Nondipole effects in the atomic dynamic interference are investigated by numerically solving the time-dependent Schrödinger equation (TDSE) of hydrogen. It is found that the inclusion of nondipole corrections in the TDSE can induce momentum shifts of photoelectrons in the opposite direction of the laser propagation. The magnitude of the momentum shift is roughly proportional to the laser peak intensity and to the momentum component of the photoelectron along the laser propagation. By including the nondipole corrections of the Volkov phase into a semi-analytical model previously developed under the dipole approximation, all the main features of the momentum shifts can be nicely reproduced. Through an analytic expression, the origin of such momentum shifts is attributed to the nondipole phase difference between the two electron wave packets ejected in the rising edge and the falling edge, which will interfere with each other and result in the final fringe pattern. One important consequence of such momentum shifts is that they can smooth out the peak splitting induced by the dynamic interference in the photoelectron energy spectrum. Nevertheless, it should be emphasized that the dynamic interference persists in the photoelectron momentum distributions and is not suppressed at all for the laser parameters considered in this work.

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In this review, we will focus on recent progress on the investigations of nondipole effects in few-electron atoms and molecules interacting with light fields. We first briefly survey several popular theoretical methods and relevant concepts in strong field and attosecond physics beyond the dipole approximation. Physical phenomena stemming from the breakdown of the dipole approximation are then discussed in various topics, including the radiation pressure and photon-momentum transfer, the atomic stabilization, the dynamic interference, and the high-order harmonic generation. Whenever available, the corresponding experimental observations of these nondipole effects are also introduced respectively in each topics.

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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...