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Journal of Physics B Atomic Molecular and Optical Physics

Statistics of the population difference for cold fermions in a double well potential

Tomasz Górski, Kazimierz Rza̧żewski

Published Sep 10, 2012• 0 citations
Publisher

Abstract

Sensitive measurements of the density fluctuations in ultracold gases performed recently evidenced quantum statistical effects, i.e. an enhancement of the density fluctuations in Bose gas and a suppression of the fluctuations in Fermi gas. In this paper we study thermal equilibrium fluctuations in the atomic number difference between the two halves of a harmonically trapped Fermi gas split by a delta potential. We show how splitting the potential strength affects the fluctuations.

DOI
10.1088/0953-4075/45/20/205302

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Sensitive measurements of the density fluctuations in ultracold gases performed recently evidenced quantum statistical effects, i.e. an enhancement of the density fluctuations in Bose gas and a suppression of the fluctuations in Fermi gas. In this paper we study thermal equilibrium fluctuations in the atomic number difference between the two halves of a harmonically trapped Fermi gas split by a delta potential. We show how splitting the potential strength affects the fluctuations.
We study fluctuations in the atom number difference between two halves of a harmonically trapped Bose gas in three dimensions. We solve the problem analytically for noninteracting atoms. In the interacting case we find an analytical solution in the Thomas-Fermi and high temperature limit in good agreement with classical field simulations. In the large system size limit, fluctuations in the number difference are maximal for a temperature $T\ensuremath{\simeq}0.7{T}_{c}$ where Tc{T}_{c}Tc​ is the critical temperature, independently of the trap anisotropy. The occurrence of this maximum is due to an interference effect between the condensate and the noncondensed fields.
We measure atom number statistics after splitting a gas of ultracold 87Rb atoms in a purely magnetic double-well potential created on an atom chip. Well below the critical temperature for Bose-Einstein condensation Tc, we observe reduced fluctuations down to -4.9 dB below the atom shot noise level. Fluctuations rise to more than +3.8 dB close to Tc, before reaching the shot noise level for higher temperatures. We use two-mode and classical field simulations to model these results. This allows us to confirm that the supershot noise fluctuations directly originate from quantum statistics.
We theoretically study atom number fluctuations between the halves of a double-well trap containing a Bose-Einstein condensate. The basic tool is the two-mode approximation, which assumes that only two one-particle states are involved. An analytical harmonic-oscillator-like model is developed and verified numerically for both stationary fluctuations in the ground state of the system, and for the fluctuations resulting from splitting of a single trap by dynamically erecting a barrier in the middle. With increasing strength of the atom-atom interactions and/or increasing height of the potential barrier, the fluctuations tend to evolve from Poissonian to sub-Poissonian. Limits of validity of the two-mode model and its relations to the phase-atom-number approach of Leggett and Sols [A. J. Leggett and F. Sols, Found. Phys. 21, 353 (1991)] are discussed in detail.
An elongated trap potential for cold atoms is designed based on a quadrupole-Ioffe configuration. Phase fluctuations in a Bose–Einstein condensate (BEC), which is confined by the trap, are studied. We simulate the atom density distribution induced by fluctuation after time of flight from this elongated trap potential and study the temperature measurement method related to the distribution. Furthermore, taking advantage of the tight confinement and radio frequency dressing technique, we propose a double well potential for splitting BECs. Our results are helpful for improving understanding of low-dimensional quantum gases and provide important guidance for atomic interferometry.