arXiv subjects

Tatsuhiko N. Ikeda

Publications and source records attributed to Tatsuhiko N. Ikeda.

At least 37 records · Page 2Linked to original sources

arXiv2021

Analytical WKB theory for high-harmonic generation and its application to massive Dirac electrons

We propose an analytical approach to high-harmonic generation (HHG) for nonperturbative low-frequency and high-intensity fields based on the (Jeffreys-)Wentzel-Kramers-Brillouin (WKB) approximation. By properly taking into account Stokes phenomena of WKB solutions, we obtain wavefunctions that systematically include the repetitive dynamics of production and acceleration of electron-hole pairs and quantum interference due to phase accumulation between different pair production times (Stückelberg phase). Using the obtained wavefunctions without relying on any phenomenological assumptions, we explicitly compute electric current (including intra- and inter-band contributions) as the source of HHG for a massive Dirac system in (1+1)-dimensions under an ac electric field. We demonstrate that the WKB approximation agrees well with numerical results obtained by solving the time-dependent Schrödinger equation and point out that the quantum interference is important in HHG. We also predict in the deep nonperturbative regime that (1) harmonic intensities oscillate with respect to electric-field amplitude $E_0$ and frequency $Ω$, with a period determined by the Stückelberg phase; (2) the cutoff order of HHG is determined by $2eE_0/\hbar Ω^2$, with $e$ being the electron charge; and that (3) non-integer harmonics, controlled by the Stückelberg phase, appear as a transient effect. Our WKB theory is particularly suited for a parameter regime, where the Keldysh parameter $γ=(Δ/2)Ω/eE_0$, with $Δ$ being the gap size, is small. This parameter regime corresponds to intense lasers in the terahertz regime for realistic massive Dirac materials. Our analysis implies that the so-called HHG plateau can be observed at the terahertz frequency within the current technology.

cond-mat.str-el↗

arXiv2021

Fermi's golden rule for heating in strongly driven Floquet systems

We study heating dynamics in isolated quantum many-body systems driven periodically at high frequency and large amplitude. Combining the high-frequency expansion for the Floquet Hamiltonian with Fermi's golden rule (FGR), we develop a master equation termed the Floquet FGR. Unlike the conventional one, the Floquet FGR correctly describes heating dynamics, including the prethermalization regime, even for strong drives, under which the Floquet Hamiltonian is significantly dressed, and nontrivial Floquet engineering is present. The Floquet FGR depends on system size only weakly, enabling us to analyze the thermodynamic limit with small-system calculations. Our results also indicate that, during heating, the system approximately stays in the thermal state for the Floquet Hamiltonian with a gradually rising temperature.

cond-mat.stat-mech↗

arXiv2021

Linear and Nonlinear Optical Responses in Kitaev Spin Liquids

We theoretically study THz-light-driven high-harmonic generation (HHG) in the spin-liquid states of the Kitaev honeycomb model with a magnetostriction coupling between spin and electric polarization. To compute the HHG spectra, we numerically solve the Lindblad equation, taking account of the dissipation effect. We find that isotropic Kitaev models possess a dynamical symmetry, which is broken by a static electric field, analogous to HHG in electron systems. We show that the HHG spectra exhibit characteristic continua of Majorana fermion excitations, and their broad peaks can be controlled by applying static electric or magnetic fields. In particular, the magnetic-field dependence of the HHG spectra drastically differs from those of usual ordered magnets. These results indicate that an intense THz laser provides a powerful tool to observe dynamic features of quantum spin liquids.

cond-mat.str-el↗

arXiv2020

Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems

The generalized Gibbs ensemble (GGE), which involves multiple conserved quantities other than the Hamiltonian, has served as the statistical-mechanical description of the long-time behavior for several isolated integrable quantum systems. The GGE may involve a noncommutative set of conserved quantities in view of the maximum entropy principle, and show that the GGE thus generalized (noncommutative GGE, NCGGE) gives a more qualitatively accurate description of the long-time behaviors than that of the conventional GGE. Providing a clear understanding of why the (NC)GGE well describes the long-time behaviors, we construct, for noninteracting models, the exact NCGGE that describes the long-time behaviors without an error even at finite system size. It is noteworthy that the NCGGE involves nonlocal conserved quantities, which can be necessary for describing long-time behaviors of local observables. We also give some extensions of the NCGGE and demonstrate how accurately they describe the long-time behaviors of few-body observables.

cond-mat.stat-mech↗

arXiv2020

Time Crystals Protected by Floquet Dynamical Symmetry in Hubbard Models

We investigate an unconventional symmetry in time-periodically driven systems, the Floquet dynamical symmetry (FDS). Unlike the usual symmetries, the FDS gives symmetry sectors that are equidistant in the Floquet spectrum and protects quantum coherence between them from dissipation and dephasing, leading to two kinds of time crystals: the discrete time crystal and discrete time quasicrystal that have different periodicity in time. We show that these time crystals appear in the Bose- and Fermi-Hubbard models under ac fields and their periodicity can be tuned only by adjusting the strength of the field. These time crystals arise only from the FDS and thus appear in both dissipative and isolated systems and in the presence of disorder as long as the FDS is respected. We discuss their experimental realizations in cold atom experiments and generalization to the SU($N$)-symmetric Hubbard models.

cond-mat.stat-mech↗

arXiv2020

High-order nonlinear optical response of a twisted bilayer graphene

Focusing on the twist angle for the minimal commensurate structure, we perform nonperturbative calculations of electron dynamics in the twisted bilayer graphene (TBG) under intense laser fields. We show that the TBG exhibits enriched high-harmonic generation that cannot occur in monolayer or conventional bilayers. We elucidate the mechanism of these nonlinear responses by analyzing dynamical symmetries, momentum-resolved dynamics, and roles of interlayer coupling. Our results imply nonlinear "optotwistronics," or controlling optical properties of layered materials by artificial twists.

cond-mat.str-el↗

arXiv2020

General description for nonequilibrium steady states in periodically driven dissipative quantum systems

Laser technology has developed and accelerated photo-induced nonequilibrium physics from both scientific and engineering viewpoints. The Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is a forefront of quantum physics of light-matter interaction, but limited to ideal dissipationless systems. For the Floquet engineering extended to a variety of materials, it is vital to understand the quantum states emerging in a balance of the periodic drive and energy dissipation. Here we derive the general description for nonequilibrium steady states (NESS) in periodically driven dissipative systems by focusing on the systems under high-frequency drive and time-independent Lindblad-type dissipation with the detailed balance condition. Our formula correctly describes the time-average, fluctuation, and symmetry property of the NESS, and can be computed efficiently in numerical calculations. Our approach will play fundamental roles in Floquet engineering in a broad class of dissipative quantum systems such as atoms and molecules, mesoscopic systems, and condensed matter.

cond-mat.stat-mech↗

arXiv2020

Efficient Terahertz Harmonic Generation with Coherent Acceleration of Electrons in the Dirac Semimetal Cd3As2

We report strong terahertz (~10^12 Hz) high harmonic generation in thin films of Cd3As2, a three-dimensional Dirac semimetal at room temperature. The third harmonics is detectable with tabletop light source and can be as strong as 100 V/cm by applying the fundamental field of 6.5 kV/cm inside the film, showing an unprecedented efficiency for terahertz frequency conversion. Our time-resolved terahertz spectroscopy and calculations also clarify the microscopic mechanism of the nonlinearity originating in the coherent acceleration of Dirac electrons in momentum space. Our results provide clear insights for nonlinear current of Dirac electrons driven by terahertz field under an influence of scattering, paving the way toward novel devices for high-speed electronics and photonics based on topological semimetals.

cond-mat.mtrl-sci↗

arXiv2020

High-harmonic generation by electric polarization, spin current, and magnetization

High-harmonic generation (HHG), a typical nonlinear optical effect, has been actively studied in electron systems such as semiconductors and superconductors. As a natural extension, we theoretically study HHG from electric polarization, spin current and magnetization in magnetic insulators under terahertz (THz) or gigahertz (GHz) electromagnetic waves. We use simple one-dimensional spin chain models with or without multiferroic coupling between spins and the electric polarization, and study the dynamics of the spin chain coupled to an external ac electric or magnetic field. We map spin chains to two-band fermions and invoke an analogy of semiconductors and superconductors. With a quantum master equation and Lindblad approximation, we compute the time evolution of the electric polarization, spin current, and magnetization, showing that they exhibit clear harmonic peaks. We also show that the even-order HHG by magnetization dynamics can be controlled by static magnetic fields in a wide class of magnetic insulators. We propose experimental setups to observe these HHG, and estimate the required strength of the ac electric field $E_0$ for detection as $E_0\sim100$kV/cm--1MV/cm, which corresponds to the magnetic field $B_0\sim0.1$T--1T. The estimated strength would be relevant also for experimental realizations of other theoretically-proposed nonlinear optical effects in magnetic insulators such as Floquet engineering of magnets.

cond-mat.str-el↗

arXiv2019

Disorder Effects on the Origin of High-Order Harmonic Generation in Solids

We consider noninteracting electrons coupled to laser fields, and study perturbatively the effects of the lattice potential involving disorder on the harmonic components of the electric current, which are sources of high-order harmonic generation (HHG). By using the Floquet-Keldysh Green functions, we show that each harmonic component consists of the coherent and the incoherent parts, which arise respectively from the coherent and the incoherent scatterings by the local ion potentials. As the disorder increases, the coherent part decreases, the incoherent one increases, and the total harmonic component of the current first decreases rapidly and then approaches a nonzero value. Our results highlight the importance of the periodicity of crystals, which builds up the Bloch states extending over the solid. This is markedly different from the traditional HHG in atomic gases, where the positions of individual atoms are irrelevant.

cond-mat.dis-nn↗

arXiv2019

Generation of dc, ac, and second-harmonic spin currents by electromagnetic fields in an inversion-asymmetric antiferromagnet

Manipulating spin currents in magnetic insulators is a key technology in spintronics. We theoretically study a simple inversion-asymmetric model of quantum antiferromagnets, where both the exchange interaction and the magnetic field are staggered. We calculate spin currents generated by external electric and magnetic fields by using a quantum master equation. We show that an ac electric field with amplitude $E_0$ leads, through exchange-interaction modulation, to the dc and second-harmonic spin currents proportional to $E_0^2$. We also show that dc and ac staggered magnetic fields $B_0$ generate the dc and ac spin currents proportional to $B_0$, respectively. We elucidate the mechanism by an exactly solvable model, and thereby propose the ways of spin current manipulation by electromagnetic fields.

cond-mat.mes-hall↗

arXiv2019

Origin of Stripe and Quasi-Stripe CDW Structures in Monolayer MX$ _2$ compounds: Multivalley Free Energy Landscape

Ultrathin sheets of transition metal dichalcogenides (MX$ _2$) with charge density waves (CDWs) is increasingly gaining interest as a promising candidate for graphene-like devices. Although experimental data including stripe/quasi-stripe structure and hidden states have been reported, the ground state of ultrathin MX$ _2$ compounds and, in particular, the origin of anisotropic (stripe and quasi-stripe) CDW phases is a long-standing problem. Anisotropic CDW phases have been explained by Coulomb interaction between domain walls and inter-layer interaction. However, these models assume that anisotropic domain walls can exist in the first place. Here, we report that anisotropic CDW domain walls can appear naturally without assuming anisotropic interactions: We explain the origin of these phases by topological defect theory (line defects in a two-dimensional plane) and interference between harmonics of macroscopic CDW wave functions. We revisit the McMillan-Nakanishi-Shiba model for monolayer 1$T$-TaS$ _2$ and 2$H$-TaSe$ _2$ and show that CDWs with wave vectors that are separated by $120^\circ$ (i.e. the three-fold rotation symmetry of the underlying lattice) contain a free-energy landscape with many local minima. Then, we remove this $120^\circ$ constraint and show that free energy local minima corresponding to the stripe and quasi-stripe phase appear. Our results imply that Coulomb interaction between domain walls and inter-layer interaction may be secondary factors for the appearance of these phases. Furthermore, this model can predict new CDW phases, hence it may become the basis to study CDW further. We anticipate our results to be a starting point for further study in two-dimensional physics, such as explanation of "Hidden CDW states", study the interplay between supersolid symmetry and lattice symmetry, and application to other van der Waals structures.

cond-mat.mtrl-sci↗

arXiv2018

Photoinduced Dynamics of Commensurate Charge Density Wave in 1T-TaS$_{2}$ Based on Three-Orbital Hubbard Model

We study the coupled charge-lattice dynamics in the commensurate charge density wave (CDW) phase of the layered compound 1T-TaS$_{2}$ driven by an ultrashort laser pulse. For describing its electronic structure, we employ a tight-binding model of previous studies including the effects of lattice distortion associated with the CDW order. We further add on-site Coulomb interactions and reproduce an energy gap at the Fermi level within a mean-field analysis. On the basis of coupled equations of motion for electrons and the lattice distortion, we numerically study their dynamics driven by an ultrashort laser pulse. We find that the CDW order decreases and even disappears during the laser irradiation while the lattice distortion is almost frozen. We also find that the lattice motion sets in on a longer time scale and causes a further decrease in the CDW order even after the laser irradiation.

cond-mat.str-el↗

arXiv2018

Floquet-Theoretical Formulation and Analysis of High-Harmonic Generation in Solids

By using the Floquet eigenstates, we derive a formula to calculate the high-harmonic components of the electric current (HHC) in the setup where a monochromatic laser field is turned on at some time. On the basis of this formulation, we study the HHC spectrum of electrons on a one-dimensional chain with the staggered potential to study the effect of multiple sites in the unit cell such as the systems with charge density wave (CDW) order. With the help of the solution for the Floquet eigenstates, we analytically show that two plateaus of different origins emerge in the HHC spectrum. The widths of these plateaus are both proportional to the field amplitude, but inversely proportional to the laser frequency and its square, respectively. We also show numerically that multi-step plateaus appear when both the field amplitude and the staggered potential are strong.

cond-mat.other↗

arXiv2018

Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries

We numerically study the unitary time evolution of a nonintegrable model of hard-core bosons with an extensive number of local Z2 symmetries. We find that the expectation values of local observables in the stationary state are described better by the generalized Gibbs ensemble (GGE) than by the canonical ensemble. We also find that the eigenstate thermalization hypothesis fails for the entire spectrum, but holds true within each symmetry sector, which justifies the GGE. In contrast, if the model has only one global Z2 symmetry or a size-independent number of local Z2 symmetries, we find that the stationary state is described by the canonical ensemble. Thus, the GGE is necessary to describe the stationary state even in a nonintegrable system if it has an extensive number of local symmetries.

cond-mat.stat-mech↗

arXiv2018

Revisiting the Floquet-Bloch theory for an exactly solvable model of one-dimensional crystals in strong laser fields

We revisit the Floquet-Bloch eigenstates of a one-dimensional electron gas in the presence of the periodic Kronig-Penny potential and an oscillating electric field. Considering the appropriate boundary conditions for the wave function and its derivative, we derive the determining equations for the Floquet-Bloch eigenstates, which are represented by a single-infinite matrix rather than a double-infinite matrix needed for a generic potential. We numerically solve these equations, showing that there appear anticrossings at the crossing points of the different Floquet bands as well as the band gaps at the edges and the center of the Brillouin zone. We also calculate the high-harmonic components of the electric current carried by the Floquet-Bloch eigenstates, showing that the harmonic spectrum shows a plateau for a strong electric field.

physics.optics↗

arXiv2018

Thermalization and prethermalization in isolated quantum systems: a theoretical overview

The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal system to study the nonequilibrium dynamics in isolated quantum systems, triggering intensive recent theoretical endeavors on this fundamental subject. Besides thermalization, many isolated quantum systems show intriguing behavior in relaxation processes, especially prethermalization. Prethermalization occurs when there is a clear separation in relevant time scales and has several different physical origins depending on individual systems. In this review, we overview theoretical approaches to the problems of thermalization and prethermalization.

cond-mat.stat-mech↗

arXiv2018

Exploring the Kondo model in and out of equilibrium with alkaline-earth atoms

We propose a scheme to realize the Kondo model with tunable anisotropy using alkaline-earth atoms in an optical lattice. The new feature of our setup is Floquet engineering of interactions using time-dependent Zeeman shifts, that can be realized either using state-dependent optical Stark shifts or magnetic fields. The properties of the resulting Kondo model strongly depend on the anisotropy of the ferromagnetic interactions. In particular, easy-plane couplings give rise to Kondo singlet formation even though microscopic interactions are all ferromagnetic. We discuss both equilibrium and dynamical properties of the system that can be measured with ultracold atoms, including the impurity spin susceptibility, the impurity spin relaxation rate, as well as the equilibrium and dynamical spin correlations between the impurity and the ferromagnetic bath atoms. We analyze the non-equilibrium time evolution of the system using a variational non-Gaussian approach, which allows us to explore coherent dynamics over both short and long timescales, as set by the bandwidth and the Kondo singlet formation, respectively. In the quench-type experiments, when the Kondo interaction is suddenly switched on, we find that real-time dynamics shows crossovers reminiscent of poor man's renormalization group flow used to describe equilibrium systems. For bare easy-plane ferromagnetic couplings, this allows us to follow the formation of the Kondo screening cloud as the dynamics crosses over from ferromagnetic to antiferromagnetic behavior. On the other side of the phase diagram, our scheme makes it possible to measure quantum corrections to the well-known Korringa law describing the temperature dependence of the impurity spin relaxation rate. Theoretical results discussed in our paper can be measured using currently available experimental techniques.

cond-mat.quant-gas↗