Quantum Atom Optics with Fermions from Molecular Dissociation

We study a fermionic atom optics counterpart of parametric down-conversion with photons. This can be realized through dissociation of a Bose-Einstein condensate of molecular dimers consisting of fermionic atoms. We present a theoretical model describing the quantum dynamics of dissociation and find analytic solutions for mode occupancies and atomic pair correlations, valid in the short time limit. The solutions are used to identify upper bounds for the correlation functions, which are applicable to any fermionic system and correspond to ideal particle number-difference squeezing.

Figure 1

(a) Average occupancies of one of the resonant modes $q_0=\sqrt{|\delta |}$ and two sidebands $q_i$ (solid lines) as a function of time, for $\delta =-16$. The dashed line is the solution for the $q_0$ mode in the case of bosons, which grows exponentially. The inset shows the slice through the origin of the fermionic 3D momentum distribution $n_{\mathbf{q}}(\tau )$ at $\tau =0.6$. (b) Total number of atoms $N_{\sigma }/l^3$ (solid line) as a function of time, for $\delta =-16$. The normalization with respect to $l^3$ makes this quantity independent of the quantization volume. The dashed line is the respective bosonic result, while the straight dotted line is the total number of atoms $N_{\sigma }(\tau )/l^3\simeq \sqrt{|\delta |}\tau /(4\pi )$ obtained using Fermi’s golden rule calculation of the molecular spontaneous decay rate [20] in the linear regime.

Figure 2

Snapshots of the average column density in momentum space ${\overline{n}}_{\mathbf{p}}(\tau )/l$ at different times $\tau$, for $\delta =-16$.

Figure 3

(a) Correlation between momentum column density fluctuations, ${\overline{g}}_{\uparrow \downarrow }(\mathbf{p},-\mathbf{p},\tau )$, as a function of the absolute 2D momentum $p=|\mathbf{p}|$ at different times $\tau$, for $\delta =-16$. The correlation is larger initially, in the few-particle regime, and decreases as the number of atoms grows. Similar relationship is seen within the low-density tails and the higher-density central part of the momentum distribution. (b) Correlation signal as a function of time, for two different values of the $p$.