Correlations and Counting Statistics of an Atom Laser

We demonstrate time-resolved counting of single atoms extracted from a weakly interacting Bose-Einstein condensate of ${}^{87}\mathrm{R}\mathrm{b}$ atoms. The atoms are detected with a high-finesse optical cavity and single atom transits are identified. An atom laser beam is formed by continuously output coupling atoms from the Bose-Einstein condensate. We investigate the full counting statistics of this beam and measure its second order correlation function $g^{(2)}(\tau )$ in a Hanbury Brown–Twiss type experiment. For the monoenergetic atom laser we observe a constant correlation function $g^{(2)}(\tau )=1.00\pm 0.01$ and an atom number distribution close to a Poissonian statistics. A pseudothermal atomic beam shows a bunching behavior and a Bose distributed counting statistics.

Figure 1

Schematic of the experimental setup. A weak continuous atom laser beam is released from a Bose-Einstein condensate. After dropping a distance of 36 mm the atoms enter a high-finesse optical cavity and single atoms in the beam are detected. For the actual measurement the atomic flux is reduced by factor ${10}^4$ as compared to the image.

Figure 2

(a) Light transmission through the high-finesse optical cavity when an atom laser beam is transversing. (b) Details of the single atom transits. The photon count rate is averaged over $20\mu \mathrm{s}$.

Figure 3

(a) Second order correlation function of an atom laser beam. The data are binned with a time bin size of $50\mu \mathrm{s}$. The average count number is $2\times {10}^5$ per bin. We have omitted the first two data points since they are modified by the dead time of our detector. (b) Probability distribution $p(N)$ of the atom number $N$ detected within a time interval of $T=1.5\mathrm{ms}$. The (+) symbols show a Poissonian distribution for the same mean value of $⟨n⟩=1.99$ as the measured data. The errors indicate statistical errors.

Figure 4

(a) Second order correlation functions of pseudothermal atomic beams. The square symbols correspond to a filter band width (FWHM) of 90 Hz, the triangles to a bandwidth of 410 Hz, and the circles to a bandwidth of 1870 Hz. The data are binned with a time bin size of $50\mu \mathrm{s}$ in which the average count number is $8\times {10}^4$. We have omitted the first two data points since they are modified by the dead time of our detector. The lines are the experimentally determined correlation functions of the broadband microwave fields. (b) Probability distribution $p(N)$ of the atom number $N$ within a time interval of $T=1.5\mathrm{ms}$ for the 90 Hz bandwidth data. The (+) symbols indicate a Bose distribution with the same mean value of $⟨n⟩=1.99$. The errors indicate statistical errors.