Dynamical Creation of Bosonic Cooper-Like Pairs

We propose a scheme to create a metastable state of paired bosonic atoms in an optical lattice. The most salient features of this state are that the wave function of each pair is a Bell state and that the pair size spans half the lattice, similar to fermionic Cooper pairs. This mesoscopic state can be created with a dynamical process that involves crossing a quantum phase transition and which is supported by the symmetries of the physical system. We characterize the final state by means of a measurable two-particle correlator that detects both the presence of the pairs and their size.

Figure 1

We plot the (a) triplet and (b) singlet correlators for the evolution of ${\psi }_T$ and ${\psi }_S$, respectively, at a ramp speed $v=1$ [see Eq. (16)] and in a lattice of $L=20$ sites. The circles, triangles, and squares denote $\overline{G}$, $G_0$, and their difference. (c) Pair size $R$ for the singlet (line) and triplet (cross) states, for a ramp speed $v=0.5$, 1, and 2 (solid curves, dashed curves, dash-dotted curves). The vertical line $J/U=1/3.84$ marks the location of the phase transition.