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arXiv:1904.05714 · Physical review. B./Physical review. B

Rabi-resonant behavior of periodically driven correlated fermion systems

Marcin Płodzień, Marcin M. Wysokiński

Published Jul 31, 2019• 5 citations
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Abstract

A Fermi-Hubbard system with a periodically-modulated interaction has been recently shown to resonantly absorb energy at a series of drive frequencies. In the present work, with the help of static perturbation theory, we argue that driving couples to Hubbard bands in a similar fashion as a classical field couples to a two-level atom. The latter, significantly simpler setup, described by the Rabi model, is known to support resonant rapid energy absorption at virtually the same series of driving frequencies. Our interpretation is also supported by the equivalency between dynamics of the two-site periodically driven Hubbard and Rabi models. Relying on this insight, we establish that the same Rabi-resonant behavior is displayed also by fermions confined in a harmonic trap with periodically driven contact interactions.

DOI
10.1103/physrevb.100.041116

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A Fermi-Hubbard system with a periodically-modulated interaction has been recently shown to resonantly absorb energy at a series of drive frequencies. In the present work, with the help of static perturbation theory, we argue that driving couples to Hubbard bands in a similar fashion as a classical field couples to a two-level atom. The latter, significantly simpler setup, described by the Rabi model, is known to support resonant rapid energy absorption at virtually the same series of driving frequencies. Our interpretation is also supported by the equivalency between dynamics of the two-site periodically driven Hubbard and Rabi models. Relying on this insight, we establish that the same Rabi-resonant behavior is displayed also by fermions confined in a harmonic trap with periodically driven contact interactions.
We study the dynamics and timescales of a periodically driven Fermi-Hubbard model in a three-dimensional hexagonal lattice. The evolution of the Floquet many-body state is analyzed by comparing it to an equivalent implementation in undriven systems. The dynamics of double occupancies for the near- and off-resonant driving regime indicate that the effective Hamiltonian picture is valid for several orders of magnitude in modulation time. Furthermore, we show that driving a hexagonal lattice compared to a simple cubic lattice allows us to modulate the system up to 1 s, corresponding to hundreds of tunneling times, with only minor atom loss. Here, driving at a frequency close to the interaction energy does not introduce resonant features to the atom loss.
We perform an ab initio comparison between nonequilibrium dynamical mean-field theory and optical lattice experiments by studying the time evolution of double occupations in the periodically driven Fermi-Hubbard model. For off-resonant driving, the range of validity of a description in terms of an effective static Hamiltonian is determined and its breakdown due to energy absorption close to resonance is demonstrated. For near-resonant driving, we investigate the response to a change in driving amplitude and discover an asymmetric excitation spectrum with respect to the detuning. In general, we find good agreement between experiment and theory, which cross validates the experimental and numerical approaches in a strongly correlated nonequilibrium system.
We study the dynamics of the Fermi-Hubbard model driven by a time-periodic modulation of the interaction within nonequilibrium dynamical mean-field theory. For moderate interaction, we find clear evidence of thermalization to a genuine infinite-temperature state with no residual oscillations. Quite differently, in the strongly correlated regime, we find a quasistationary extremely long-lived state with oscillations synchronized with the drive (Floquet prethermalization). Remarkably, the nature of this state dramatically changes upon tuning the drive frequency. In particular, we show the existence of a critical frequency at which the system rapidly thermalizes despite the large interaction. We characterize this resonant thermalization and provide an analytical understanding in terms of a breakdown of the periodic Schrieffer-Wolff transformation.
We generalize the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory. The method is applied to the periodically driven, strongly interacting Fermi-Hubbard model, for which we identify two regimes resulting in different effective low-energy Hamiltonians. In the nonresonant regime, we realize an interacting spin model coupled to a static gauge field with a nonzero flux per plaquette. In the resonant regime, where the Hubbard interaction is a multiple of the driving frequency, we derive an effective Hamiltonian featuring doublon association and dissociation processes. The ground state of this Hamiltonian undergoes a phase transition between an ordered phase and a gapless Luttinger liquid phase. One can tune the system between different phases by changing the amplitude of the periodic drive.
Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a time-independent effective Hamiltonian, which is generally identified through a perturbative treatment. Here, we present a general formalism that describes time-modulated physical systems, in which the driving frequency is large, but resonant with respect to energy spacings inherent to the system at rest. Such a situation is currently exploited in optical-lattice setups, where superlattice (or Wannier-Stark-ladder) potentials are resonantly modulated so as to control the tunneling matrix elements between lattice sites, offering a powerful method to generate artificial fluxes for cold-atom systems. The formalism developed in this work identifies the basic ingredients needed to generate interesting flux patterns and band structures using resonant modulations. Additionally, our approach allows for a simple description of the micromotion underlying the dynamics; we illustrate its characteristics based on diverse dynamic-lattice configurations. It is shown that the impact of the micromotion on physical observables strongly depends on the implemented scheme, suggesting that a theoretical description in terms of the effective Hamiltonian alone is generally not sufficient to capture the full time evolution of the system.
In this article we study quantum phases and the phase diagram of a Fermi-Hubbard model under periodic driving that has been realized in recent cold-atom experiments, in particular, when the driving frequency is nearly resonant with the interaction energy. Due to the driving, the effective Hamiltonian contains a correlated hopping term where the density occupation strongly modifies the hopping strength. Focusing on half filling, in addition to the charge- and spin-density wave phases, large regions of ferromagnetic phase and phase separation are discovered in the weakly interacting regime. The mechanism of this ferromagnetism is attributed to the correlated hopping, because the hopping strength within a ferromagnetic domain is normalized to a larger value than the hopping strength across the domain. Thus, the kinetic energy drives the system into a ferromagnetic phase. We note that this is a different mechanism, in contrast to the well-known Stoner mechanism for ferromagnetism where the ferromagnetism is driven by interaction energy.