Extended Coherence Time with Atom-Number Squeezed States

Coherence properties of Bose-Einstein condensates offer the potential for improved interferometric phase contrast. However, decoherence effects due to the mean-field interaction shorten the coherence time, thus limiting potential sensitivity. In this work, we demonstrate increased coherence times with number squeezed states in an optical lattice using the decay of Bloch oscillations to probe the coherence time. We extend coherence times by a factor of 2 over those expected with coherent state Bose-Einstein condensate interferometry. We observe quantitative agreement with theory both for the degree of initial number squeezing as well as for prolonged coherence times.

Figure 1

(a) Lattice intensity is shown for the experimental sequence. The lattice intensity is ramped up in $T_{\mathrm{ramp}}=350\mathrm{ms}$ and then held constant for $T_{\mathrm{Bloch}}$ during which time a magnetic field gradient is applied. The lattice and magnetic fields are turned off, and the atoms ballistically expand for a 12 ms time of flight (TOF) before being imaged with a probe pulse. (b) Absorptive images indicating a Bloch oscillation are shown. (c) Peak width vs energy offset $E$ is shown with widths converted to units of $2\hslash k$. The insets show absorptive images both with and without dephasing.

Figure 2

(a) The fraction of atoms observed in the incoherent background of the interference signature is plotted vs lattice depth. This fraction from the simulated interference of an array of Gaussian wave packets is shown with a solid line. The calculated quantum depletion vs lattice depth is shown with a dashed line. (b) Peak width is plotted vs $T_{\mathrm{Bloch}}$ for $U=10E_R$ and $E/\hslash =2\pi \times 900\mathrm{Hz}$. The solid line is a fit to data to extract ${\tau }_c=14.2\pm 1.3\mathrm{ms}$. (c) ${\tau }_c$ is plotted vs lattice depth. The solid (dashed) line denotes theoretical dephasing of number squeezed (coherent) states.

Figure 3

(a) Peak width vs ${\omega }_{\mathrm{RF}}/2\pi$. $T_c=1.6\mathrm{MHz}$ for a BEC in the bare harmonic trap. (b) Peak width vs. $T_{\mathrm{ramp}}$.

Figure 4

Peak width is plotted vs continued hold time in lattice after removing the external field gradient $T_{\mathrm{rephase}}$. The insets are absorptive images showing initial dephasing of the phase contrast and subsequent revival.