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Quantum-Atom Optics Downunder (QAO)

Number counting in a Bose Josephson Junction

Joseph H. Thywissen

Published Jan 1, 2007• 0 citations
Publisher

Abstract

Correlations in quantum degenerate matter can be created by even weak interactions. A double well provides a simple system in which to observe this effect, since relative occupation has sub-Poissonian fluctuation when the charging energy becomes greater than the Josephson energy of the superfluid. I will discuss our efforts to observe this effect directly in the number statistics of a split Bose-Einstein condensate. We have a sensitivity to standard deviation at the level of tens of atoms, giving us sub-Poissonian noise and uncertainty in our measurement of several thousand atoms. We report statistical results for various preparations and splitting sequences.

DOI
10.1364/qao.2007.qmc1

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Correlations in quantum degenerate matter can be created by even weak interactions. A double well provides a simple system in which to observe this effect, since relative occupation has sub-Poissonian fluctuation when the charging energy becomes greater than the Josephson energy of the superfluid. I will discuss our efforts to observe this effect directly in the number statistics of a split Bose-Einstein condensate. We have a sensitivity to standard deviation at the level of tens of atoms, giving us sub-Poissonian noise and uncertainty in our measurement of several thousand atoms. We report statistical results for various preparations and splitting sequences.
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.
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 report manipulation of the atom number statistics associated with Bose-Einstein condensed atoms confined in an array of weakly linked mesoscopic traps. We used the interference of atoms released from the traps as a sensitive probe of these statistics. By controlling relative strengths of the tunneling rate between traps and atom-atom interactions within each trap, we observed trap states characterized by sub-Poissonian number fluctuations and adiabatic transitions between these number-squeezed states and coherent states of the atom field. The quantum states produced in this work may enable substantial gains in sensitivity for atom interference-based instruments as well as fundamental studies of quantum phase transitions.
We have studied quantum statistical properties in a zero-temperature two-species Bose–Einstein condensate system in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunneling interaction. It is found that the two condensates may periodically exhibit sub-Poissonian distribution. It is revealed that the correlation between the two condensates can be nonclassical, which means that there exists a violation of Cauchy–Schwartz inequality. The nonclassical effect about the correlation between the two condensates can be realized experimentally by properly preparing the total number of atoms in the two condensates.
Using the quantum collapse and revival phenomenon of a Bose--Einstein condensate in three-dimensional optical lattices, the atom number statistics on each lattice site are experimentally investigated. We observe an interaction driven time evolution of on-site number fluctuations in a constant lattice potential with the collapse and revival time ratio as the figure of merit. Through a shortcut loading procedure, we prepare a three-dimensional array of coherent states with Poissonian number fluctuations. The following dynamics clearly show the interaction effect on the evolution of the number fluctuations from Poissonian to sub-Poissonian. Our method can be used to create squeezed states, which are important in precision measurement.