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arXiv:1105.1375 · Physical Review A

Quench-induced Mott-insulator-to-superfluid quantum phase transition

Jay Deep Sau, Bin Wang, S. Das Sarma

Published Jan 31, 2012• 10 citations
arXivHTMLPDF

Abstract

Mott-insulator-to-superfluid quenches have been used by recent experiments to generate exotic superfluid phases. While the final Hamiltonian following the sudden quench is that of a superfluid, it is not a priori clear whether the final state of the system actually enters the superfluid phase. To understand the nature of the final state the temporal evolution of the momentum distribution is calculated following a Mott-insulator-to-superfluid quench. Using the numerical infinite time-evolving block decimation approach and the analytical rotor model approximation it is established that the one- and two-dimensional Mott insulators following the quench equilibrate to thermal states with spatially short-ranged coherence peaks in the final momentum distribution and therefore are not superfluids. However, in three dimensions a divergence in the momentum distribution indicating the emergence of true superfluid order is found.

DOI
10.1103/physreva.85.013644

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Mott-insulator-to-superfluid quenches have been used by recent experiments to generate exotic superfluid phases. While the final Hamiltonian following the sudden quench is that of a superfluid, it is not a priori clear whether the final state of the system actually enters the superfluid phase. To understand the nature of the final state the temporal evolution of the momentum distribution is calculated following a Mott-insulator-to-superfluid quench. Using the numerical infinite time-evolving block decimation approach and the analytical rotor model approximation it is established that the one- and two-dimensional Mott insulators following the quench equilibrate to thermal states with spatially short-ranged coherence peaks in the final momentum distribution and therefore are not superfluids. However, in three dimensions a divergence in the momentum distribution indicating the emergence of true superfluid order is found.
We study the quench from the Mott-insulator to the superfluid phase in the Bose-Hubbard model and investigate the spatial-temporal growth of phase coherence, that is, phase locking between initially uncorrelated sites. To this end, we establish a hierarchy of correlations via a controlled expansion into inverse powers of the coordination number 1/Z1/Z1/Z. It turns out that the off-diagonal long-range order spreads with a constant propagation speed, forming local condensate patches, whereas the phase correlator follows a diffusionlike growth rate.
The ground state of the one-dimensional Bose-Hubbard model at unit filling undergoes the Mott-superfluid quantum phase transition. It belongs to the Kosterlitz-Thouless universality class with an exponential divergence of the correlation length in place of the usual power law. We present numerical simulations of a linear quench both from the Mott insulator to superfluid and back. The results satisfy the scaling hypothesis that follows from the Kibble-Zurek mechanism (KZM). In the superfluid-to-Mott quenches there is no significant excitation in the superfluid phase despite its gaplessness. Since all critical superfluid ground states are qualitatively similar, the excitation begins to build up only after crossing the critical point when the ground state begins to change fundamentally. The last process falls into the KZM framework.
We investigate the time evolution of correlations in the Bose-Hubbard model following a quench from the superfluid to the Mott insulator. For large values of the final interaction strength the system approaches a distinctly nonequilibrium steady state that bears strong memory of the initial conditions. In contrast, when the final interaction strength is comparable to the hopping, the correlations are rather well approximated by those at thermal equilibrium. The existence of two distinct nonequilibrium regimes is surprising given the nonintegrability of the Bose-Hubbard model. We relate this phenomenon to the role of quasiparticle interactions in the Mott insulator.
We study the quantum phase transition between the superfluid and the Mott insulator in the one-dimensional (1D) Bose-Hubbard model. Using the time-evolving block-decimation method, we numerically calculate the tunneling splitting of two macroscopically distinct states with different winding numbers. From the scaling of the tunneling splitting with respect to the system size, we determine the critical point of the superfluid-to-Mott-insulator transition for arbitrary integer filling factors. We find that the critical values versus the filling factor in 1D, 2D, and 3D are well approximated by a simple analytical function. We also discuss the condition for determining the transition point from a perspective of the instanton method.
The ground state of the one-dimensional Bose-Hubbard model at unit filling undergoes the Mott-superfluid quantum phase transition. It belongs to the Kosterlitz-Thouless universality class with an exponential divergence of the correlation length in place of the usual power law. We present numerical simulations of a linear quench both from the Mott insulator to superfluid and back. The results satisfy the scaling hypothesis that follows from the Kibble-Zurek mechanism (KZM). In the superfluid-to-Mott quenches there is no significant excitation in the superfluid phase despite its gaplessness. Since all critical superfluid ground states are qualitatively similar, the excitation begins to build up only after crossing the critical point when the ground state begins to change fundamentally. The last process falls into the KZM framework.
Recent advances in cooling techniques make possible the experimental study of quantum phase transitions, which are transitions near absolute zero temperature accessed by varying a control parameter. A paradigmatic example is the superfluid-Mott transition of interacting bosons on a periodic lattice. From the relativistic Ginzburg-Landau action of this superfluid-Mott transition we derive the elementary excitations of the bosonic system, which contain in the superfluid phase a gapped Higgs mode and a gapless Goldstone mode. We show that this energy spectrum is in good agreement with the available experimental data and we use it to extract, with the help of dimensional regularization, meaningful analytical formulas for the beyond-mean-field equation of state in two and three spatial dimensions. We find that, while the mean-field equation of state always gives a second-order quantum phase transition, the inclusion of Gaussian quantum fluctuations can induce a first-order quantum phase transition. This prediction is a strong benchmark for future experiments on quantum phase transitions.