Floquet Quasienergy Research Articles

Predicting edge-localized monovacancy defects in zigzag graphene nanoribbons from Floquet quasienergy spectrum

Predicting edge-localized monovacancy defects in zigzag graphene nanoribbons from Floquet quasienergy spectrum

Anomalous Floquet non-Hermitian skin effect in a ring resonator lattice

We present a one-dimensional coupled ring resonator lattice exhibiting a variant of the non- Hermitian skin effect (NHSE) that we call the anomalous Floquet NHSE. Unlike existing approaches to achieving the NHSE by engineering gain and loss on different ring segments, our design uses fixed on-site gain or loss in each ring. The anomalous Floquet NHSE is marked by the existence of skin modes at every value of the Floquet quasienergy, allowing for broadband asymmetric transmission. Varying the gain/loss induces a non-Hermitian topological phase transition, reversing the localization direction of the skin modes. An experimental implementation in an acoustic lattice yields good agreement with theoretical predictions, with a very broad relative bandwidth of around 40%.

Periodically driven perturbed CFTs: The sine-Gordon model

We analyze a version of the sine-Gordon model in which the strength of the cosine potential has a periodic dependence on time. This model can be considered as the continuum limit of the many-body generalization of the Kapitza pendulum. Based on the perturbed CFT point of view, we develop a truncated conformal space approach (TCSA) to investigate the Floquet quasienergy spectrum. We focus on the effective behaviour for large driving frequencies, which we also derive exactly. Depending on the driving protocol, we can recover the original sine-Gordon model or its two-frequency version. The rich structure of the two-frequency model implies that the time-periodic drive can break integrability, can lead to new states in the spectrum, or can result in a phase transition. Our method is applicable for any periodically driven perturbed conformal field theories.

Driving Enhanced Quantum Sensing in Partially Accessible Many-Body Systems.

The ground-state criticality of many-body systems is a resource for quantum-enhanced sensing, namely, the Heisenberg precision limit, provided that one has access to the whole system. We show that, for partial accessibility, the sensing capabilities of a block of spins in the ground state reduces to the sub-Heisenberg limit. To compensate for this, we drive the Hamiltonian periodically and use a local steady state for quantum sensing. Remarkably, the steady-state sensing shows a significant enhancement in precision compared to the ground state and even achieves super-Heisenberg scaling for low frequencies. The origin of this precision enhancement is related to the closing of the Floquet quasienergy gap. It is in close correspondence with the vanishing of the energy gap at criticality for ground-state sensing with global accessibility. The proposal is general to all the integrable models and can be implemented on existing quantum devices.

Floquet Spectrum and Dynamics for Non-Hermitian Floquet One-Dimension Lattice Model

Periodically driven non-Hermitian quantum systems have become the center of interest in recent years due to their rich physical phenomena. In this work, we consider a one-dimensional non-Hermitian lattice model induced by partially asymmetric coupling with time-periodic and spatially periodic modulations upon on-site potentials. Within Floquet theorem, we obtain the Floquet quasienergy spectrum of this one-dimensional non-Hermitian system. We show that the robust zero-energy modes exist in the band gap from the real parts of quasienergy spectrum. Compared with the case of no modulations, two pairs of the conjugate imaginary parts are added, which can be attributed to the combined modulations upon the on-site potentials. With the increase of non-Hermitian degree, the imaginary parts of the spectra are enlarged. We also observe the dynamical characteristics that, for different kinds of tunneling amplitudes between lattices, the amplitude of evolution gradually either decays to zero or eventually stabilizes at one particular value. Our protocol, possible to realize in photonic lattices, may facilitate the engineering of novel Floquet topological phases in non-Hermitian systems.

Controlling the direction of topological transport in a non-Hermitian time-reversal symmetric Floquet ladder

We propose a one-dimensional Floquet ladder that possesses two distinct topological transport channels with opposite directionality. The transport channels occur due to a Z2 non-Hermitian Floquet topological phase that is protected by time-reversal symmetry. The signatures of this phase are two pairs of Kramers degenerate Floquet quasienergy bands that are separated by an imaginary gap. We discuss how the Floquet ladder can be implemented in a photonic waveguide lattice and show that the direction of transport in the resulting waveguide structure can be externally controlled by focusing two light beams into adjacent waveguides. The relative phase between the two light beams selects which of the two transport channels is predominantly populated, while the angles of incidence of the two light beams determine which of the transport channels is suppressed by non-Hermitian losses. We identify the optimal lattice parameters for the external control of transport and demonstrate the robustness of this mechanism against disorder.

Solvable Model of a Generic Driven Mixture of Trapped Bose-Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles.

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of interacting bosons of mass driven by a force of amplitude and interacting bosons of mass driven by a force of amplitude , is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces and . As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.

Controlling stable tunneling in a non-Hermitian spin–orbit coupled bosonic junction

In this paper, we study how to apply a periodic driving field to control stable spin tunneling in a non-Hermitian spin–orbit (SO) coupled bosonic double-well system. By means of a high-frequency approximation, we obtain the analytical Floquet solutions and their associated quasienergies and thus construct the general non-Floquet solutions of the dissipative SO coupled bosonic system. Based on detailed analysis of the Floquet quasienergy spectrum, the profound effect of system parameters and the periodic driving field on the stability of spin-dependent tunneling is investigated analytically and numerically for both balanced and unbalanced gain–loss between two wells. Under balanced gain and loss, we find that the stable spin-flipping tunneling is preferentially suppressed with the increase of gain–loss strength. When the ratio of Zeeman field strength to periodic driving frequency Ω/ω is even, there is a possibility that continuous stable parameter regions will exist. When Ω/ω is odd, nevertheless, only discrete stable parameter regions are found. Under unbalanced gain and loss, whether Ω/ω is even or odd, we can get parametric equilibrium conditions for the existence of stable spin tunneling. The results could be useful for the experiments of controlling stable spin transportation in a non-Hermitian SO coupled system.

Destructive Quantum Interference and Exceptional Points in the High-Frequency Response of a Two-State System

We consider the high-frequency conductance of a two-state quantum system within non-equilibrium Green’s function formalism. Multiply connected configurations possessing Fano-Feshbach antiresonances in stationary transmission show a trivial behavior in the dynamical regime. Whereas the simply connected linear configuration, demonstrates an exceptional point in dynamics and destructive quantum interference for frequency equal the energy split between the eigenstates. This is manifestation of “synthetic dimension” introduced by the Floquet quasienergy spectrum.

Entanglement entropy and computational complexity of the periodically driven Anderson impurity model

We study the growth of entanglement entropy and bond dimension with time in density matrix renormalization group simulations of the periodically driven single-impurity Anderson model. The growth of entanglement entropy is found to be related to the ordering of the bath orbitals in the matrix product states of the bath and to the relation of the driving period $T$ to the convergence radius of the Floquet-Magnus expansion. Reordering the bath orbitals in the matrix product state by their Floquet quasi-energy is found to reduce the exponential growth rate of the computation time at intermediate driving periods, suggesting new ways to optimize matrix product state calculations of driven systems.

Floquet engineering to entanglement protection of distant nitrogen vacancy centers

It remains challenging to preserve entanglement between distant solid-state qubits with high-fidelity, such as nitrogen vacancy centers (NVCs). We propose a Floquet engineering strategy to protect the maximal entanglement between two weakly interacting NVCs separated in long spatial distance by locally applying periodic strong driving on the NVCs. It is found that entanglement of the Floquet states of the NVCs resonantly reaches its maximum during the whole driving period at certain values of the driving parameters. Our analysis reveals that it is the occurrence of the avoided level crossing in the Floquet quasienergy spectrum which results in such entanglement resonance. The dissipation effect on the generated entanglement has also been analyzed. Our results may be of both theoretical and experimental interests in exploring the long-lasting entanglement between weakly interacting spins to long distances in realistic environments.

Floquet–Gibbs state in open quantum systems

We study long-time asymptotic states of periodically driven quantum systems coupled to a thermal bath. In order to describe a class of such a system, we introduce the Floquet-Gibbs state, i.e. the state whose density matrix is diagonalized in the basis of the Floquet state of the system Hamiltonian, and its diagonal element obeys the Boltzmann distribution over its Floquet quasienergy. We obtain sufficient conditions for the realization of the Floquet-Gibbs state in a system with infinitesimal system-bath coupling [T. Shirai, et al., Phys. Rev. E 91, 030101 (2015)]. These conditions severely restrict a class of suitable physical models attaining the Floquet-Gibbs state. We also show that some of the conditions can be lifted by imposing conditions on timescales of the thermal bath with the aid of the truncated Floquet Hamiltonian in the Floquet-Magnus expansion [T. Shirai, et al., New Journal of Physics 18, 053008 (2016)]. In this paper we give a overview of this theory and reconsider it by looking at the dynamics from a rotating frame.

Disordered Chern insulator with a two-step Floquet drive

We explore the physics of a Chern insulator subjected to a two step Floquet drive. We analytically obtain the phase diagram and show that the system can exhibit different topological phases characterized by presence and chirality of edge-modes in the two bulk gaps of the Floquet quasienergy spectrum, around $0$ and $\pi$. We find that the phase of the system depends on the mean but not on the amplitude of the drive. The bulk topological invariants characterizing the phases can be extracted by mapping the unitary evolution within a time period to an energetically trivial but topologically non-trivial time evolution. An extensive numerical study of the bulk topological invariants in the presence of quenched disorder reveals new transitions induced by strong disorder (i) from the different topological to trivial insulator phases and (ii) from a trivial to a topological Anderson insulator phase at intermediate disorder strengths. Careful analysis of level statistics of the quasienergy spectrum indicates a `levitation-annihilation' mechanism near these transitions.

Corner transfer matrices for 2D strongly coupled many-body Floquet systems

We develop, based on Baxter’s corner transfer matrices, a renormalizable numerically exact method for computation of the level density of the quasienergy spectra of two-dimensional (2D) locally interacting many-body Floquet systems. We demonstrate its functionality exemplified by the kicked 2D quantum Ising model. Using the method, we are able to treat systems of arbitrarily large finite size (for example lattices of the order of 108 spins). We clearly demonstrate that the density of the Floquet quasienergy spectrum tends to a flat function in the thermodynamic limit for generic values of model parameters. However, contrary to the prediction of random matrices of the circular orthogonal ensemble, the decay rates of the Fourier coefficients of the Floquet level density exhibit rich and non-trivial dependence on the system’s parameters. Remarkably, we find that the method is renormalizable and gives thermodynamically convergent results only in certain regions of the parameter space where the corner transfer matrices have effectively a finite rank for any system size. In the complementary regions, the corner transfer matrices effectively become of full rank and the method becomes non-renormalizable. This may indicate an interesting phase transition from an area- to volume-law of entanglement in the thermodynamic state of a Floquet system.

Maximum population transfer in a periodically driven quantum system

We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which population transfer is optimal and takes place through a series of well defined steps of fixed duration. We also show how the corresponding evolution operator can be approximated at all times by a very simple analytical expression. We propose this model as being specially suitable for treating periodic driving at avoided crossings found in complex multi-level systems, and thus show a relevant application of our results to designing a control protocol in a realistic molecular model

Two dimensional kicked quantum Ising model: dynamical phase transitions

Using an efficient one and two qubit gate simulator operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin model on a two-dimensional lattice, which is periodically driven by a δ-pulsed transverse magnetic field. We consider three different dynamical properties: (i) level density, (ii) level spacing distribution of the Floquet quasienergy spectrum, and (iii) time-averaged autocorrelation function of magnetization components. Varying the parameters of the model, we found transitions between ordered (non-ergodic) and quantum chaotic (ergodic) phases, but the transitions between flat and non-flat spectral density do not correspond to transitions between ergodic and non-ergodic local observables. Even more surprisingly, we found good agreement of level spacing distribution with the Wigner surmise of random matrix theory for almost all values of parameters except where the model is essentially non-interacting, even in regions where local observables are not ergodic or where spectral density is non-flat. These findings question the versatility of the interpretation of level spacing distribution in many-body systems and stress the importance of the concept of locality.

Complex band structure eigenvalue method adapted to Floquet systems: topological superconducting wires as a case study

For systems that can be modeled as a single-particle lattice extended along a privileged direction, such as, for example, quantum wires, the so-called eigenvalue method provides full information about the propagating and evanescent modes as a function of energy. This complex band structure method can be applied either to lattices consisting of an infinite succession of interconnected layers described by the same local Hamiltonian or to superlattices: systems in which the spatial periodicity involves more than one layer. Here, for time-dependent systems subject to a periodic driving, we present an adapted version of the superlattice scheme capable of obtaining the Floquet states and the Floquet quasienergy spectrum. Within this scheme the time periodicity is treated as existing along a spatial dimension added to the original system. The solutions at a single energy for the enlarged artificial system provide the solutions of the original Floquet problem. The method is suited for arbitrary periodic excitations, including strong and anharmonic drivings. We illustrate the capabilities of the methods for both time-independent and time-dependent systems by discussing: (a) topological superconductors in multimode quantum wires with spin–orbit interaction and (b) microwave driven quantum dots in contact with a topological superconductor.

Second-order tunneling of two interacting bosons in a driven triple well

In this study we have investigated the quantum tunneling of two repulsive bosons in a triple-well potential, subject to a high-frequency driving field. By means of the multiple-time-scale asymptotic analysis, we evidence a far-off-resonant strongly interacting regime in which the dominant tunneling of doublons (paired states) is a second-order process and the selected coherent destruction of tunneling occurs either between doublons or between unpaired states. Two Floquet quasienergy bands of both kinds of states are given analytically, where a fine structure up to the second-order corrections is displayed. The analytical results are confirmed numerically, based on the exact model, and may be particularly relevant to controlling correlated tunneling in experiments.

Coherent control of quantum tunneling in an open double-well system

We investigate how to apply a high-frequency driving field to the quantum control of a single particle in an open double-well system. The linear stability analysis points out that the stability depends on the external-field parameters and the loss (or gain) coefficients of the system, and the instability leads to a transition of the Floquet quasienergy from real to complex values and results in decaying probabilities for the particle to be in the double well. By combining analytical solutions in the high-frequency approximation with numerical calculations based on an accurate model, we exhibit quantum-dynamical behavior of the particle such as Floquet oscillation, coherent destruction of tunneling, quasi-NOON-state population, partial one-particle tunneling, and the decay of the probabilities of occupation, which are due to the competition and balance between the quantum coherence and the loss (or gain) effect. The results suggest an experimental method for testing quantum motion in an open system by adjusting the driving field.

Coherent control of atomic tunneling in a driven triple well

Coherent control of quantum tunneling is investigated for a single atom held in a driven triple-well potential without tight-binding approximation. In the high-frequency regime within or without multiphoton resonance, we find the analytical solutions and their numerical correspondences, including the special Floquet states of invariant populations and the non-Floquet states of slowly varying populations. The Floquet quasienergy spectrum exhibits anticrossings and crossings for different values of the driving parameters, which are associated with different tunneling properties described by the non-Floquet states. Applying the presented results, we suggest a scheme for transporting a single atom between nonadjacent wells or between adjacent wells.