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arXiv:2204.07598 · Physical review. B./Physical review. B

Many-body parametric resonances in the driven sine-Gordon model

Izabella Lovas, R. Citro, Eugene Demler, Thierry Giamarchi, Michael Knap, E. Orignac

Published Aug 25, 2022• 18 citations
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Abstract

We study a quantum many-body variant of the parametric oscillator by investigating the driven sine-Gordon model with a modulated tunnel coupling via a semiclassical truncated Wigner approximation (TWA). We first analyze the parametric resonant regime for driving protocols that retain our model gapped, and compare the TWA to a time-dependent Gaussian variational ansatz (TGVA). We then turn to a drive which closes the gap, resulting in an enhanced energy absorption. While the TGVA approach breaks down in this regime, we can apply TWA to explore the dynamics of the mode-resolved energy density and the higher-order correlations between modes in the prethermal heating regime. For weak driving amplitude, we find an exponentially fast energy absorption in the main resonant mode, while the heating of all remaining modes is almost perfectly suppressed on short timescales. At later times, the highly excited main resonance provides effective resonant driving terms for its higher harmonics through the nonlinearities in the Hamiltonian, and gives rise to an exponentially fast heating in these particular modes. We capture the strong correlations induced by these resonant processes by evaluating higher-order connected correlation functions. Our results can be experimentally probed in ultracold-atomic settings, with parallel one-dimensional quasicondensates in the presence of a modulated tunnel coupling.

DOI
10.1103/physrevb.106.075426

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We study a quantum many-body variant of the parametric oscillator by investigating the driven sine-Gordon model with a modulated tunnel coupling via a semiclassical truncated Wigner approximation (TWA). We first analyze the parametric resonant regime for driving protocols that retain our model gapped, and compare the TWA to a time-dependent Gaussian variational ansatz (TGVA). We then turn to a drive which closes the gap, resulting in an enhanced energy absorption. While the TGVA approach breaks down in this regime, we can apply TWA to explore the dynamics of the mode-resolved energy density and the higher-order correlations between modes in the prethermal heating regime. For weak driving amplitude, we find an exponentially fast energy absorption in the main resonant mode, while the heating of all remaining modes is almost perfectly suppressed on short timescales. At later times, the highly excited main resonance provides effective resonant driving terms for its higher harmonics through the nonlinearities in the Hamiltonian, and gives rise to an exponentially fast heating in these particular modes. We capture the strong correlations induced by these resonant processes by evaluating higher-order connected correlation functions. Our results can be experimentally probed in ultracold-atomic settings, with parallel one-dimensional quasicondensates in the presence of a modulated tunnel coupling.
We investigate a one-dimensional Bose--Hubbard model in a parametrically driven global harmonic trap. The delicate interplay of both the local interaction of the atoms in the lattice and the driving of the global trap allows us to control the dynamical stability of the trapped quantum many-body state. The impact of the atomic interaction on the dynamical stability of the driven quantum many-body state is revealed in the regime of weak interaction by analyzing a discretized Gross--Pitaevskii equation within a Gaussian variational ansatz, yielding a Mathieu equation for the condensate width. The parametric resonance condition is shown to be modified by the atom interaction strength. In particular, the effective eigenfrequency is reduced for growing interaction in the mean-field regime. For a stronger interaction, the impact of the global parametric drive is determined by the numerically exact time-evolving block decimation scheme. When the trapped bosons in the lattice are in a Mott insulating state, the absorption of energy from the driving field is suppressed due to the strongly reduced local compressibility of the quantum many-body state. In particular, we find that the width of the local Mott region shows a breathing dynamics. Finally, we observe that the global modulation also induces an effective time-independent inhomogeneous hopping strength for the atoms.
We study the nonequilibrium dynamics of the quantum sine-Gordon model describing a pair of Josephson-coupled one-dimensional bosonic quasicondensates. Motivated by experimentally accessible quench procedures where the zero mode of the quasicondensates is weakly coupled to finite momentum modes, we develop a Hamiltonian truncation scheme relying on a mini-superspace treatment of the zero mode (MSTHA). We apply this method to simulate the time evolution after both weak and strong quantum quenches, injecting a low or high energy density into the system, and we demonstrate that MSTHA accurately captures the dynamics from the hard-core boson limit to the experimentally relevant weakly interacting regime for sufficiently mild quenches. In the case of high energy densities, MSTHA breaks down for weak interaction but still extends the range of validity of previous Hamiltonian truncation schemes. We also compare these results to the semiclassical truncated Wigner approximation, and we establish that the dynamics can be well approximated by the semiclassical description in the weakly interacting regime realized in the experiments. In addition, we clarify the importance of the phononic modes depending on the sine-Gordon interaction strength.
Quench dynamics in a two-dimensional system of interacting fermions is analyzed within the semiclassical truncated Wigner approximation (TWA). The models with short-range and long-range interactions are considered. We show that in the latter case, the TWA is very accurate, becoming asymptotically exact in the infinite-range limit, provided that the semiclassical Hamiltonian is correctly identified. Within the TWA, different dynamical timescales of charges and spins can be clearly distinguished. Interestingly, for a weak and moderate disorder strength, we observe subdiffusive behavior of charges, while spins exhibit diffusive dynamics. At strong disorder, the quantum Fisher information shows logarithmic growth in time with a slower increase for charges than for spins. It is shown that in contrast to the short-range model, strong inhomogeneities such as domain walls in the initial state can significantly slow down thermalization dynamics, especially at weak disorder. This behavior can put additional challenges in designing cold-atom experimental protocols aimed to analyze possible many-body localization in such systems. While within this approach we cannot make any definite statements about the existence of a many-body localized phase, we see a very fast crossover as a function of disorder strength from rapidly thermalizing to a slow glassylike regime both for the short-range and long-range models.
A parametrically driven classical harmonic oscillator exhibits resonant instability when driven at twice its natural frequency, with the lowest energy configuration remaining unaffected by the drive. In contrast, the ground state of the quantum mechanical counterpart shows a non-trivial response to such a drive due to the spatial delocalization of the wavefunction. The standard realization of PR involves modulating the natural frequency of the oscillator. Here we study a different drive protocol in which the coupling between two such quantum harmonic oscillators is modulated parametrically. We show that the drive frequency can in principle be tuned to selectively excite any desired normal mode, while leaving the other close to its ground state. Only states with even quantum numbers in each normal mode are populated. Within the parametric resonance window the excitations follow a power-law decay with respect to occupation number, in contrast to the exponential decay observed off-resonance. We also briefly discuss how this framework can be extended to a system of N coupled oscillators
This work presents a theoretical investigation of dynamic stabilization in interacting quantum many-body systems via high-frequency periodic driving. Using Floquet theory and the Magnus expansion, we derive the effective time-independent Hamiltonian governing the slow dynamics of a driven spin chain. We show that the external field induces a parametric renormalization of the transverse tunneling terms through a zeroth-order Bessel function dependence, leading to a critical drive amplitude at which transport is strongly suppressed. This suppression of the lowest-order hopping term gives rise to a long-lived prethermal regime in which many-body thermalization is significantly delayed. The resulting dynamics exhibit a sharp reduction in the short-to-intermediate time entanglement entropy growth rate. The framework is consistent with known results in Floquet engineering and coherent destruction of tunneling, and provides a unified interpretation of transport suppression and delayed scrambling in periodically driven systems. A falsifiable experimental protocol using ultracold atoms in optical lattices is proposed to validate the predicted threshold behavior and prethermal stabilization mechanism.
Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general rigorous bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as 1/r^{α} with α>d/2. We show that the disorder averaged energy absorption rate at high temperatures decays exponentially with the driving frequency. This strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times, and we provide numerical evidence to support such a statement. Our results are relevant for understanding timescales of heating and new dynamical regimes described by effective Hamiltonians in such long-range systems.