Michelson interferometry of high-order harmonic generation in solids

Abstract

For the high-order harmonic generation in solids, we find a distinct and clean interference pattern in the high-energy end of the spectrum which can be interpreted as a Michelson interferometer of the Bloch electron. Our results are achieved by a numerical solution to the time-dependent Schrödinger equation of the quasi-electron in solids and can be explained by an analytical model based on the principle of the Michelson interferometry. The present study deepens our understanding of the HHG mechanism in crystalline materials and may find potential applications in imaging of the dispersion relation or topological structure of the energy bands in solids.Waveform-controllable short laser pulses have become available in a large range of wavelengths from the x-ray to the THz regime [1][2][3][4][5]. These new light sources have provided us with the feasibilities to trace or even control many ultrafast dynamics happening in the gas, solid, and liquid phase with a simultaneous high temporal and spatial resolution [6][7][8][9][10]. Very recently, currents induced by a waveform-controllable few-cycle laser pulse has been observed in the monolayer graphene [11], which has been interpreted as repeated Landau-Zener transitions.As a typical ultrafast nonlinear phenomena, the highorder harmonic generation (HHG) has attracted intensive investigations and found many applications in the past three decades [12,13]. In very recent years, great experimental and theoretical attention has been paid to the HHG processes in solids [14][15][16][17][18][19][20][21][22]. Various light-fielddriven effects have been explored in both semiconductors [10] and narrow band-gap systems [11]. Some studies have shown the possibilities of potential applications of nonlinear ultrafast phenomena to the material sciences and devices [23][24][25][26][27].The Michelson interferometer has served as a milestone in physics [28] and has shown its great power in many fields of basic research and practical applications. It can be realized by a photon, an electron or other microscopic particles under many circumstances. The Michelson interferometer has enabled multiple breakthroughs in many fields [29][30][31]. The Landau-Zener transition happens between two energy levels when the system is swept accross an avoided crossing [32]. It plays vital roles in various quantum systems and has found many important applications [33][34][35][36]. During the Landau-Zener tunneling, the phase accumulated between the transitions may result in a constructive or destructive interference [37]. These kinds of interferometry have been applied to various systems [38][39][40][41][42]. Some interferometric methods have been * These authors equally contribute to this work. † Corresponding author: liangyou.peng@pku.edu.cn used to measure Berry phases and topological properties of materials [43,44]. In this Letter, by varying the peak intensity of the laser pulse, we identify an unusual overall oscillation in the high-energy end of the harmonic spectra in solids. Our results are based on...

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

“…In the case of the Bloch bands, these effects also include Bloch oscillations, which are the periodic motion of particles in a superlattice subjected to a constant external field. These take place in Bose-Einstein condensates in tilted and driven optical superlattices (Reid et al, 2016;Witthaut et al, 2011), in graphene and topological insulators (Krueckl and Richter, 2012;Sun et al, 2018), in photonic Lieb lattices (Long and Ren, 2017), for trapped ions (Gagge and Larson, 2018), and for the high-order harmonic generation in solids (Jin et al, 2018), and in moiré systems under a uniform magnetic field (Paul et al, 2022).…”

High-order harmonic generation in imperfect crystals

“…Note that breaking the lattice periodicity increases the theoretical complexity, since Bloch's theorem becomes inapplicable and one cannot simply use periodic boundary conditions in calculations. Previous theoretical investigations on HHG in solids are typically based on the semiconductor Bloch equations [12,[20][21][22][23] or the time-dependent Schrödinger equation in single-active-electron (SAE) models [24][25][26][27][28][29][30][31]. In pursuit of going beyond the SAE models, there are also theoretical works that employ many-electron approaches such as the time-dependent density-functional theory (TDDFT) [32][33][34][35][36][37] and the time-dependent Hartree-Fock theory [38].…”

Spectral shift in high-order harmonic generation from periodic potentials

“…The phenomenon that the harmonic intensity is not continuous by increasing the laser peak strength of the laser field has been presented in [27], and an explanation has been given based on the principle of the Michelson interferometer. In our paper, we try to use the TDPI picture to illustrate the appearance of the optical Michelson interference.…”