Quantum fluctuations in atomic Josephson junctions: the role of dimensionality

Abstract We investigate the role of quantum fluctuations in the dynamics of a bosonic Josephson junction in D spatial dimensions, by using beyond-mean-field Gaussian corrections. We derive some key dynamical properties in a systematic way for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:math> . In particular, we compute the Josephson frequency in the regime of low population imbalance. We also obtain the critical strength of the macroscopic quantum self-trapping. Our results show that quantum corrections increase the Josephson frequency in spatial dimensions D = 2 and D = 3, but they decrease it in the D = 1 case. The critical strength of macroscopic quantum self-trapping is instead reduced by quantum fluctuations in D = 2 and D = 3 cases, while it is enhanced in the D = 1 configuration. We show that the difference between the cases of D = 2 and D = 3 on one side, and D = 1 on the other, can be related to the qualitatively different dependence of the interaction strength on the scattering length in the different dimensions.

Перевод пока недоступен