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arXiv:1204.6331 · Europhysics Letters (EPL)

Dynamics-induced freezing of strongly correlated ultracold bosons

S. Mondal, D. Pekker, K. Sengupta

Published Dec 1, 2012• 52 citations
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Abstract

We study the non-equilibrium dynamics of ultracold bosons in an optical lattice with a time dependent hopping amplitude J(t)=J_0 +δJ \cos(ωt) which takes the system from a superfluid phase near the Mott-superfluid transition (J= J_0+δJ) to a Mott phase (J=J_0-δJ) and back through a quantum critical point (J=J_c) and demonstrate dynamic freezing of the boson wavefunction at specific values of ω. At these values, the wavefunction overlap F (defect density P=1-F) approaches unity (zero). We provide a qualitative explanation of the freezing phenomenon, show it's robustness against quantum fluctuations and the presence of a trap, compute residual energy and superfluid order parameter for such dynamics, and suggest experiments to test our theory.

DOI
10.1209/0295-5075/100/60007

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We study the non-equilibrium dynamics of ultracold bosons in an optical lattice with a time dependent hopping amplitude J(t)=J_0 +δJ \cos(ωt) which takes the system from a superfluid phase near the Mott-superfluid transition (J= J_0+δJ) to a Mott phase (J=J_0-δJ) and back through a quantum critical point (J=J_c) and demonstrate dynamic freezing of the boson wavefunction at specific values of ω. At these values, the wavefunction overlap F (defect density P=1-F) approaches unity (zero). We provide a qualitative explanation of the freezing phenomenon, show it's robustness against quantum fluctuations and the presence of a trap, compute residual energy and superfluid order parameter for such dynamics, and suggest experiments to test our theory.
We use a time-dependent hopping expansion technique to study the non-equilibrium dynamics of strongly interacting bosons in an optical lattice in the presence of a harmonic trap characterized by a force constant K. We show that after a sudden quench of the hopping amplitude J across the superfluid (SF)-Mott insulator (MI) transition, the SF order parameter [Formula: see text] and the local density fluctuation [Formula: see text] exhibit sudden decoherence beyond a trap-induced time scale [Formula: see text]. We also show that after a slow linear ramp down of J, [Formula: see text] and the boson defect density [Formula: see text] display a novel non-monotonic spatial profile. Both these phenomena can be explained as consequences of trap-induced time and length scales affecting the dynamics and can be tested by concrete experiments.
We study the equilibrium and nonequilibrium properties of strongly interacting bosons on a lattice in the presence of a random bounded disorder potential. Using a Gutzwiller projected variational technique, we study the equilibrium phase diagram of the disordered Bose-Hubbard model and obtain the Mott insulator, Bose glass, and superfluid phases. We also study the nonequilibrium response of the system under a periodic temporal drive where, starting from the superfluid phase, the hopping parameter is ramped down linearly in time, and back to its initial value. We study the density of excitations created, the change in the superfluid order parameter, and the energy pumped into the system in this process as a function of the inverse ramp rate $\ensuremath{\tau}$. For the clean case the density of excitations goes to a constant, while the order parameter and energy relax as $1/\ensuremath{\tau}$ and $1/{\ensuremath{\tau}}^{2}$ respectively. With disorder, the excitation density decays exponentially with $\ensuremath{\tau}$, with the decay rate increasing with the disorder, to an asymptotic value independent of the disorder. The energy and change in order parameter also decrease as $\ensuremath{\tau}$ is increased.
Bose-Einstein condensates of cold atoms in optical lattices are interesting because the dynamics of the transition from a Mott insulator to a superfluid driven by a quench into the superfluid phase exemplifies non-equilibrium evolutions of gauge-symmetry broken quantum phases. Here we have actually visualised features in real space, which have domain structures that depend on the stage of the transition dynamics. Namely, the system after the quench relaxes in three processes: (i) an exponential growth of the superfluid density, (ii) collapse of the domain structure, and (iii) vortex-antivortex pair-annihilation as the long-range superfluid order is formed. Topological picture due to Kibble-Zurek mechanism and Zurek's freeze-out scenario for slow quenches are confirmed.
We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points belonging to the Potts universality class. Such critical points separate a uniform and a Z3Z_3Z3​ or Z4Z_4Z4​ symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation for finite-size boson chains with L≤24L \le 24L≤24 using exact-diagonalization (ED) of the excitation density DDD, the wavefunction overlap FFF, and the excess energy QQQ at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which DDD and QQQ shows Kibble-Zurek scaling and show that such scaling is consistent with that expected from critical exponents of the qqq-state Potts universality class with q=3,4q=3,4q=3,4. For periodic protocol, we show that the model display near-perfect dynamical freezing at specific frequencies; at these frequencies D,Q→0D, Q \to 0D,Q→0 and ∣F∣→1|F| \to 1∣F∣→1. We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.
Bose-Einstein condensates of cold atoms in optical lattices are interesting because the dynamics of the transition from a Mott insulator to a superfluid driven by a quench into the superfluid phase exemplifies non-equilibrium evolutions of gauge-symmetry broken quantum phases. Here we have actually visualised features in real space, which have domain structures that depend on the stage of the transition dynamics. Namely, the system after the quench relaxes in three processes: (i) an exponential growth of the superfluid density, (ii) collapse of the domain structure, and (iii) vortex-antivortex pair-annihilation as the long-range superfluid order is formed. Topological picture due to Kibble-Zurek mechanism and Zurek's freeze-out scenario for slow quenches are confirmed.
We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a Z3{Z}_{3}Z3​ or Z4{Z}_{4}Z4​ symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with $L\ensuremath{\le}24$ using exact diagonalization (ED), of the excitation density DDD, the wave function overlap FFF, and the excess energy QQQ at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which DDD and QQQ show Kibble-Zurek scaling. We find, based on numerical analysis with $L\ensuremath{\le}24$, that such scaling is consistent with that expected from critical exponents of the qqq-state Potts universality class with q=3,4q=3,4q=3,4. For the periodic protocol, we show that the model displays near-perfect dynamical freezing at specific frequencies; at these frequencies $D,Q\ensuremath{\rightarrow}0$ and $|F|\ensuremath{\rightarrow}1$. We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.