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Probability in the Engineering and Informational Sciences

STOCHASTIC MODEL FOR THE NUMBER OF ATOMS IN A MAGNETO-OPTICAL TRAP

Andrew L. Rukhin, Ionut Bebu

Published Mar 6, 2006• 1 citation
Publisher

Abstract

In this article a Markov chain for the distribution of single atoms is suggested and studied. We explore a recursive model for the number of atoms present in a magneto-optical trap under a feedback regime with a Poisson-distributed load. Formulas for the stationary distribution of this process are derived. They can be used to adjust the loading rate of atoms to maximize the proportion of time that a single atom spends in the trap. The (approximate) optimal regime for the Poisson loading and loss processes is found.

DOI
10.1017/s0269964806060219

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In this article a Markov chain for the distribution of single atoms is suggested and studied. We explore a recursive model for the number of atoms present in a magneto-optical trap under a feedback regime with a Poisson-distributed load. Formulas for the stationary distribution of this process are derived. They can be used to adjust the loading rate of atoms to maximize the proportion of time that a single atom spends in the trap. The (approximate) optimal regime for the Poisson loading and loss processes is found.
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A magneto-optical trap with feedback-controlled loading and loss rates is used to realize a deterministic source of single chromium atoms with single-atom occupation probability as high as 0.987±0.001. We present a series of measurements of the performance of this source and discuss the dependence of the probability of not having a single atom in the trap (error rate) on experimental parameters. We describe a simple analytical model that considers mean load rate, trap lifetime, stray load rate, and feedback response time, and we also present results of Monte Carlo calculations that take into account all experimental conditions. We find that the analytical model describes the behavior well for error rates as small as about 0.03, but the Monte Carlo simulations must be used to model behavior at error rates lower than this, as the occupation probability approaches unity.
Various regimes of the loading of a magneto-optical trap formed near an atom chip, such as loading from thermal atomic vapors and from a low-velocity atomic beam, have been studied on an example of 87Rb atoms. The possibility of controlling the loading of the magneto-optical trap by spatially controlling the atomic beam has been demonstrated. This has made it possible to increase the loading rate of atoms into the magneto-optical trap with keeping ultrahigh vacuum near the atom chip. The maximum number of atoms in the magneto-optical trap at optimal loading regimes is 4.9 × 107. In this case, the measured lifetime of atoms in the magneto-optical trap is 4.1 s.
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 3/43/43/4 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.