Coherent Collisions between Bose-Einstein Condensates

We study the nondegenerate parametric amplifier for matter waves, implemented by colliding two Bose-Einstein condensates. The coherence of the amplified waves is shown by observing high contrast interference with a reference wave and by reversing the amplification process. Since our experiments also place limits on all known sources of decoherence, we infer that relative number squeezing is most likely present between the amplified modes. Finally, we suggest that reversal of the amplification process may be used to detect relative number squeezing without requiring subshot-noise detection.

Figure 1

The two source waves ${\mathbf{k}}_1$ and ${\mathbf{k}}_2$, the seed ${\mathbf{k}}_3$, the conjugate wave ${\mathbf{k}}_4$, and the detection state ${\mathbf{k}}_4^{\prime }$ after 20 ms ballistic expansion. Also seen is the collisional halo around all four waves as well as several small unlabeled waves, generated by off-resonant scattering. The field of view is $1.0\times 1.9\mathrm{m}\mathrm{m}$.

Figure 2

Coherence of the conjugate wave. Shown is the interference of the conjugate wave with a reference wave. The relative phase shift was introduced by shifting the phase of the rf wave which drives the lower-frequency acousto-optic modulator in the Bragg setup.

Figure 3

Phase coherent amplification and deamplification: (•) Deamplification of the conjugate wave. (∘) Continued amplification due to a $\pi$ pulse with a $180°$ phase shift applied in midpulse (see text). (×) Uninterrupted amplification. The region below the horizontal axis gives the sequence of events for deamplification: The shaded regions correspond to Bragg pulses and clear regions correspond to free system evolution. The solid, dashed, and dotted lines are independent numerical simulations of the respective processes.

Figure 4

Deamplification of perfectly squeezed modes with off-resonant scattering (solid line). Identical process but with coherent waves (dashed line). The vertical scale is the expectation value of the mode occupation.