Quantum Simulation Meets Nonequilibrium Dynamical Mean-Field Theory: Exploring the Periodically Driven, Strongly Correlated Fermi-Hubbard Model

Abstract

We study the dynamics of double occupations in a strongly interacting, periodically driven Fermi-Hubbard model using ultracold, fermionic atoms in an optical lattice and the nonequilibrium extension of dynamical mean field theory. Ramping up the amplitude and varying the frequency of the drive we demonstrate the validity of the effective static Hamiltonian description in the far offresonant regime and its breakdown due to energy absorption closer to the resonance. In the case of near-resonant driving, we investigate the effect of the driving amplitude and detuning as well as the adiabaticity of the switching into a state with effectively reduced interaction. A good agreement between experiment and theory is found in both regimes, which establishes a high level of control in the quantum simulations and the predictive power of the numerical approach.Quantum simulation exploits the high degree of control over a quantum system, such as ultracold atoms, to study many-body effects which are difficult to predict analytically or numerically [1][2][3][4]. One of the target systems in the condensed matter context is the Fermi-Hubbard model, which captures essential effects of electronic correlations in solids. For equilibrium properties, cold atom simulators and powerful numerical techniques provide access to temperature regimes, where nontrivial quantum correlations start to emerge. These methods have been successfully benchmarked against each other and used to reveal the physics of the model [5][6][7][8][9][10][11]. Exposing such correlated lattice models to a periodic driving force creates a broad range of interesting effects [12,13]. Applications of this so-called Floquet engineering concept range from the coherent control of high-temperature superconductors by intense laser fields [14,15] to the realization of topological phases in cold atomic systems [13,16]. The nonequilibrium nature of these effects however pushes quantum simulators and numerical methods to their limits, where a direct comparison demands exceptionally high control over experimental parameters and a sufficient accuracy of the numerical methods. Here, we address this challenge of an experiment-theory comparison for the driven Fermi-Hubbard model on a three-dimensional lattice.The properties of periodically driven systems are often described in terms of an effective Floquet Hamiltonian, which is static and can be derived from high-frequency expansions or time-dependent Schrieffer-Wolff transformations [17][18][19][20]. However, these expansions are only useful if there exists a hierarchy of energy scales which makes it possible to neglect higher order terms. Furthermore, a realistic description of a Floquet-engineered state must take into account the possibly non-thermal energy distribution in the system as well as the switch-on procedure and the continuous energy absorption from the periodic drive [18,[21][22][23][24]. In experiments, unwanted excitation processes are induced by the driving [25][26][27][28][29][30] or by fluctu-ations of static param...

Enhancement of local pairing correlations in periodically driven Mott insulators

“…Our results are relevant for current experiments on laser-pumped organic Mott insulators [5,6] and ultracold Fermi gases in driven optical lattices [37,38]. We discuss the latter in particular, suggesting to explore a possibly overlooked regime in future experiments.…”

“…More direct control is achieved with ultracold atoms in optical lattices. Recent experiments [37,38] have studied the Floquet prethermal state and remarkably found large double occupancy for drive above resonance. We suggest that also in these cases a key role is played by dissipation, which is unavoidable even in cold atoms.…”

Low rank compression in the numerical solution of the nonequilibrium Dyson equation

“…The numerical solution of the quantum many-body problem out of equilibrium is an outstanding challenge in modern physics, required to simulate the effect of strong radiation fields on atoms and molecules [1,2], quantum materials [3][4][5], nuclear physics [6][7][8], ultracold atomic gases [9][10][11], and many other systems. Various theoretical frameworks for equilibrium problems have been extended to the nonequilibrium situation, including density functional theory [12], the density matrix renormalization group (DMRG) [13], and field theory approaches based on the Keldysh formalism [14][15][16][17].…”

“…The Keldysh formalism is a particularly versatile approach, as it is not limited by the dimension of the problem (like DMRG), and can be efficiently adjusted to realistic setups. Several recent studies have used these techniques in direct comparisons with experiments, including those involving transport properties [27] and periodic driving [11] in ultra-cold atomic systems, and pump-probe experiments in correlated solids [5,[28][29][30][31][32]. Many have already reached the level of first-principles description [33][34][35][36][37].…”

Rabi-resonant behavior of periodically driven correlated fermion systems

“…In this light, the perturbative approaches to correlated fermions based on the Floquet theorem [11][12][13][14][15][16][17][18][19], though restricted to time-periodic drivings, have turned out to be very efficient and powerful tools, capturing well the experimental realizations [20][21][22][23]. Usually, the accurate determination of the energy absorption in an arbitrarily driven correlated fermion system involves heavy numerical simulation [7,24,25].…”