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arXiv:2404.00533 · Physical Review A

Gauge potentials and vortices in the Fock space of a pair of periodically driven Bose-Einstein condensates

J. Mumford, D. Kamp, Duncan H J O’Dell

Published Oct 10, 2024• 2 citations
arXivHTMLPDF

Abstract

We perform a theoretical study of the coupled dynamics of two species of Bose-Einstein condensates (BECs) in a double-well potential where both the tunneling and the interatomic interactions are driven periodically in time. The population difference between the wells of each species gives rise to a two-dimensional lattice in Fock space with dimensions given by the number of atoms in each BEC. We use a Floquet analysis to derive an effective Hamiltonian that acts in this Fock space and find that it contains an artificial gauge field. This system simulates noninteracting particles in a tight-binding lattice subject to an additional harmonic potential and vector potential. When the intraspecies interactions are attractive there is a critical value at which the ground state undergoes a transition from a Gaussian state to a quantized vortex state in Fock space. The transition can be quantified in terms of the angular momentum and the entanglement entropy of the ground state with both showing sudden jumps as the intraspecies interactions become stronger. The stability of the vortex state vanishes in the thermodynamic limit.

DOI
10.1103/physreva.110.043310

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We investigate the quantum phases of ultracold atoms trapped in a vortex lattice using a mixture of two bosonic species (AAA and BBB), in the presence of an artificial gauge field. Heavy atoms of species BBB are confined in the array of vortices generated in species AAA, and they are described through a Bose-Hubbard model. In contrast to the optical-lattice setups, the vortex lattice has an intrinsic dynamics, given by its Tkachenko modes. Including these quantum fluctuations in the effective model for BBB atoms yields an extended Bose-Hubbard model, with an additional ``phonon'' -mediated long-range attraction. The ground-state phase diagram of this model is computed through a variational Ansatz and the quantum Monte Carlo technique. When compared with the ordinary Bose-Hubbard case, the long-range interatomic attraction causes a shift and resizing of the Mott-insulator regions. Finally, we discuss the experimental feasibility of the proposed scheme, which relies on the proper choice of the atomic species and on a large control of physical parameters, like the scattering lengths and the vorticity.
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