Dynamical Franz-Keldysh Effect Research Articles

Dynamical Franz-Keldysh Effect in Diamond in the Deep Ultraviolet Probed by Transient Absorption and Dispersion Spectroscopy Using a Miniature Beamline.

Here, we introduce a miniature beamline for transient absorption and dispersion spectroscopy, using a tailored deep ultraviolet field immediately after the noncollinear generation without subsequent optical elements. We explore the near-band-gap region in diamond in the presence of a few-femtosecond pump pulse where the delayed dynamical Franz-Keldysh effect and the almost instantaneous optical Kerr effect coexist.

Ultrafast transient absorption spectroscopy of the charge-transfer insulator NiO: Beyond the dynamical Franz-Keldysh effect

We demonstrate that a dynamical modification of the Hubbard U in the model charge-transfer insulator NiO can be observed with state-of-the-art time-resolved absorption spectroscopy. Using a self-consistent time-dependent density functional theory plus U computational framework, we show that the dynamical modulation of screening and Hubbard U significantly changes the transient optical spectroscopy. Whereas we find the well-known dynamical Franz-Keldysh effect when the U is frozen, we observe a dynamical band-gap renormalization for dynamical U. The renormalization of the optical gap is found to be smaller than the renormalization of U. This work opens up the possibility of driving a light-induced transition from a charge-transfer into a Mott insulator phase.

Symmetry properties of attosecond transient absorption spectroscopy in crystalline dielectrics

We theoretically investigate a relation between the crystalline symmetry and the transient modulation of optical properties of crystalline dielectrics in pump-probe measurements using intense pump and attosecond probe fields. When the photon energy of the pump field is much below the bandgap energy, the modulation of the optical conductivity is caused by the intraband electronic motion, that is, the dynamical Franz-Keldysh effect. We analytically investigate symmetry properties of the modulated optical conductivity utilizing the Houston function, and derive a formula that relates the temporal oscillation in the absorption with the transformation properties of the modulated optical conductivity. To verify the validity of the formula, we perform real-time first-principles calculations based on the time-dependent density functional theory for a pump-probe process taking 4H-SiC crystal as an example.

Attosecond timing of the dynamical Franz–Keldysh effect

To what extent do intra- or inter-band transitions dominate the optical response of dielectrics when pumped by a few-cycle near-infrared transient electric field? In order to find an answer to this question we investigate the dynamical Franz–Keldysh effect in polycrystalline diamond and discuss in detail the attosecond delay of the induced electron dynamics with regard to the driving transient electric field while the peak intensity is varied between 1 × 1012 and 10 × 1012 W cm−2. We found that the main oscillating feature in transient absorption at 43 eV is in phase with the electric field of the pump, to within 49 ± 78 as. However, the phase delay shows a slightly asymmetric V-shaped linear energy dispersion with a rate of about 200 as eV–1. Theoretical calculations within the dipole approximation reproduce the data and allow us to conclude that intra-band motion dominates under our experimental conditions.

Attosecond transient-absorption spectroscopy in one-dimensional periodic crystals

We investigate theoretically the application of attosecond transient-absorption spectroscopy to a one-dimensional periodic crystal in a regime where the dynamical Franz-Keldysh effect is presented around the energy gap. It is found that in the presence of a few-cycle dressing pulse the delay-dependent absorption spectrogram from the numerically exactly solvable model exhibits a general feature of the V-shaped fringes of subcycle oscillations. This structure represents femtosecond-resolved transient modulation of the conductivity, which is similar to recent experimental observation. We identify a regime where the higher-order even oscillation frequency becomes remarkable in the absorption spectrum for using the midinfrared pump laser. An analytical formula is also developed with the two-band approximation in order to facilitate analysis of the absorption spectrum. Our result shows that the full information on the momentum-dependent band gap across the entire Brillouin zone is encoded into the absorption spectrogram, thus suggesting an all-optical method to reconstruct the one-dimensional gap structure. The reconstruction feasibility is successfully demonstrated by a two-step algorithm even if considering the effect of noise. Moreover, we derive an analytical expression of the delay- and frequency-dependent conductivity with some additional assumptions. Some important features are successfully interpreted in terms of this analytical approach.

Attosecond electro-optic effect in zinc sulfide induced by a laser field

An ultrafast anisotropic electro-optic effect of the zinc sulfide crystal is predicted employing a numerical pump-probe simulation. The numerical results indicate that the time-dependence of the anisotropic response of ZnS exhibits a phase shift with respect to the pump laser field. The phase shift coincides with the time-resolved dynamical Franz-Keldysh effect, which is the modulation of the isotropic part of the dielectric function. While the probe frequency dependence around the band gap is not intense, it becomes intense at higher photon energies of approximately 42~eV.

Ab Initio Simulation of Attosecond Transient Absorption Spectroscopy in Two-Dimensional Materials

We extend the first-principles analysis of attosecond transient absorption spectroscopy to two-dimensional materials. As an example of two-dimensional materials, we apply the analysis to monolayer hexagonal boron nitride (h-BN) and compute its transient optical properties under intense few-cycle infrared laser pulses. Nonadiabatic features are observed in the computed transient absorption spectra. To elucidate the microscopic origin of these features, we analyze the electronic structure of h-BN with density functional theory and investigate the dynamics of specific energy bands with a simple two-band model. Finally, we find that laser-induced intraband transitions play a significant role in the transient absorption even for the two-dimensional material and that the nonadiabatic features are induced by the dynamical Franz–Keldysh effect with an anomalous band dispersion.

Analytical formulation for modulation of time-resolved dynamical Franz-Keldysh effect by electron excitation in dielectrics

Analytical formulation of sub-cycle modulation (SCM) of dielectrics including electron excitation is presented. The SCM is sensitive to not only the time-resolved dynamical Franz-Keldysh effect (Tr-DFKE) [T. Otobe, et al., Phys. Rev. B 93, 045124 (2016)], which is the nonlinear response without the electron excitation, but also the excited electrons. The excited electrons enhance the modulation with even-harmonics of pump laser frequency, and generate the odd-harmonics components. The new aspect of SCM is a consequence of i) the interference between the electrons excited by the pump laser and those excited by the probe pulse laser and ii) oscillation of the generated wave packed by the pump laser. When the probe- and pump-pulse polarizations are parallel, the enhancement of the even harmonics and the generation of the odd harmonics modulation appear. However, if the polarizations are orthogonal, the effect arising from the electron excitations becomes weak. By comparing the parabolic and cosine band models, I found that the electrons under the intense laser field move as quasi-free particles.

Subcycle Response of Dielectrics by the Time-Resolved Dynamical Franz-Keldysh Effect under a Laser Field

Subcycle Response of Dielectrics by the Time-Resolved Dynamical Franz-Keldysh Effect under a Laser Field

Time-resolved dynamical Franz-Keldysh effect produced by an elliptically polarized laser

The analytical formula for the time-resolved dynamical Franz-Keldysh effect (Tr-DFKE) under an elliptically polarized laser in sub-femtosecond time-scale is reported. The Houston function is assumed as the time-dependent wave function of the parabolic two-band system. The resulting formula shows the sub-cycle change of the optical properties for elliptically polarization; the modulation of the dielectric function becomes smaller than that of linear polarization. On the other hand, the subcycle modulation of the dielectric function disappears for a circularly polarized laser, which is a significant feature of the Tr-DFKE. This analytical formulas show good qualitative agreement with the first-principle calculation employing the time-dependent density functional theory for diamond.

Attosecond dynamical Franz-Keldysh effect in polycrystalline diamond.

Short, intense laser pulses can be used to access the transition regime between classical and quantum optical responses in dielectrics. In this regime, the relative roles of inter- and intraband light-driven electronic transitions remain uncertain. We applied attosecond transient absorption spectroscopy to investigate the interaction between polycrystalline diamond and a few-femtosecond infrared pulse with intensity below the critical intensity of optical breakdown. Ab initio time-dependent density functional theory calculations, in tandem with a two-band parabolic model, accounted for the experimental results in the framework of the dynamical Franz-Keldysh effect and identified infrared induction of intraband currents as the main physical mechanism responsible for the observations.

Femtosecond time-resolved dynamical Franz-Keldysh effect

We theoretically investigate the dynamical Franz-Keldysh effect in femtosecond time resolution, that is, the time-dependent modulation of a dielectric function at around the band gap under an irradiation of an intense laser field. We develop a pump-probe formalism in two distinct approaches: first-principles simulation based on real-time time-dependent density functional theory and analytic consideration of a simple two-band model. We find that, while time-average modulation may be reasonably described by the static Franz-Keldysh theory, a remarkable phase shift is found to appear between the dielectric response and the applied electric field.

Mixed regime of light-matter interaction revealed by phase sensitive measurements of the dynamical Franz-Keldysh effect

Significant changes of the optical properties of semiconductors can be observed by applying strong electric fields capable to modify the band structure at equilibrium. This is known as the Franz-Keldysh effect (FKE). Here we study the FKE in bulk GaAs by combining single cycle THz pumps and broadband optical probes. The experiments show that the phase content of the selected electromagnetic pulses can be used to measure the timescales characteristic for the different regimes of matter-light interactions. Furthermore, the present phase-resolved measurements allow to identify a novel regime of saturation where memory effects are of relevance.

Quantum Physics With Ultrabroadband and Intense Terahertz Pulses

We present recent advances in the generation of highly intense multiterahertz transients and their application to nonlinear spectroscopy of bulk semiconductors. An optimized scheme of parametric amplification results in broadband single- or few-cycle terahertz transients with peak electric fields up to 10 or 25 MV/cm, respectively. Time-resolved four-wave mixing terahertz spectroscopy of InSb far away from the interband resonance demonstrates clear signatures of a nonperturbative regime of Rabi flopping. We qualitatively explain the observed behavior within a model of a quantum two-level system. In addition, we demonstrate the dynamical Franz-Keldysh effect in InP resolved on a subcycle timescale. The field-induced modulation of the interband optical absorption at the second harmonic of the driving terahertz field is observed in full agreement with theoretical predictions.

THz Nonlinear Spectroscopy of Solids

We present a review of the recent progress in the generation methods of intense terahertz (THz) single-cycle pulses and their application to THz nonlinear spectroscopy in condensed matters. Special attentions are paid to various aspects of nonlinearity in semiconductors including dynamical Franz-Keldysh effect, ballistic acceleration of free carriers, and coherent control of the exciton system.

Optical response of graphene under intense terahertz fields

Optical responses of graphene in the presence of intense circularly and linearly polarized terahertz fields are investigated based on the Floquet theory. We examine the energy spectrum and density of states. It is found that gaps open in the quasi-energy spectrum due to the single-photon/multi-photon resonances. These quasi-energy gaps are pronounced at small momentum, but decrease dramatically with the increase of momentum and finally tend to be closed when the momentum is large enough. Due to the contribution from the states at large momentum, the gaps in the density of states are effectively closed, in contrast to the prediction in the previous work by Oka and Aoki [Phys. Rev. B {\bf 79}, 081406(R) (2009)]. We also investigate the optical conductivity for different field strengths and Fermi energies, and show the main features of the dynamical Franz-Keldysh effect in graphene. It is discovered that the optical conductivity exhibits a multi-step-like structure due to the sideband-modulated optical transition. It is also shown that dips appear at frequencies being the integer numbers of the applied terahertz field frequency in the case of low Fermi energy, originating from the quasi-energy gaps at small momentums. Moreover, under a circularly polarized terahertz field, we predict peaks in the middle of the "steps" and peaks induced by the contribution from the states around zero momentum in the optical conductivity.

Dynamical Franz–Keldysh effect in GaAs/AlGaAs multiple quantum wells induced by single-cycle terahertz pulses

We studied absorption spectra near the band gap of GaAs/AlGaAs multiple quantum wells subjected to strong single-cycle terahertz pulses. With an increasing terahertz electric field, the heavy-hole 1s exciton energy near the band gap redshifts, reaches a maximum, and turns to blueshift. The blueshift increases proportionally to the ponderomotive energy, i.e., the terahertz electric field squared, which differs from the response expected from the Frantz–Keldysh effect (FKE) in a dc electric field. This fact suggests that the observed ponderomotive energy dependence of the blueshift can be ascribed to the dynamical FKE.

Excitonic optical absorption in semiconductors under intense terahertz radiation

The excitonic optical absorption of GaAs bulk semiconductors under intense terahertz (THz) radiation is investigated numerically. The method of solving initial-value problems, combined with the perfect matched layer technique, is used to calculate the optical susceptibility. In the presence of a driving THz field, in addition to the usual exciton peaks, 2p replica of the dark 2p exciton and even-THz-photon-sidebands of the main exciton resonance emerge in the continuum above the band edge and below the main exciton resonance. Moreover, to understand the shift of the position of the main exciton peak under intense THz radiation, it is necessary to take into consideration both the dynamical Franz–Keldysh effect and ac Stark effect simultaneously. For moderate frequency fields, the main exciton peak decreases and broadens due to the field-induced ionization of the excitons with THz field increasing. However, for high frequency THz fields, the characteristics of the exciton recur even under very strong THz fields, which accords with the recent experimental results qualitatively.

Nonlinear optical properties of semiconductor quantum wells under intense terahertz radiation

The nonlinear optical properties of semiconductor quantum wells driven by intense in-plane terahertz electric fields are investigated theoretically by employing the extended semiconductor Bloch equations. The dynamical Franz-Keldysh effect of the optical absorption near the band edge is analyzed with Coulomb correlation among the carriers included. The in-plane terahertz field induces a variety of behavior in the absorption spectra, including terahertz replicas of the (dark) 2p exciton and terahertz sidebands of the 1s exciton. The dependence of these interesting features on the intensity, frequency, and phase of the terahertz field is explored in detail.

Franz-Keldysh effect and dynamical Franz-Keldysh effect of cylindrical quantum wires

We investigate the interband optical absorption spectra near the band edge of a cylindrical semiconductor quantum wire in the presence of a static electric field and a terahertz electric field polarized along the axis. Optical absorption spectra are nonperturbatively calculated by solving the low-density semiconductor Bloch equations in real space and real time. The influence of the Franz-Keldysh (FK) effect and dynamical FK effect on the absorption spectrum is investigated. To highlight the physics behind the FK effect and dynamical FK effect, the spatiotemporal dynamics of the polarization wave packet are also presented. Under a reasonable static electric field, substantial and tunable absorption oscillations appear above the band gap. A terahertz field, however, will cause the Autler-Townes splitting of the main exciton peak and the emergence of multiphoton replicas. The presented results suggest that semiconductor quantum wires have potential applications in electro-optical devices.