Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates

We study atom scattering from two colliding Bose-Einstein condensates using a position sensitive, time resolved, single atom detector. In analogy to quantum optics, the process can also be thought of as spontaneous, degenerate four-wave mixing of de Broglie waves. We find a clear correlation between atoms with opposite momenta, demonstrating pair production in the scattering process. We also observe a Hanbury Brown–Twiss correlation for collinear momenta, which permits an independent measurement of the size of the pair production source and thus the size of the spatial mode. The back-to-back pairs occupy very nearly two oppositely directed spatial modes, a promising feature for future quantum optics experiments.

Figure 1

(a) View of the magnetically trapped condensate (in the $m_x=1$ state) and the three laser beams which create two cigar shaped counterpropagating free condensates (in the $m_x=0$ state) by ${\sigma }^{-}/\pi$ Raman transfers induced by $L_1-L_2$ and $L_1-L_2^{\prime }$, respectively (see inset). $L_1$ is $\pi$-polarized (along $x$) while $L_2$ and $L_2^{\prime }$ are ${\sigma }^{-}$-polarized. (b) Representation in velocity space of the expected atomic density after the collision. The scattered atoms are on a sphere and the remaining condensates, pancake-shaped after expansion, lie on the edge of the sphere along the $x$ axis. A collision process involving an atom of each condensate is also represented. The shape of the scattering modes is related to the uncertainty limited momentum spread of the condensates.

Figure 2

(a)–(i) Images of the collision of two condensates. Each frame represents a 2.4 ms time slice of the atomic cloud as it passes the plane of the detector ($x\mathrm{\text{−}}y$). 150 shots have been averaged to obtain these images. The two colliding condensates I, II and the collision sphere are clearly visible. Other features visible in the images are discussed in the text. The axes are marked in units of the recoil velocity.

Figure 3

Back-to-back [panel (a)] and collinear [panel (b)] correlation peaks. (a) Projection of $g^{(2)}(\mathbf{V}={\mathbf{V}}_{\mathbf{1}}+{\mathbf{V}}_{\mathbf{2}})$ along the different axes of the experiment and around $\mathbf{V}=\mathbf{0}$. The projection consists in averaging the correlation in the two other directions over a surface equal to the products of the corresponding correlation lengths. This averaging makes the height smaller than the 3D fitted value ${\eta }^{\mathrm{BB}}=0.19\pm 0.02$. The peak is the signature for correlated atoms with opposite velocities. (b) Projection of $g^{(2)}({\mathbf{V}}^{\prime }={\mathbf{V}}_{\mathbf{1}}-{\mathbf{V}}_{\mathbf{2}})$ along the different axes of the experiment. This peak is due to the Hanbury Brown–Twiss bunching effect. All velocities are expressed in units of the recoil velocity.

Figure 4

Projections of $g^{(2)}(\mathbf{V})$ along the $x$ axis and around $\mathbf{V}=\mathbf{0}$. Bin of mean number of detected atoms of (a) 50, (b) 125, and (c) 190.