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arXiv:1510.02671 · Physical Review A

Quantum phase transitions in two-dimensional tilted optical lattices

Andrey R. Kolovsky

Published Mar 14, 2016• 10 citations
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Abstract

We discuss the quantum phase transition between the Mott-insulator state and the density-wave state of cold Bose atoms in a two-dimensional (2D) square lattice as the lattice is adiabatically tilted along one of its primary axes. It is shown that a small misalignment of the tilt drastically changes the result of the adiabatic passage and, instead of the density-wave state, one obtains a disordered state. An intrinsic relation of the problem to Bloch oscillations of hard-core bosons in a 2D lattice is illuminated.

DOI
10.1103/physreva.93.033626

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We discuss the quantum phase transition between the Mott-insulator state and the density-wave state of cold Bose atoms in a two-dimensional (2D) square lattice as the lattice is adiabatically tilted along one of its primary axes. It is shown that a small misalignment of the tilt drastically changes the result of the adiabatic passage and, instead of the density-wave state, one obtains a disordered state. An intrinsic relation of the problem to Bloch oscillations of hard-core bosons in a 2D lattice is illuminated.
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The Mott insulator and superfluid phase transition is one of the most prominent phenomena in ultracold atoms. We report the observation of a novel 2D quantum phase transition between the Mott insulator and π superfluid in a shaking optical lattice. In the deep optical lattice regime, the lowest S band can be tuned to Mott phase, while the higher px,y bands are itinerant for having larger bandwidth. Through a shaking technique coupling the s-orbital to px,y -orbital states, we experimentally observe the transition between the states of the S and px,y bands, leading to a quantum phase transition from two-dimensional s-orbital Mott phase to the px,y -orbital superfluid which condensed at (π, π) momentum. Using the band-mapping method, we also observe the changes of atomic population in different energy bands during the transition, and the experimental results are well consistent with theoretical expectations.
We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle $\ensuremath{\theta}$ of the dipolar bosons. At low tilt angles, ${0}^{\ensuremath{\circ}}\ensuremath{\leqslant}\ensuremath{\theta}\ensuremath{\lesssim}{25}^{\ensuremath{\circ}}$, the ground states of the system are phases with checkerboard order, which can be either checkerboard supersolids or checkerboard density waves. For high tilt angles, ${35}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{55}^{\ensuremath{\circ}}$, phases with striped order of the supersolid or density wave are preferred. In the intermediate domain, ${25}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{35}^{\ensuremath{\circ}}$, an emulsion or superfluid phase intervenes the transition between the checkerboard and the striped phases. The attractive interaction dominates at $\ensuremath{\theta}\ensuremath{\gtrsim}{55}^{\ensuremath{\circ}}$, which renders the system unstable, and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second-order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results. In our study, the incompressible phases have an average occupancy per site $\ensuremath{\rho}\ensuremath{\le}1$, but the compressible phases can have $\ensuremath{\rho}>1$.
The extended effective multiorbital Bose–Hubbard-type Hamiltonian which takes into account higher Bloch bands is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation to current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean-field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid–Mott insulator transition and the absorption spectroscopy, that is, the energy absorption rate when the lattice depth is periodically modulated.
We study quantum fluctuation-driven first-order phase transitions of a two-species bosonic system in a three-dimensional optical lattice. Using effective potential method we find that the superfluid-Mott insulator phase transition of one type of bosons can be changed from second order to first order by the quantum fluctuations of the other type of bosons. The study of the scaling behaviors near the quantum critical point shows that the first-order phase transition has a different universality from the second-order one. We also discuss the observation of this phenomenon in the realistic cold-atom experiments based on the in situ density measurements.