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arXiv:1111.5203 · Physical Review A

Sub-Poissonian atom-number fluctuations using light-assisted collisions

Yvan R. P. Sortais, Andreas Fuhrmanek, Ronan Bourgain, Antoine Browaeys

Published Mar 13, 2012• 22 citations
arXivHTMLPDF

Abstract

We investigate experimentally the number statistics of a mesoscopic ensemble of cold atoms in a microscopic dipole trap loaded from a magneto-optical trap and find that the atom-number fluctuations are reduced with respect to a Poisson distribution due to light-assisted two-body collisions. For numbers of atoms $N\ensuremath{\gtrsim}2$, we measure a reduction factor (Fano factor) of $0.72\ifmmode\pm\else\textpm\fi{}0.07$, which differs from 1 by more than four standard deviations. We analyze this fact by a general stochastic model describing the competition between the loading of the trap from a reservoir of cold atoms and multiatom losses, leading to a master equation. Applied to our experimental regime, this model indicates an asymptotic value of $3/4$ for the Fano factor at large $N$ and in the steady state. We thus show that we have reached the ultimate level of reduction in number fluctuations in our system.

DOI
10.1103/physreva.85.035403

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We investigate experimentally the number statistics of a mesoscopic ensemble of cold atoms in a microscopic dipole trap loaded from a magneto-optical trap and find that the atom-number fluctuations are reduced with respect to a Poisson distribution due to light-assisted two-body collisions. For numbers of atoms N\ensuremath≳2N\ensuremath{\gtrsim}2N\ensuremath≳2, we measure a reduction factor (Fano factor) of 0.72\ifmmode±\else\textpm\fi0.070.72\ifmmode\pm\else\textpm\fi{}0.070.72\ifmmode±\else\textpm\fi0.07, which differs from 1 by more than four standard deviations. We analyze this fact by a general stochastic model describing the competition between the loading of the trap from a reservoir of cold atoms and multiatom losses, leading to a master equation. Applied to our experimental regime, this model indicates an asymptotic value of 3/43/43/4 for the Fano factor at large NNN and in the steady state. We thus show that we have reached the ultimate level of reduction in number fluctuations in our system.
We show that three-body loss of trapped atoms leads to sub-Poissonian atom-number fluctuations. We prepare hundreds of dense ultracold ensembles in an array of magnetic microtraps which undergo rapid three-body decay. The shot-to-shot fluctuations of the number of atoms per trap are sub-Poissonian, for ensembles comprising 50-300 atoms. The measured relative variance or Fano factor F=0.53+/-0.22 agrees very well with the prediction by an analytic theory (F=3/5) and numerical calculations. These results will facilitate studies of quantum information science with mesoscopic ensembles.
We study light-assisted collisions in an ensemble containing a small number (~3) of cold Rb87 atoms trapped in a microscopic dipole trap. Using our ability to operate with one atom exactly in the trap, we measure the one-body heating rate associated to a near-resonant laser excitation, and we use this measurement to extract the two-body loss rate associated to light-assisted collisions when a few atoms are present in the trap. Our measurements indicate that the two-body loss rate can reach surprisingly large values beta>10^{-8} cm^{3}.s^{-1} and varies rapidly with the trap depth and the parameters of the excitation light.
We study light-assisted collisions in an ensemble containing a small number ($\ensuremath{\sim}$3) of cold 87{}^{87}87Rb atoms trapped in a microscopic dipole trap. Using our ability to operate with one atom exactly in the trap, we measure the one-body heating rate associated with a near-resonant laser excitation, and we use this measurement to extract the two-body loss rate associated with light-assisted collisions when a few atoms are present in the trap. Our measurements indicate that the two-body loss rate can reach surprisingly large values $\ensuremath{\beta}>{10}^{\ensuremath{-}8}$ cm3{}^{3}3 s${}^{\ensuremath{-}1}$ and varies rapidly with the trap depth and the parameters of the excitation light.
A method is proposed to produce atomic ensembles with sub-Poissonian atom-number distributions. The method consists of removing the excess atoms using the interatomic interactions induced by Rydberg dressing. The selective removal of atoms occurs via spontaneous decay into untrapped states using an electromagnetically induced transparency scheme. Ensembles with the desired number of atoms can be produced almost deterministically. Numerical simulations predict a strong reduction of the atom-number fluctuations, with the variance 20 times less than the Poisson noise level (the predicted Fano factor is $F\ensuremath{\simeq}0.05$). Strikingly, the method is suitable for both fermions and bosons. It solves the problem of the atom-number fluctuations in bosons, whose weak interactions have usually been an obstacle to controlling the number of atoms.
The dynamics of Bose-condensate generation by a cw atom laser with simultaneous stimulated evaporative cooling in a magnetic trap was analyzed using a quantum-mechanical master equation. The model of the atom laser includes irreversible processes of incoherent trap mode pumping and spontaneous atomic transitions due to the interaction of the atomic ensemble with heat reservoirs. The inelastic atomic collisions in the trap and the continual coherent Bose-condensate output coupling from the trap were considered. At certain values of parameters, the Bose condensate created in this laser scheme occurs in a compressed sub-Poisson state. For large Bose condensates with a mean number of atoms ∼10 6 , the Fano factor may be as high as ≅0.5. The influence of spontaneous transitions from the excited trap modes on the statistics of Bose condensate was analyzed.
The statistics of the beam of excited atoms that pumps a micromaser influence the photon number distribution of the cavity field. Of the cases studied so far, regular injection statistics minimize the number fluctuations and Poisson statistics maximize them. Here we extend these studies in two directions. Previous master equations describing sub-Poissonian injection statistics were derived by using standard reservoir theory. Recently, corrections to these equations have been found that involve the commutator of the gain and loss operators. Describing the system by a discrete map, we can avoid the approximations inherent in reservoir theory. The results are compared to those of the master equation. Differences are found to be small for large photon number but increasingly important for decreasing photon number and pump beam intensity, indicating the breakdown of reservoir theory in this regime. We give an approximate expression for the photon number distribution for weak damping and discuss its connection with semiclassical theory. Finally, we generalize our treatment for super-Poissonian pump fluctuations.