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arXiv:2301.10379 · Physical review. B./Physical review. B

Suppression of heating by multicolor driving protocols in Floquet-engineered strongly correlated systems

Yuta Murakami, Michael Schüler, Ryotaro Arita, Philipp Werner

Published Jul 28, 2023• 9 citations
arXivHTMLPDF

Abstract

Heating effects in Floquet-engineered systems are detrimental to the control of physical properties. In this paper, we show that the heating of periodically driven strongly correlated systems can be suppressed by multicolor driving, i.e., by applying auxiliary excitations which interfere with the absorption processes from the main drive. We focus on the Mott insulating single-band Hubbard model and study the effects of multicolor driving with nonequilibrium dynamical mean-field theory. The main excitation is a periodic electric field with frequency $\mathrm{\ensuremath{\Omega}}$ smaller than the Mott gap, while for the auxiliary excitations, we consider additional electric fields and/or hopping modulations with a higher harmonic of $\mathrm{\ensuremath{\Omega}}$. To suppress the three-photon absorption of the main excitation, which is a parity-odd process, we consider auxiliary electric-field excitations and a combination of electric-field excitations and hopping modulations. On the other hand, to suppress the two-photon absorption, which is a parity-even process, we consider hopping modulations. The conditions for an efficient suppression of heating are well captured by the Floquet effective Hamiltonian derived with the high-frequency expansion in a rotating frame. As an application, we focus on the exchange couplings of the spins (pseudospins) in the repulsive (attractive) model and demonstrate that the suppression of heating allows us to realize and clearly observe a significant Floquet-induced change of the low energy physics.

DOI
10.1103/physrevb.108.035151

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Heating effects in Floquet-engineered systems are detrimental to the control of physical properties. In this paper, we show that the heating of periodically driven strongly correlated systems can be suppressed by multicolor driving, i.e., by applying auxiliary excitations which interfere with the absorption processes from the main drive. We focus on the Mott insulating single-band Hubbard model and study the effects of multicolor driving with nonequilibrium dynamical mean-field theory. The main excitation is a periodic electric field with frequency \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ smaller than the Mott gap, while for the auxiliary excitations, we consider additional electric fields and/or hopping modulations with a higher harmonic of \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ. To suppress the three-photon absorption of the main excitation, which is a parity-odd process, we consider auxiliary electric-field excitations and a combination of electric-field excitations and hopping modulations. On the other hand, to suppress the two-photon absorption, which is a parity-even process, we consider hopping modulations. The conditions for an efficient suppression of heating are well captured by the Floquet effective Hamiltonian derived with the high-frequency expansion in a rotating frame. As an application, we focus on the exchange couplings of the spins (pseudospins) in the repulsive (attractive) model and demonstrate that the suppression of heating allows us to realize and clearly observe a significant Floquet-induced change of the low energy physics.
The concept of "Floquet engineering" relies on an external periodic drive to realize novel, effectively static Hamiltonians.This technique is being explored in experimental platforms across physics, including ultracold atoms, laser-driven electron systems, nuclear magnetic resonance, and trapped ions.The key challenge in Floquet engineering is to avoid the uncontrolled absorption of photons from the drive, especially in interacting systems in which the excitation spectrum becomes effectively dense.The resulting dissipative coupling to higher-lying modes, such as the excited bands of an optical lattice, has been explored in recent experimental and theoretical works, but the demonstration of a broadly applicable method to mitigate this effect is lacking.Here, we show how two-path quantum interference applied to strongly correlated fermions in a driven optical lattice suppresses dissipative coupling to higher bands and increases the lifetime of double occupancies and spin correlations by 2 to 3 orders of magnitude.Interference is achieved by introducing a weak second modulation at twice the fundamental driving frequency with a definite relative phase.This technique is shown to suppress dissipation in both weakly and strongly interacting regimes of an offresonantly driven Hubbard system, opening an avenue to realizing low-temperature phases of matter in interacting Floquet systems.
The concept of “Floquet engineering” relies on an external periodic drive to realize novel, effectively static Hamiltonians. This technique is being explored in experimental platforms across physics, including ultracold atoms, laser-driven electron systems, nuclear magnetic resonance, and trapped ions. The key challenge in Floquet engineering is to avoid the uncontrolled absorption of photons from the drive, especially in interacting systems in which the excitation spectrum becomes effectively dense. The resulting dissipative coupling to higher-lying modes, such as the excited bands of an optical lattice, has been explored in recent experimental and theoretical works, but the demonstration of a broadly applicable method to mitigate this effect is lacking. Here, we show how two-path quantum interference applied to strongly correlated fermions in a driven optical lattice suppresses dissipative coupling to higher bands and increases the lifetime of double occupancies and spin correlations by 2 to 3 orders of magnitude. Interference is achieved by introducing a weak second modulation at twice the fundamental driving frequency with a definite relative phase. This technique is shown to suppress dissipation in both weakly and strongly interacting regimes of an offresonantly driven Hubbard system, opening an avenue to realizing low-temperature phases of matter in interacting Floquet systems.
We investigate multi-photon interband excitation processes in an optical lattice that is driven periodically in time by a modulation of the lattice depth. Assuming the system to be prepared in the lowest band, we compute the excitation spectrum numerically. Moreover, we estimate the effective coupling parameters for resonant interband excitation processes analytically, employing degenerate perturbation theory in Floquet space. We find that below a threshold driving strength, interband excitations are suppressed exponentially with respect to the inverse driving frequency. For sufficiently low frequencies, this leads to a rather sudden onset of interband heating, once the driving strength reaches the threshold. We argue that this behavior is rather generic and should also be found in lattice systems that are driven by other forms of periodic forcing. Our results are relevant for Floquet engineering, where a lattice system is driven periodically in time in order to endow it with novel properties like the emergence of a strong artificial magnetic field or a topological band structure. In this context, interband excitation processes correspond to detrimental heating.
Floquet engineering, the control of a quantum system by means of time-periodic driving, allows to modify the properties of a system so that it is described by an approximate effective time-independent Hamiltonian. However, in the presence of interactions the stabilization of interesting many-body ground states of such effective Hamiltonians is possible only on a certain time scale, beyond which Floquet heating sets in, as it results from unwanted driving induced resonant excitation. Moreover, the preparation of the ground state of such Floquet engineered effective Hamiltonians usually has to be accomplished adiabatically, which is another source of heating, especially when a phase transition has to be passed in a large system. Here, we propose a general dissipative strategy for the preparation and stabilization of effective ground states that are protected by an energy gap, such as topologically ordered states. It is scalable and relies on coupling the driven system to a thermal bath, the properties of which are chosen so that it both suppresses Floquet heating and guides the system into a non-equilibrium steady state with a large occupation of the effective ground-state. The small residual occupations of effective excited states are non-thermal, reflecting the non-equilibrium nature of the scheme. We use the Floquet-Born-Markov master equation to verify the proposed strategy. In particular, we discuss the preparation of both a one-dimensional Mott insulator and a two-dimensional fractional Chern insulator in strongly driven Bose-Hubbard systems.
Abstract We investigate multi-“photon” interband excitation processes in an optical lattice that is driven periodically in time by a modulation of the lattice depth. Assuming the system to be prepared in the lowest band, we compute the excitation spectrum numerically. Moreover, we estimate the effective coupling parameters for resonant interband excitation processes analytically, employing degenerate perturbation theory in Floquet space. We find that below a threshold driving strength, interband excitations are suppressed exponentially with respect to the inverse driving frequency. For sufficiently low frequencies, this leads to a rather sudden onset of interband heating, once the driving strength reaches the threshold. We argue that this behavior is rather generic and should also be found in lattice systems that are driven by other forms of periodic forcing. Our results are relevant for Floquet engineering, where a lattice system is driven periodically in time in order to endow it with novel properties like the emergence of a strong artificial magnetic field or a topological band structure. In this context, interband excitation processes correspond to detrimental heating.
Abstract We demonstrate the existence of exact Floquet flat bands in a class of non-integrable quantum many-body Hamiltonians leading to strong violation of the eigenstate thermalization hypothesis in the presence of a two-tone drive characterized by frequencies Ω1 and Ω 2 = ν Ω 1 , where ν is an integer. We provide the exact analytic condition for this phenomenon to occur for a generic protocol. A small departure from the flat band conditions leads to suppression of heating over a long prethermal timescale in an otherwise ergodic many-body system away from integrable or perturbative regimes; we elucidate the central role of the flat band behind such heating suppression. Our analysis indicates the existence of a perturbative Floquet Hamiltonian, away from high drive frequency/amplitude limit, which controls the dynamics of the driven system near such flat bands. We demonstrate this phenomenon by exact numerical studies of Floquet bandwidth, spectral form factor, entanglement and Shannon entropies, heat absorption, and correlation functions of a driven Rydberg chain. We also study the corresponding micromotion which exhibits coherent reversal of excitations reminiscent of echoes; in addition, it harbors an exact reflection symmetry about t = T 1 / 2 , where T 1 = 2 π / Ω 1 , which we elucidate. We discuss experiments which can test our theory.