Dynamics-induced freezing of strongly correlated ultracold bosons

Abstract

We study the non-equilibrium dynamics of ultracold bosons in an optical lattice with a time dependent hopping amplitude J(t) = J0 +δJ cos(ωt) which takes the system from a superfluid phase near the Mott-superfluid transition (J = J0 + δJ) to a Mott phase (J = J0 − δJ) and back through a quantum critical point (J = Jc) 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. PACS numbers: 64.60.Ht, 05.30.Jp, 05.30.Rt Theoretical study of non-equilibrium dynamics in closed quantum systems has seen great progress in recent years [1] mainly due to the possibility of realization of such dynamics using ultracold atom in optical lattices [2,3]. For bosonic atoms, such systems are well described by the Bose-Hubbard model with on-site interaction strength U and nearest neighbor hopping amplitude J [4,5]. Several theoretical studies have been carried out on the quench and ramp dynamics of this model [6][7][8][9][10][11]; some of them have also received support from recent experiments [3]. In contrast, studies on periodically driven closed quantum systems have been undertaken in the past mainly on driven two-level systems [12,13] or on weakly interacting or integrable many-body systems which can be modeled by them [14,15]. Among these, Ref.[15] has predicted freezing of the time-averaged value of the order parameter (magnetization) of an periodically driven one-dimensional (1D) Ising or XY model, when the temporal average is performed over several drive cycles, at specific drive frequencies. Such a freezing occurs in the high frequency regime and exhibits non-monotonic dependence on the drive frequency. However, to the best of our knowledge, the phenomenon of dynamic freezing has never been demonstrated for dynamics involving a single drive cycle and/or for non-integrable quantum systems. Recent studies of periodic dynamics of the Bose-Hubbard model have not addressed this issue [16,17].In this work, we demonstrate, via designing a periodic driving protocol, that the periodically driven Bose-Hubbard model may exhibit dynamic freezing of the boson wavefunction |ψ(t = 0) = |ψ(t = T ) for specific values of the drive frequencies ω = 2π/T . Our driving protocol constitutes a time-dependent hopping amplitude of the bosons J(t) = J 0 + δJ cos(ωt) with J 0 and δJ chosen such that the drive takes the system from a superfluid (SF) (J = J 0 + δJ) to the Mott insulator (MI) state (J = J 0 − δJ) and back through the tip of the Mott lobe where µ = µ tip . We demonstrate, using mean-field theory, that such a freezing phenomenon de-rives from quantum interference of the dynamic phases acquired by the bosons and compute the defect formation probability P = 1−...

Quantum dynamics of disordered bosons in an optical lattice

“…Rather, the return of the system to its initial state (ρ d = 0) for certain rates of change of hopping has similar origins as found in Ref. 24, where the system was found to return to its initial state under the influence of a periodic drive for certain drive frequencies. The constant envelope characterizes the fact that within the canonical transformation there is a low energy state orthogonal to the initial ground state (with the degeneracy broken on a scale of ∼ J 2 /U ).…”

Ramp and periodic dynamics across non-Ising critical points

“…We find that there are special drive frequencies ω 0 = ω * 0 , which corresponds to the position of the minima in Fig. 6, for which the system, after a full period of the drive, comes remarkably close to the starting ground state exhibiting near-perfect dynamic freezing 20,21 . Consequently, Q, D → 0 and F → 1 at t = T for these frequencies; moreover in our case since we choose the starting state to be the dipole vacuum, one also has n d → 0 at these freezing frequencies.…”

Entanglement generation in periodically driven integrable systems: Dynamical phase transitions and steady state

“…Such studies are mainly motivated by presence of experimental platforms in the form of ultracold atom systems where relevant experiments can be carried out 22 . More recently, the properties of periodically closed driven quantum systems which involved multiple passage through an intermediate quantum critical point has received a lot of attention; in particular such dynamics has been shown to lead to interesting phenomenon such as dynamic freezing 23,24 and to novel steady states 25 . Moreover, such driven systems are known to undergo dynamic phase transitions which manifests itself in cusp like behavior of the Loschmidt echo and can be understood as a consequence of the non-analyticities (Fischer zeroes) of the dynamical free energy of the driven systems [26][27][28][29] .…”