Session T14: Floquet Engineering and State Preparation

Efficient Paths for Local Counter-Diabatic Driving

Adiabatic processes enable the preparation of quantum states with high fidelity, but generically require very long times. Counter-diabatic (CD) driving allows the instantaneous eigenstates to be followed exactly at any speed by the addition of a CD term to the Hamiltonian, but in general this requires the full spectrum and the implementation of highly non-local terms. However, approximate protocols can be obtained which require only local terms. In this work, we describe a systematic method for finding alternative paths in the coupling space along which local CD protocols are most efficient.   

Emergent Semi-Classical Dynamics Beyond the Born-Oppenheimer Approximation

We discuss a semi-classical scheme for computing the dynamics of a system composed of fast quantum degrees of freedom coupled to slow coordinates. Going to a reference frame co-moving with the slow degrees of freedom, we find corrections to the Born-Oppenheimer approximation, which modify the emergent equations of motion for the slow variables. This is illustrated through a few simple examples, where the emergent dynamics is complex and qualitatively different from that predicted by the Born-Oppenheimer approximation.   

Quantum spin fluctuations in dynamical quantum phase transitions

Dynamical quantum phase transitions (DQPTs), criticality in the transient time response of a many-body system being brought out of equilibrium, have been an active research area in the recent decade. Despite the plethora of studies, the understanding of the role quantum fluctuations played in DQPTs is still incomplete. In this talk, we will address this question by investigating the spin dynamics, as quantified by the spin squeezing parameter, around DQPT in quenched interacting spin systems. We find that the spin-squeezing parameter attains a maximum in the vicinity of DQPTs in most quench cases and further unveiled the dominant spin-spin correlation aligns with the direction of the spin interactions in the post-quench phase. These findings provide insight into the intricate dynamics of spin systems during DQPTs and their connection with the equilibrium phase diagrams.   

Floquet insulators and lattice fermions

Floquet insulators are periodically driven quantum systems that can host novel topological phases as a function of the drive parameters. These new phases exhibit features reminiscent of fermion doubling in discrete-time lattice fermion theories. We make this suggestion concrete by mapping the spectrum of a noninteracting (1+1)D Floquet insulator onto that of a discrete-time lattice fermion theory with a time-independent Hamiltonian. The resulting Hamiltonian is distinct from the Floquet Hamiltonian that generates stroboscopic dynamics. It can take the form of a discrete-time Su-Schrieffer-Heeger model with half the number of spatial sites of the original model, or of a (1+1)D Wilson-Dirac theory with one quarter of the spatial sites.   

Microscopic origin of unconventional relaxation process through time-dependent Landau-Ginzburg theory

The technique of light control of quantum materials is a promising way to generate exotic phases with novel strongly correlated states. However, the fundamental physics of such a non-equilibrium process induced by a laser is not yet fully understood. By critically examining the dynamics of ultrafast light-induced phase transitions, our study introduces a novel approach that seamlessly connects microscopic and macroscopic theories. We scrutinize the underlying mechanisms, particularly unconventional relaxation processes, within Time-Dependent Ginzburg-Landau (TDGL) models. Our focus centers on the investigation of relaxation mechanisms marked by non-equilibrium dynamics, non-thermal pathways, and the emergence of metastable states. Through the TDGL model, we aim to understand the intricate dynamics relating to unconventional relaxation processes.   

Laser-enhanced magnetism in SmFeO3

The cross-talk between two magnetic ions, Sm³⁺ and Fe²⁺, in samarium ferrite (SmFeO$_3$) leads to a strong interaction of spins and phonons at low temperatures, while the magnetic interactions are weak. In this work, we simulate the dissipative spin dynamics in SmFeO₃ that are coupled to laser-driven infrared-active phonons via linear and quadratic modulation of the exchange energy to coherently enhance spin interactions, referred to as magnetophononics. When linear coupling dominates, we discover a dynamical first-order phase transition in the nonequilibrium steady state which can inhibit strong enhancement of magnetic interactions. By contrast, when quadratic spin-phonon coupling dominates, no phase transition exists at experimentally relevant parameters. By utilizing a chirp protocol, we see that the phase transition can be engineered, enabling stronger magnetic interactions in the steady state, a key goal of magnetophononics. We also discuss the route for experimental observation of our results, as well as the potential application of our theory for functional materials and spintronics.   

Classical coupled parametric oscillators as an example of time crystals defined by order parameter dynamics

Discrete time crystals, which are phases of matter that break the discrete time translational symmetry of a periodically-driven system, have generated a wave of recent interest and activity. In this work, we propose a classical system of weakly nonlinear parametrically-driven coupled oscillators as a testbed to understand these phases. We show that this system belongs to a robust class of two-state time crystals defined by the criterion that over one time step, a total order parameter changes between two values with a difference proportional to the system size. Any system satisfying this requirement exhibits time-translation symmetry breaking that is robust to any perturbation as well as random noise that preserves the time-translation symmetry of the system. We then discuss applications of the general condition to existing time crystal platforms including quantum systems.   

Driving collective current oscillations using light: The time-dependent GW approach

It is well known that electron-electron interactions generate longitudinal collective charge excitations known as plasmons, which correspond to resonances in the electron density-density response function. In this work, using the non-equilibrium real-time GW approach that includes the full two-time self-energy, we show that the current-current interactions can drive a different kind of collective excitation. These transverse collective current excitations lead to resonances in the current-current response function. We also propose routes for their experimental detection.   

Floquet engineering of many-body states by the Ponderomotive potential

The Ponderomotive force is a static second order force that a particle feels in an oscillating field. The effective potential for this force may be called the Ponderomotive potential. We generalize this notion to degrees of freedom in periodically driven quantum many-body systems, and propose it as a convenient tool to engineer the non-equilibrium steady states beyond the single particle level. Applied to materials driven by light, the Ponderomotive potential is intimately related to the optical conductivity, which experiences enhancements close to resonances. We show that the Ponderomotive potential from incident light may be used to induce excitonic condensates in semiconductors, to generate attractive interactions leading to superconductivity in certain electron-phonon systems, and to create additional free energy minima in systems with charge/spin/excitonic orders. These effects are discussed for specific materials such that they can be readily verified in ultrafast experiments.   

Floquet-driven Interlayer Spin Pumping in Transition Metal Dichalcogenide Heterostructures

Spin pumping through the magnetization precession of a ferromagnet is one of the common techniques used for generating and manipulating spin currents, which is central to the implementation of spintronic devices. Using the Floquet Green's function formalism for systems driven by a time-periodic potential, we study the pumped spin current driven by the magnetization precession of a ferromagnetic layer. We consider a vertical heterostructure comprising a transition metal dichalcogenide (TMD) layer and two-dimensional electron gas separated by an insulating spacer, with the TMD layer coupled to the ferromagnetic layer through exchange coupling. A non-perturbative formulation of the tunneling spin current is developed within the Floquet-Keldysh formalism, from which we have analyzed the dependence of the tunneling spin current on the precession angle, the driving frequency, and the exchange coupling strength. Our theory of spin pumping from TMD materials allows the optimization of pumped spin currents by exploring experimentally available materials parameter space for TMDs and the two-dimensional electron gas.   

Preparation of Topological Floquet States by Quantum Optimal Control Theory

The effective electronic properties of periodically driven quantum materials are conveniently computed via the Floquet formalism. However, in practice the amplitude of the external time-periodic drive is modulated from zero to a targeted value in finite time, breaking the infinite time-periodicity of the ideal Floquet states. In that case, one is interested in how close one may steer the state from the actual time evolution to the ideal Floquet state, as quantified by an appropriate fidelity metric. For the driven quantum well model, we first determine how the fidelity varies as adjustable parameters of elementary ramping functions are varied. Then, we use the gradient ascent in function space (GRAFS) method to assess whether a quantum optimal control theory (QOCT) approach can produce non-elementary ramping functions that further improve the fidelity for a given ramping time. Of particular interest will be characterizing the attainable fidelity when certain classes of topological transitions occur, since the Chern number is provably conserved under unitary time evolution [1]. Our approach may be applied directly to the Floquet graphene antidot lattice that we introduced previously [2,3], and will provide experimentalists with the best-case ramping protocols for preparing Floquet states that are topologically distinct from the corresponding equilibrium system [4].

 

This work was supported by the NSF under grant No. OIA-1921199 and the ARO through US MURI Grant No. W911NF1810218.

 

[1] Dynamical Preparation of Floquet Chern Insulators, L. D’Alessio and M. Rigol, Nat. Commun., 6, 8336, 2015

[2] Floquet Graphene Antidot Lattices, A. Cupo et al., Phys. Rev. B, 104, 174304, 2021

[3] Optical Conductivity Signatures of Floquet Electronic Phases, A. Cupo et al., Phys. Rev. B, 108, 024308, 2023

[4] Light-Induced Anomalous Hall Effect in Graphene, J. McIver et al., Nat. Phys., 16, 38–41, 2020   

Nonequilibration, synchronization, and time crystals in isotropic Heisenberg models

Isotropic but otherwise largely arbitrary Heisenberg models in the presence of a homogeneous magnetic field are considered, including various integrable, nonintegrable, as well as disordered examples, and not necessarily restricted to one dimension or short-range interactions. Taking for granted that the nonequilibrium initial condition and the spectrum of the field-free model satisfy some very weak requirements, expectation values of generic observables are analytically shown to exhibit permanent long-time oscillations, thus ruling out equilibration. If the model (but not necessarily the initial condition) is translationally invariant, the long-time oscillations are moreover shown to exhibit synchronization in the long run, meaning that they are invariant under arbitrary translations of the observable. Analogous long-time oscillations are also recovered for temporal correlation functions when the system is already at thermal equilibrium from the outset, thus realizing a so-called time crystal [1].

[1] P. Reimann, P. Vorndamme, J. Schnack, Phys. Rev. Research 5, 043040 (2023)