Generation and Detection of a Sub-Poissonian Atom Number Distribution in a One-Dimensional Optical Lattice

We demonstrate preparation and detection of an atom number distribution in a one-dimensional atomic lattice with the variance $-14\mathrm{dB}$ below the Poissonian noise level. A mesoscopic ensemble containing a few thousand atoms is trapped in the evanescent field of a nanofiber. The atom number is measured through dual-color homodyne interferometry with a pW-power shot noise limited probe. Strong coupling of the evanescent probe guided by the nanofiber allows for a real-time measurement with a precision of $\pm 8\mathrm{atoms}$ on an ensemble of some $10^3\mathrm{atoms}$ in a one-dimensional trap. The method is very well suited for generating collective atomic entangled or spin-squeezed states via a quantum nondemolition measurement as well as for tomography of exotic atomic states in a one-dimensional lattice.

Figure 1

(a) Experimental setup. Two 1D optical lattices are formed in the nanofiber trap by two trapping beams (not shown). Two probe beams with fixed frequency difference are generated with an AOM and then coupled into the nanofiber where they interact with the atomic ensemble. They interfere with a strong LO on a $90:10\text{−}\mathrm{beam}$ splitter and a homodyne measurement is performed. (b) Absorption (red dots) and dispersion signals (blue triangles) measured with trapped atoms; arrows indicate probe and LO frequencies. (c) Atom number calibration. Resonant light pumps atoms from $|4⟩$ to $|3⟩$. The total number of trapped atoms is determined from the decay branching ratio (see inset) and the asymptote (red dashed line) of the cumulative number of scattered photons (solid blue line, average of 200 experiments).

Figure 2

Atom induced phase shift measured with weak coherent probe light of different powers. Symbols: each trace depicts real-time phase shift data, acquired with a 100 kHz detection bandwidth in a single lattice trap realization; Solid lines: average over 200 realizations. Using the same set of probe powers (see legend), data in the left (right) panel were recorded with (without) external repumping light present. Probing starts 1 ms after trap loading.

Figure 3

Top: recursive Bayesian estimation of the atom number distribution. Blue dots: atom induced optical phase shift $\phi$, as measured in a single experiment with the dual-color homodyne technique. Red line: mean of the estimated probability distribution for $N_{\mathrm{at}}$ at every time. Bottom: solid blue line: Fano factor $F=\mathrm{var}(N_{\mathrm{at}})/⟨N_{\mathrm{at}}⟩$ from the same probability distribution. Dashed red line: number of scattered photons $n_{\mathrm{sc}}$ per atom (see main text). All data were recorded with a probe power of 154 pW, 10 ms after the MOT cooling phase.