Multipartite Entangled Spatial Modes of Ultracold Atoms Generated and Controlled by Quantum Measurement

We show that the effect of measurement backaction results in the generation of multiple many-body spatial modes of ultracold atoms trapped in an optical lattice, when scattered light is detected. The multipartite mode entanglement properties and their nontrivial spatial overlap can be varied by tuning the optical geometry in a single setup. This can be used to engineer quantum states and dynamics of matter fields. We provide examples of multimode generalizations of parametric down-conversion, Dicke, and other states; investigate the entanglement properties of such states; and show how they can be transformed into a class of generalized squeezed states. Furthermore, we propose how these modes can be used to detect and measure entanglement in quantum gases.

Figure 1

(a) Setup: Light is scattered from atoms in an optical lattice. Generated spatial structure of three matter-field modes in 2D (b) and 1D (c) lattices. Sites of the same color are indistinguishable from light scattering and thus belong to the same mode. The superposition of three indistinguishable atom distributions in (c) is protected by light scattering.

Figure 2

Quantum trajectories for the growth of entanglement between two modes where the detected variables are (a) atom number difference in the diffraction minimum, (b) total atom number in the diffraction maximum, and (c) absolute value of atom number difference in the minimum. The insets show the final entanglement distribution functions. $⟨N⟩=50$, $\tau =2|C{|}^2\kappa t$.

Figure 3

Quantum circuit for the measurement of density matrix moments. Spatially overlapped matter modes are used as multiple copies for the generalized SWAP (permutation) gate. Diagram of the setup for measuring entanglement between illuminated and nonilluminated regions.