Time-periodic Modulation Research Articles

Compare of analytic and numerical solution of parametric oscillator with perturbation and its analytical solution

In this paper we deal with an approximative analytical solution of a second order differential equation with a fast time periodic modulation. We use for this type of the equation a homotopy perturbation method. The validity of this approximative solution is verified by numerical experiments, where we achieve considerable consistency of doth soliutions.

Nonlinearity-induced localization in a periodically driven semidiscrete system.

We demonstrate that nonlinearity plays a constructive role in supporting the robustness of dynamical localization in a system which is discrete in one dimension and continuous in the orthogonal one. In the linear regime, time-periodic modulation of the gradient strength along the discrete axis leads to the usual rapid spread of an initially confined wave packet. Addition of the cubic nonlinearity makes the dynamics drastically different, inducing robust localization of moving wave packets. Similar nonlinearity-induced effects are also produced in the presence of a combination of static and oscillating linear potentials. The predicted dynamical localization in the nonlinear medium can be realized in photonic lattices and Bose-Einstein condensates.

Extracting the quantum metric tensor through periodic driving

We propose a generic protocol to experimentally measure the quantum metric tensor, a fundamental geometric property of quantum states. Our method is based on the observation that the excitation rate of a quantum state directly relates to components of the quantum metric upon applying a proper time-periodic modulation. We discuss the applicability of this scheme to generic two-level systems, where the Hamiltonian's parameters can be externally tuned, and also to the context of Bloch bands associated with lattice systems. As an illustration, we extract the quantum metric of the multiband Hofstadter model. Moreover, we demonstrate how this method can be used to directly probe the spread functional, a quantity which sets the lower bound on the spread of Wannier functions and signals phase transitions. Our proposal offers a universal probe for quantum geometry, which could be readily applied in a wide range of physical settings, ranging from superconducting quantum circuits to ultracold atomic gases.

Stability of temperature modulated convection in a vertical fluid layer

• Time-periodic modulation of boundary temperatures on natural convection is considered. • Floquet analysis of the basic flow is done leading to a generalized eigenvalue problem. • The numerical results are computed using MATLAB programming. • The instability appears in form of harmonic or subharmonic oscillations . • Transition between these oscillations occurs through a bicritical state. We investigate the effect of time periodic oscillations of the boundary temperatures on the onset of natural convection in a fluid layer bounded by two vertical planes. The fluids with Prandtl number up to 12.5 are considered. For these fluids, the mode of instability with constant temperature gradient is the steady convection mode. The parametric instability of the modulated fluid layer is found to appear either in the form of harmonic oscillations or in the form of subharmonic oscillations, depending upon the modulation parameters and the Prandtl number. The transition of the instability between harmonic and subharmonic oscillations occurs via an intermediate bicritical state in which the fluid layer oscillates with coexistence of distinct harmonic and subharmonic wave numbers. A proper tuning of the modulation parameters offers a good control over the mode of instability in the fluid layer.

Resonant Thermalization of Periodically Driven Strongly Correlated Electrons.

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.

Photoinduced half-integer quantized conductance plateaus in topological-insulator/superconductor heterostructures

The past few years have witnessed increased attention to the quest for Majorana-like excitations in the condensed matter community. As a promising candidate in this race, the one-dimensional chiral Majorana edge mode (CMEM) in topological insulator-superconductor heterostructures has gathered renewed interests during recent months after an experimental breakthrough. In this paper, we study the quantum transport of topological insulator-superconductor hybrid devices subject to light-matter interaction or general time-periodic modulation. We report half-integer quantized conductance plateaus at $\frac{1}{2}\frac{e^2}{h}$ and $\frac{3}{2}\frac{e^2}{h}$ upon applying the so-called sum rule in the theory of quantum transport in Floquet topological matter. In particular, in a photoinduced topological superconductor sandwiched between two Floquet Chern insulators, it is found that for each Floquet sideband, the CMEM admits equal probability for normal transmission and local Andreev reflection over a wide range of parameter regimes, yielding half-integer quantized plateaus that resist static and time-periodic disorder. The $\frac{3}{2}\frac{e^2}{h}$ plateau has not yet been computationally or experimentally observed in any other superconducting system, and indicates the possibility to simultaneously create and manipulate multiple pairs of CMEMs by light. The robust half-quantized conductance plateaus, due to CMEMs at quasienergies zero or half the driving frequency, are both fascinating and subtle because they only emerge after a summation over contributions from all Floquet sidebands. Such a distinctive transport signature can thus serve as a hallmark of photoinduced CMEMs in topological insulator-superconductor junctions.

Study of mass transport in rotating couple stress liquid under concentration modulation

A weakly non-linear stability analysis has been performed to examine the effect of time-periodic concentration modulation on the mass transport. We consider an infinite horizontal fluid layer is rotating with angular velocity Ω1 about Z-axis subjected to an imposed time-periodic boundary concentration (ITBC). The concentration gradient between the plates of the fluid layer consists of a steady part and a time-dependent oscillatory part. The concentration of both walls is modulated in this case. We have expanded the infinitesimal disturbances in terms of power series of amplitude of modulation, which is assumed to be small. Ginzburg–Landau equation is obtained to find the rate of mass transfer. It is found that, the effect of Taylor number is to stabilize the system. Effect of Schmidt number and Couple stress parameter on mass transfer are also discussed. Further, it is found that the mass transport can be controlled by suitably adjusting the frequency and amplitude of modulation .

Nonreciprocal Gain in Non-Hermitian Time-Floquet Systems.

We explore the unconventional wave scattering properties of non-Hermitian systems in which amplification or damping are induced by time-periodic modulation. These non-Hermitian time-Floquet systems are capable of nonreciprocal operations in the frequency domain, which can be exploited to induce novel physical phenomena such as unidirectional wave amplification and perfect nonreciprocal response with zero or even negative insertion losses. This unique behavior is obtained by imparting a specific low-frequency time-periodic modulation to the complex coupling between lossless resonators, promoting only upward frequency conversion, and leading to nonreciprocal parametric gain. We provide a full-wave demonstration of our findings in a one-way microwave amplifier, and establish the potential of non-Hermitian time-Floquet devices for insertion-loss free microwave isolation and unidirectional parametric amplification.

Parametric amplification and bidirectional invisibility in PT -symmetric time-Floquet systems

Parity-Time (PT) symmetric wave devices, which exploit balanced interactions between material gain and loss, exhibit extraordinary properties, including lasing and flux-conserving scattering processes. In a seemingly different research field, periodically driven systems, also known as time-Floquet systems, have been widely studied as a relevant platform for reconfigurable active wave control and manipulation. In this article, we explore the connection between PT-symmetry and parametric time-Floquet systems. Instead of relying on material gain, we use parametric amplification by considering a time-periodic modulation of the refractive index at a frequency equal to twice the incident signal frequency. We show that the scattering from a simple parametric slab, whose dynamics follow Mathieu equation, can be described by a PT-symmetric scattering matrix, whose PT-breaking threshold corresponds to the Mathieu instability threshold. By combining different parametric slabs modulated out-of-phase, we create PT-symmetric time-Floquet systems that feature exceptional scattering properties, such as CPA/Laser operation and bidirectional invisibility. These bidirectional properties, rare for regular PT-symmetric systems, are related to a compensation of parametric amplification due to multiple scattering between two parametric systems modulated with a phase difference.

Sensing Floquet-Majorana fermions via heat transfer

Time periodic modulations of the transverse field in the closed XY spin-1/2 chain generate a very rich dynamical phase diagram, with a hierarchy of topological phases characterized by differing numbers of Floquet-Majorana modes. We show that this rich phase diagram survives when the system is coupled to dissipative end reservoirs. Circumventing the obstacle of preparing and measuring quasi energy configurations endemic to Floquet-Majorana detection schemes, we show that stroboscopic heat transport and spin density are robust observables to detect both the dynamical phase transitions and Majorana modes. In particular, we find that the derivative of the heat current, with respect to a control parameter, changes sign at the boundaries separating topological phases with different numbers of Floquet Majorana modes. We present a simple scheme to directly count the number of Floquet-Majorana modes in a phase from the Fourier transform of the local spin density profile. Our results are valid provided the anisotropies are not strong and can be easily implemented in quantum engineered systems.

Nonequilibrium superconductivity in driven alkali-doped fullerides

We investigate the formation of non-equilibrium superconducting states in driven alkali-doped fullerides A$_3$C$_{60}$. Within a minimal three-orbital model for the superconductivity of these materials, it was recently demonstrated theoretically that an orbital-dependent imbalance of the interactions leads to an enhancement of superconductivity at equilibrium [M. Kim et al. Phys. Rev. B 94, 155152 (2016)]. We investigate the dynamical response to a time periodic modulation of this interaction imbalance, and show that it leads to the formation of a transient superconducting state which survives much beyond the equilibrium critical temperature $T_c$. For a specific range of modulation frequencies, we find that the driving reduces superconductivity when applied to a superconducting state below $T_c$, while still inducing a superconducting state when the initial temperature is larger than $T_c$. These findings reinforce the relevance of the interaction-imbalance mechanism as a possible explanation of the recent experimental observation of light-induced superconductivity in alkali-doped fullerenes.

Analytical study of weakly nonlinear mass transfer in rotating fluid layer under time-periodic concentration/gravity modulation

The article deals with a weakly nonlinear stability analysis in rotating fluid subjected to time-periodic concentration/gravity modulation. Navier–Stoke’s momentum equation with Coriolis term has been used to describe the flow. The system is considered rotating about z-axis with uniform angular velocity. We consider three types of imposed time-periodic boundary concentration (ITBC). The effect of time dependent sinusoidal gravitational acceleration i.e. imposed time-periodic gravity modulation (ITGM) is also studied in this problem. In the case of ITBC, the concentration gradient between the plates of the fluid layer consists of a steady part and a time-dependent periodic part. The concentration of both plates is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally imposed time-periodic part. The Ginzburg–Landau amplitude equation is obtained by using power series expansion in terms of the amplitude of modulation, which is assumed to be small. The individual effects of concentration and gravity modulation on mass transports have been investigated in terms of Sherwood number. Further, the effects of various parameters on mass transports have been analyzed and depicted graphically. It is found that the effect of increasing Taylor number is decreases the value of Sherwood number. Effect of Schmidt number and various parameters occurring in the system on mass transfer is also discussed. Further, it is found that the mass transport can be controlled by suitably adjusting the frequency and amplitude of the modulation.

Topological phase transition and charge pumping in a one-dimensional periodically driven optical lattice

Experimental realizations of topological quantum systems and detections of topological invariants in ultracold atomic systems have been a greatly attractive topic. In this work, we propose a scheme to realize topologically different phases in a bichromatic optical lattice subjected to a periodically driven tilt harmonic oscillation, which can be effectively described by a superlattice model with tunable long-range hopping processes. By tuning the ratio of nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes, the system undergoes a topological phase transition accompanied by the change of topological numbers of the lowest band from -1 to 2. Using a slowly time-periodic modulation, the system emerges distinct quantized topological pumped charges (TPCs) of atoms in the filled band for different topological phases. Our scheme is realizable in current cold atomic technique.

Nonlinear stability of modulated Horton–Rogers–Lapwood problem

Nonlinear stability theory is used to investigate free convection arising in a particular class of Horton–Rogers–Lapwood (HRL) problem. Time periodic modulation is imposed on either the temperature at the bounding surfaces or the gravitational field permeating the medium. The Brinkman model and the Boussinesq approximation govern the fluid flow. The energy formulation is followed and the Galerkin method is used to determine the relevant threshold for arbitrary values of the modulational amplitude and frequency. In general it is found that an increase in the modulational amplitude encourages convection ensuing at the threshold. The existence of a subcritical region is predicted and the importance of the nonlinear theory is established.

Effective theory of interacting fermions in shaken square optical lattices

We develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in circularly shaken square lattice with near resonance frequencies, i.e., tuned close to the energy separation between $s$-band and the $p$-bands. First, we derive a time-independent four-band effective Hamiltonian in the non-interacting limit. Diagonalization of the effective Hamiltonian yields a quasi-energy spectrum consistent with the full numerical Floquet solution that includes all higher bands. In particular, we find that the hybridized $s$-band develops multiple minima and therefore non-trivial Fermi surfaces at different fillings. We then obtain the effective interactions for atoms in the hybridized $s$-band analytically and show that they acquire momentum dependence on the Fermi surface even though the bare interaction is contact-like. We apply the theory to find the phase diagram of fermions with weak attractive interactions and demonstrate that the pairing symmetry is $s+d$-wave. Our theory is valid for a range of shaking frequencies near resonance, and it can be generalized to other phases of interacting fermions in shaken lattices.

Loading ultracold gases in topological Floquet bands: the fate of current and center-of-mass responses

Topological band structures can be designed by subjecting lattice systems to time-periodic modulations, as was proposed for irradiated graphene, and recently demonstrated in two-dimensional (2D) ultracold gases and photonic crystals. However, changing the topological nature of Floquet Bloch bands from trivial to non-trivial, by progressively launching the time-modulation, is necessarily accompanied with gap-closing processes: this has important consequences for the loading of particles into a target Floquet band with non-trivial topology, and hence, on the subsequent measurements. In this work, we analyse how such loading sequences can be optimized in view of probing the topology of 2D Floquet bands through transport measurements. In particular, we demonstrate the robustness of center-of-mass responses, as compared to current responses, which present important irregularities due to an interplay between the micro-motion of the drive and inter-band interference effects. The results presented in this work illustrate how probing the center-of-mass displacement of atomic clouds offers a reliable method to detect the topology of Floquet bands, after realistic loading sequences.

Control over few-photon pulses by a time-periodic modulation of the photon emitter coupling

We develop a Floquet scattering formalism for the description of quasistationary states of microwave photons in a one-dimensional waveguide interacting with a nonlinear cavity by means of a periodically modulated coupling. This model is inspired by the recent progress in engineering of tunable coupling schemes with superconducting qubits. We argue that our model can realize the quantum analog of an optical chopper. We find strong periodic modulations of the transmission and reflection envelopes in the scattered few-photon pulses, including photon compression and blockade, as well as dramatic changes in statistics. Our theoretical analysis allows us to explain these nontrivial phenomena as arising from nonadiabatic memory effects.

Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice

Topological quantum matter can be realized by subjecting engineered systems to time-periodic modulations. In analogy with static systems, periodically driven quantum matter can be topologically classified by topological invariants, whose non-zero value guarantees the presence of robust edge modes. In the high-frequency limit of the drive, topology is described by standard topological invariants, such as Chern numbers. Away from this limit, these topological numbers become irrelevant, and novel topological invariants must be introduced to capture topological edge transport. The corresponding edge modes were coined anomalous topological edge modes, to highlight their intriguing origin. Here we demonstrate the experimental observation of these topological edge modes in a 2D photonic lattice, where these propagating edge states are shown to coexist with a quasi-localized bulk. Our work opens an exciting route for the exploration of topological physics in time-modulated systems operating away from the high-frequency regime.

Stability Analysis and Internal Heating Effect on Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium Under Gravity Modulation

In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

Exponential wave-packet spreading via self-interaction time modulation

The time-periodic modulation of the self-interaction of a Bose--Einstein condensate or a nonlinear optics system has been recognized as an exciting tool to explore interesting physics that was previously unavailable. This tool is exploited here to examine the exotic dynamics of a nonlinear system described by the Gross--Pitaevskii equation. We observe three remarkable and closely related dynamical phenomena, exponentially localized profile of wave functions in momentum space with localization length exponentially increasing in time, exponential wave-packet spreading, and exponential sensitivity to initial conditions. A hybrid quantum-classical theory is developed to partly explain these findings. Time-periodic self-interaction modulation is seen to be a robust method to achieve superfast spreading and induce genuine chaos even in the absence of any external potential.