Two-Particle Interference with Double Twin-Atom Beams

We demonstrate a source for correlated pairs of atoms characterized by two opposite momenta and two spatial modes forming a Bell state only involving external degrees of freedom. We characterize the state of the emitted atom beams by observing strong number squeezing up to $-10\mathrm{dB}$ in the correlated two-particle modes of emission. We furthermore demonstrate genuine two-particle interference in the normalized second-order correlation function $g^{(2)}$ relative to the emitted atoms.

Figure 1

Sketch of the experimental procedure. (a) The quasi-BEC (gray) lies initially in the transverse ground state of a single-well potential characterized by a tightly confined direction ($y$ axis or transverse axis) and a weakly confined direction ($x$ axis or longitudinal axis, potential curve along this axis not displayed). An rf field with variable amplitude is used to excite the condensate and at the same time reach a double-well configuration along the $y$ axis. (b) The final double-well potential with its vibrational states along the $y$ axis: the second-excited state (green), which constitutes the source state, the first-excited (orange), and the ground state (blue) are defined by $|n_y⟩$, where $n_y=0$, 1, 2 is the vibrational quantum number. Two atoms from the source state can collide and decay into a twin pair (opposite momenta along the $x$ axis). Since the atoms in the twin pair can be emitted either in the symmetric $|0⟩$ (blue) or the antisymmetric $|1⟩$ (orange) transverse state, we define the emitted two-particle state as double twin-atom beam (DTB) state. (c) The DTB state can also be expressed in terms of the localized left- $|L⟩$ (blue curve) and right-well state $|R⟩$ (red curve). The gray arrows represent the process of quickly lifting up the barrier height and pushing the well’s minima away from each other.

Figure 2

Intramode correlations. (a) Experimental fluorescence image averaged over 825 experimental runs obtained with the separation procedure. Each run involves 2000–2200 total atoms, in average 150 of which are DTB atoms (75 pairs). The long time of flight makes the initial $y$-axis momentum distribution accessible (see Supplemental Material [23]). The central cloud corresponds to the source state, while the emitted DTB atoms are found at $\pm k_0$. The black boxes define the regions used for the correlation analysis. (b) Color scheme definition of the different combinations of DTB modes considered. (c) Histogram of different number-squeezing values ${\xi }^2$ for each combination of DTB modes defined in (b).

Figure 3

Two-particle interference pattern. (a) Theoretical unnormalized $G^{(2)}(k_{-}^y,k_{+}^y)=⟨n(k_y,-k_0)n(k_y,+k_0)⟩$ pattern assuming a DTB state of the form Eq. (1). (b) Experimental $g_{\mathrm{expt}}^{(2)}(k_{-}^y,k_{+}^y)$ pattern. This set of data involves 1498 experimental runs, where each run contains 700–760 total atoms, 20 of which are DTB atoms (10 pairs), on average. (c) One-dimensional mean profiles obtained from averaging along the diagonal within the white box superimposed in Fig. 3. The mean antidiagonal profile of $g_{\mathrm{expt}}^{(2)}(k_{-}^y,k_{+}^y)$ (black dots) is compared to the mean antidiagonal profile of $⟨n(k_y,-k_0)⟩⟨n(k_y,+k_0)⟩$ (light blue curve). The red curve represents a fit of the data from which we extract a value of the contrast of the two-atom interference $C=0.032\pm 0.004$. Units are scaled by the diagonal $\sqrt{2}$ factor and then normalized by the wells spacing $2y_0=1.3\mu \mathrm{m}$. The shaded areas represent the standard error of the mean.