Time-dependent density functional theory for strong electromagnetic fields in crystalline solids

Yabana, Kazuhiro; Sugiyama, Tsukasa; Shinohara, Yuji; Otobe, Tomohito; Bertsch, G. F.

doi:10.1103/physrevb.85.045134

Cited by 234 publications

(241 citation statements)

References 43 publications

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“…Their success can be attributed to the unprecedented balance between accuracy and numerical feasibility [12], which allows us at present to treat several thousands of atoms [13]. Although the different flavors of density-functional theories cover most of the traditional problems of physics and chemistry (including approaches that combine classical Maxwell dynamics with the quantum particles [14][15][16][17][18]), by construction these theories can not treat problems involving the quantum nature of light.…”

Section: Introductionmentioning

confidence: 99%

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

et al. 2014

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In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the densityfunctional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photon field. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.

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Section: Introductionmentioning

confidence: 99%

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

et al. 2014

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“…In Ref. 26, the frequency of the pulse is close to the interband gap, i.e., the system is close to the resonance conditions. Therefore, although the duration of the pulse is small, ∼ 10 fs, the dielectric system experiences a non-adiabatic dynamics with high residual excitation and a strong increase of the pulse reflectance.…”

Section: Introductionmentioning

confidence: 99%

“…[24][25][26]. In these publications, a coupled system of Maxwell equations and timedependent density-functional theory equations is solved numerically for diamond or silicon.…”

Section: Introductionmentioning

confidence: 99%

Theory of dielectric nanofilms in strong ultrafast optical fields

Apalkov

Stockman

2012

Phys. Rev. B

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We theoretically predict that a dielectric nanofilm subjected to a normally-incident strong but ultrashort (a few optical oscillations) laser pulse exhibits deeply nonlinear (non-perturbative) optical responses which are essentially reversible and driven by the instantaneous optical field. Among them is a high optical polarization and a significant population of the conduction band, which develop at the peak of the pulse and almost disappear after its end. There is also a correspondingly large increase of the pulse reflectivity. These phenomena are related to Wannier-Stark localization and anticrossings between the Wannier-Stark ladders originating from the valence and conduction bands leading to optical "softening" of the dielectric. Theory is developed by solving self-consistently the Maxwell equations and the time-dependent Schrödinger equation. The results point out to a fundamental possibility of optical-field effect devices with the bandwidth on the order of optical frequency.

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“…We account for the propagation through the extended system by combining the microscopic SBE solution for the current density J(t) of individual cells with the solution of Maxwell's equations [36] where the cells are placed on a mesoscopic grid along the propagation direction [ A( r, t) → A(X, t)] with grid spacing ∆X = 8 nm and a crystal thickness of up to 1 µm. We use a 5-point stencil for the approximation of the second derivative in space and a standard 4-th order RungeKutta propagator to solve the differential equations in time.…”

mentioning

confidence: 99%

“…We use TDDFT in a real-space real-time implementation [36,37] to simulate the electronic dynamics driven by the strong IR field F (t) employing the adiabatic localdensity approximation (LDA). Alternatively, we implement the SBEs by propagating the elements of the density matrix ρ k mn ,…”

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confidence: 99%

Ab initio multiscale simulation of high-order harmonic generation in solids

et al. 2018

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High-harmonic generation by a highly non-linear interaction of infrared laser fields with matter allows for the generation of attosecond pulses in the XUV spectral regime. This process, well established for atoms, has been recently extended to the condensed phase. Remarkably well pronounced harmonics up to order ∼ 30 have been observed for dielectrics. We present the first ab-initio multiscale simulation of solid-state high-harmonic generation. We find that mesoscopic effects of the extended system, in particular the realistic sampling of the entire Brillouin zone, the pulse propagation in the dense medium, and the inhomogeneous illumination of the crystal have a strong effect on the formation of clean harmonic spectra. Our results provide a novel explanation for the formation of clean harmonics and have implications for a wide range of non-linear optical processes in dense media.PACS numbers: 42.65. Ky, 42.50.Hz, 72.20.Ht The generation of high harmonics (HHG) in the nonlinear interaction of intense ultrashort infrared (IR) laser pulses with matter has turned out to be a highly successful route towards the generation of attosecond pulses in the EUV and XUV spectral regimes [1][2][3][4]. It has become the workhorse of investigation of a vast array of electronic processes on the attosecond time scale [5]. Expanding the range of accessible photon energies and intensities faces, however, fundamental limitations. Experimental and theoretical investigations have established a scaling of the cut-off energy E cut ∝ λ 2 for HHG from atoms in the gas phase raising hopes to reach ever higher photon energies by increasing the wavelength λ of the driving laser pulse. However, the intensity in the cut-off region was found to scale unfavorably I cut ∝ λ −5.3 due to the large spatial dispersion of the electron wave packet upon return to its parent atom [6][7][8][9][10]. Propagation effects in gas filled capillaries have been found to partially offset this suppression at high λ [11].Extending HHG to the condensed phase promises to overcome some of these limitations to enable compact and brighter light sources and to open up the novel field of solid-state photonics on the attosecond scale. The recent observation of HHG in solids for intensities below the damage threshold [12][13][14][15][16][17][18] suggests opportunities for controlling electronic dynamics [16,17] and for an alloptical reconstruction of the band structure [19].The observed solid-state HHG substantially differs from the corresponding atomic spectra. For example, while for atoms the cut-off frequency ω HHG cut scales linearly with the (peak) intensity I 0 of the driving pulse [20,21] One major puzzle has remained so far unresolved: while many experiments display remarkably "clean" harmonic spectra with pronounced peaks near multiples of the driving frequency (odd multiples when inversion symmetry is preserved) all the way up to the cutoff frequency, corresponding simulations display a noisy spectrum lacking any clear harmonic structure over a wide range of fre...

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Time-dependent density functional theory for strong electromagnetic fields in crystalline solids

Cited by 234 publications

References 43 publications

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

Theory of dielectric nanofilms in strong ultrafast optical fields

Ab initio multiscale simulation of high-order harmonic generation in solids

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