Direct Observation of Sub-Poissonian Number Statistics in a Degenerate Bose Gas

We report the direct observation of sub-Poissonian number fluctuation for a degenerate Bose gas confined in an optical trap. Reduction of number fluctuations below the Poissonian limit is observed for average numbers that range from 300 to 60 atoms.

Figure 1

The optical trap. (a) Beam pictorial. Gravity points in $-z$ direction in this pictorial. (b) This plot shows the potential energy $U$ at $y=z=0$. In the $x$ direction, the atoms are confined by two Gaussian sheets with a separation of $l_x=5\mu \mathrm{m}$. (c) Confinement in the $y$ direction is of similar shape to the $x$ direction but deeper. (d) In the $z$ direction, gravity and a Gaussian sheet form a gravito-optical trap. The dashed curves in (c) and (d) show the same potentials for the different scales given on the right axes. Each potential plot is calculated based on measured beam characteristics and are appropriate for order 100 atoms.

Figure 2

Step-wise signal of the APD. The atom number from CCD fluorescence imaging is calibrated by an APD operating in photon counting mode. The fluorescence counting rate per atom is ${10}^4{\mathrm{s}}^{-1}$ with a background of $2\times {10}^4{\mathrm{s}}^{-1}$. The signals shown are for random loading of the MOT from background vapor. The time step of fluorescence binning is 100 ms.

Figure 3

Observation of sub-Poissonian number statistics. (a) The solid circles show the measured fluctuation normalized to the Poissonian case as a function of atom number. The vertical error bars are the 68% confidence intervals for each measurement. The horizontal error bars represent the absolute accuracy in atom number. Sub-Poissonian number statistics is observed for atom numbers below 500 where the fluctuations due to technical noise are not larger than the Poissonian fluctuation. The dashed curve is the estimated fluctuation from technical noise and background capture. The inset shows the measured atom number as a function of the trap depth $U_0$. (b) Histogram of 100 sample points shows sub-Poissonian statistics for mean atom number $N=60$. The solid curve is the Gaussian fit to the distribution. The dashed curve is the Poissonian distribution with the same mean atom number.

Figure 4

Atom number fluctuations (normalized to the Poissonian case) as a function of ramp time. Adiabaticity breaks down when the ramp time is shorter than 250 ms. The error bars show the 68% confidence intervals for each measurement. The horizontal line shows the level of Poissonian fluctuation.