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Physical Review A

Superfluid–Mott-insulator transition of spin-1 bosons in optical resonators

Jun-Ni Wu, Jing Qian, Xing-Dong Zhao, Lu Zhou, Weiping Zhang

Published Dec 10, 2013• 4 citations
Publisher

Abstract

We consider an antiferromagnetic spin-1 Bose-Einstein condensate confined in a Fabry-P\'erot optical resonator in which the intracavity light field forms an optical lattice potential for the atoms. Special emphasis is paid to the cavity-mediated superfluid--Mott-insulator transition. We find that exotic phase diagrams can appear due to the competition between cavity-induced nonlinear interactions and the atomic spin-dependent collision interactions.

DOI
10.1103/physreva.88.065601

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We consider an antiferromagnetic spin-1 Bose-Einstein condensate confined in a Fabry-P'erot optical resonator in which the intracavity light field forms an optical lattice potential for the atoms. Special emphasis is paid to the cavity-mediated superfluid--Mott-insulator transition. We find that exotic phase diagrams can appear due to the competition between cavity-induced nonlinear interactions and the atomic spin-dependent collision interactions.
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We study the quantum phase transition between superfluid and Mott-insulator states for ultracold bosons with two internal states forming two bands of an optical lattice. The two atomic states are resonantly coupled by a coherent field enclosed in a single cavity mode, which mediates transitions between the two bosonic particle modes via absorption or emission of cavity photons. As nonlocal atomic coherence can build up via photon assisted tunneling, this coupling shifts the transition to the Mott-insulator phase toward deeper lattice potentials and stronger on-site interaction. Varying the intra and interband on-site interactions leads to several different atomic phase configurations. There are even parameter regions, where a mean-field approach predicts concurrence of a Mott-insulator state in one band and a superfluid in the other band.
The superfluid to Mott insulator transition and the superradiant transition are textbook examples of quantum phase transition and coherent quantum optics, respectively. Recent experiments in ETH and Hamburg have succeeded in loading degenerate bosonic atomic gases in optical lattices inside a cavity, which enables the first experimental study of the interplay between these two transitions. In this Rapid Communication we present the theoretical phase diagram for the ETH Zurich experimental setup, and determine the phase boundaries and the orders of the phase transitions between the normal superfluid phase, the superfluid with superradiant light, the normal Mott insulator, and the Mott insulator with superradiant light. We find that in contrast to the second-order superradiant transition in a weakly interacting Bose condensate, strong correlations in the superfluid nearby a Mott transition can render the superradiant transition to a first-order one. Our results will stimulate further experimental studies of interactions between cavity light and strongly interacting quantum matter.
In this paper, we consider a two-component atomic Bose lattice gas inside an optical cavity to explore a competition between the short-range collisional and cavity-mediated long-range interactions. Utilizing a self-consistent mean-field approach, we map out the ground-state phase diagrams showing the superfluid, lattice supersolid, Mott insulator, and spin-density wave phases. Unlike its single-component analog, this lattice supersolid is here characterized by the coexistence of the superfluid and the spin-density wave. Moreover, for the relatively small long-range interaction, the phase diagrams exhibit a correspondence between the parity of the lattice filling number and the spin imbalance. Finally, we propose how to detect the different quantum phases under current experimental setups.
We study the ground-state phase diagram of spinless and spin-1 bosons in optical superlattices using a Bose-Hubbard Hamiltonian that includes spin-dependent interactions. We decouple the unit cells of the superlattice via a mean-field approach and take into account the dynamics within the unit cell exactly. The system supports Mott-insulating as well as superfluid phases. The transitions between these phases are second order for spinless bosons and second or first order for spin-1 bosons. Antiferromagnetic interactions energetically penalize high-spin configurations and elongate all Mott lobes, especially the ones corresponding to an even atom number on each lattice site. We find that the quadratic Zeeman effect lifts the degeneracy between different polar superfluid phases leading to additional metastable phases and first-order phase transitions. Finally, we show that an energy offset between the two sites of the unit cell induces a staircase of single-atom tunneling resonances, which surprisingly survives well into the superfluid regime.
We study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two-dimensional optical trap. We chart out the phase diagrams for Mott states with n=1n=1n=1 and n=2n=2n=2 atoms per lattice site. It is shown that the long-range dipolar interaction stabilizes a state where the chains of the ferromagnetically aligned spins run along the longer trap direction while the spin ordering is staggered between nearby chains, leading to an antiferromagnetic ordering along the shorter trap direction. We also obtain the mean-field phase boundary for the superfluid-insulator transition in these systems and study the nature of spin ordering in the superfluid state near the transition. We show that, inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first-order antiferromagnetic-ferromagnetic spin ordering transition. We discuss implications of our results for 52Cr^{52}\mathrm{Cr}52Cr atoms and suggest possible experiments to detect different phases in such systems.