Abstract
The competition between short-range and cavity-mediated infinite-range interactions in a cavity-boson system leads to the existence of a superfluid phase and a Mott-insulator phase within the self-organized regime. In this work, we quantitatively compare the steady-state phase boundaries of this transition measured in experiments and simulated using the Multiconfigurational Time-Dependent Hartree Method for Indistinguishable Particles. To make the problem computationally feasible, we represent the full system by the exact many-body wave function of a two-dimensional four-well potential. We argue that the validity of this representation comes from the nature of both the cavity-atomic system and the Bose-Hubbard physics. Additionally, we show that the chosen representation only induces small systematic errors, and that the experimentally measured and theoretically predicted phase boundaries agree reasonably well. We thus demonstrate a new approach for the quantitative numerical modeling for the physics of the superfluid--Mott-insulator phase boundary.
Highlights
It serves as a map to identify the three different phases of matter, normal BEC phase (NP), self-organized superfluid (SSF), and self-organized Mott-insulator (SMI), which are realized in both experiments and simulations
The momentum space distribution has an elliptical shape in experiments but a circular shape in simulation. This is because the harmonic trap is anisotropic in the experimental setup ωx = ωy, while the confining potential in simulations [Eq (12b)] is isotropic in the x and y directions
In contrast to the significant dynamical effects at play and a relatively large size of the lattice in the experiments, our twodimensional simulations are limited to steady states and a small number of lattice sites
Summary
Experimental and theoretical progress using quantum gases to realize models of solid state physics has made it possible to study many-body effects in isolated and highly controllable scenarios [1,2,3]. Many-body effects in ultracold atomic systems have seen an enduring interest, the coherence between particles in the superfluid phase and its loss in the Mott-insulator phase of a lattice system The transition between these two phases is driven by the competition of the tunneling processes and the on-site interactions, and was first realized by controlling an optical lattice potential in cold-atom systems in three [16] and two dimensions [17, 18], respectively. In order to keep the computational complexity within a tractable range, we construct a simplification scheme for the simulations by exploiting the nature of the cavity-BEC system and the superfluid–Mott-insulator transition This simplification scheme retains the many-body essence of the system to a satisfactory degree, and quantitatively reproduces the phase boundary in agreement with the experiments in a wide parameter range.
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