant optical field

Guangjiong Dong, Bambi Hu, Weiping Lu

Published Dec 1, 2006• 28 citations
Publisher

Abstract

In this paper, we explore a scheme to tackle a challenging problem of stable Bose-Einstein condensates (BECs) with attractive atom interactions. In this scheme, the $s$-wave scattering length is tuned in space, rather than in time as previously studied, by a far-off-resonant Gaussian optical field, from negative to positive in the center region of the potential well. We find that this tuning leads to coexisting repulsive and attractive interactions within a single atomic gas and consequently a stable BEC in the repulsive region. We investigate the ground-state properties of the tuned BECs and show them to exhibit a strikingly different spatial density distribution from a conventional one with a positive $s$-wave scattering length. The tuned BEC is formed only when the condensed number is less than a critical number. We derive a formula for the critical number.

DOI
10.1103/physreva.74.063601

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In this paper, we explore a scheme to tackle a challenging problem of stable Bose-Einstein condensates (BECs) with attractive atom interactions. In this scheme, the sss-wave scattering length is tuned in space, rather than in time as previously studied, by a far-off-resonant Gaussian optical field, from negative to positive in the center region of the potential well. We find that this tuning leads to coexisting repulsive and attractive interactions within a single atomic gas and consequently a stable BEC in the repulsive region. We investigate the ground-state properties of the tuned BECs and show them to exhibit a strikingly different spatial density distribution from a conventional one with a positive sss-wave scattering length. The tuned BEC is formed only when the condensed number is less than a critical number. We derive a formula for the critical number.
We briefly review our recent work on spatial tuning of Bose-Einstein condensation (BEC). We first study spatially periodic tuning of the s-wave scattering length for controlling the propagation of a BEC matter wave, and find matter wave limiting processing and bistability. Second, we show that a stable BEC with natural attractive interaction could be formed by tuning the s -wave scattering length with a Gaussian optical field, but the condensed atom number should be less than a critical value. Further, we apply Thomas-Fermi approximation to obtain a formula for this critical value.
We investigate the effect of the position-dependent sss-wave scattering length (SSL) on Bose-Einstein condensate (BEC) dynamics. In particular, we study the propagation of a BEC within a finite regime where the SSL, tuned by a periodic magnetic or optical field, results in the Bragg scattering of the BEC. We have predicted a matter-wave optical limiting process and bistability, which have potential applications like a matter wave limiter, a BEC mirror or cavity, and an atomic switch. The first phenomenon is a direct result of this periodic spatial tuning, showing that the position-dependent tuning of the SSL has the potential to result in novel properties of ultracold atomic gases.
Bose-Einstein condensation (BEC) of atoms with attractive interactions is profoundly different from BEC of atoms with repulsive interactions. We describe experiments with Bose condensates of 7Li atoms, which are weakly attracting at ultralow temperature. We measure the distribution of condensate occupation numbers occurring in the gas using a near-resonant optical probe to image the atom cloud. This data shows that the number is limited and demonstrates the dynamics of condensate growth and collapse due to the attractive interactions.
We study properties of the ground state of a bosonic gas of atoms in a tight trap. The atoms interact via model molecular potentials that may have either positive or negative scattering lengths. We discuss the possibility of Bose-Einstein condensation in such a system. We show that when the size of the trap becomes comparable to the correlation length of the condensate, stable Bose-Einstein condensation might occur independent of the sign of the scattering length. \textcopyright{} 1996 The American Physical Society.
Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive 1∕r1∕r1∕r interaction, we point out that the instance of self-trapping of the condensate, without an external trap potential, is physically best understood by introducing appropriate ``atomic'' units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters N2a∕au{N}^{2}a∕{a}_{u}N2a∕au​ and $\ensuremath{\gamma}∕{N}^{2}$, where NNN is the particle number, aaa the scattering length, au{a}_{u}au​ the ``Bohr'' radius, and $\ensuremath{\gamma}$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, and for energies, sizes, and peak densities, and compare with previous variational results. We point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.
We consider a Bose-Einstein condensate (BEC) with attractive two-body interactions in a cigar-shaped trap, initially prepared in its ground state for a given negative scattering length, which is quenched to a larger absolute value of the scattering length. Using the mean-field approximation, we compute numerically, for an experimentally relevant range of aspect ratios and initial strengths of the coupling, two critical values of quench. One corresponds to the weakest attraction strength, the quench to which causes the system to collapse before completing even a single return from the narrow configuration (pericenter) in its breathing cycle. The other is a similar critical point for the occurrence of collapse before completing two returns. In the latter case, we also compute the limiting value, as we keep increasing the strength of the postquench attraction towards its critical value, of the time interval between the first two pericenters. We also use a Gaussian variational model to estimate the critical quenched attraction strength below which the system is stable against the collapse for long times. These time intervals and critical attraction strengths, apart from being fundamental properties of nonlinear dynamics of self-attractive BECs, may provide clues to the design of upcoming experiments that are trying to create robust BEC breathers.