Entanglement and Squeezing of the Optical Field Modes in High Harmonic Generation.

Squeezed optical fields are a powerful resource for a variety of investigations in basic research and technology. However, the generation of intense squeezed light is challenging. Here, we show that intense squeezed light can be produced using strongly laser driven atoms and the so far unrelated process of high harmonic generation. We demonstrate that when the intensity of the driving field significantly depletes the ground state of the atoms, leading to dipole moment correlations, the quantum state of the driving field and the generated high harmonics are entangled and squeezed. Furthermore, we analyze how the resulting quadrature squeezing of the fundamental laser mode after the interaction can be controlled. The findings open the way for the generation of high intensity squeezed light states for a wide range of applications.

High-harmonic spectroscopy of quantum phase transitions in a high-Tc superconductor.

We report on the nonlinear optical signatures of quantum phase transitions in the high-temperature superconductor YBCO, observed through high harmonic generation. While the linear optical response of the material is largely unchanged when cooling across the phase transitions, the nonlinear optical response sensitively imprints two critical points, one at the critical temperature of the cuprate with the exponential growth of the surface harmonic yield in the superconducting phase and another critical point, which marks the transition from strange metal to pseudogap phase. To reveal the underlying microscopic quantum dynamics, a strong-field quasi-Hubbard model was developed, which describes the measured optical response dependent on the formation of Cooper pairs. Further, the theory provides insight into the carrier scattering dynamics and allows us to differentiate between the superconducting, pseudogap, and strange metal phases. The direct connection between nonlinear optical response and microscopic dynamics provides a powerful methodology to study quantum phase transitions in correlated materials. Further implications are light wave control over intricate quantum phases, light-matter hybrids, and application for optical quantum computing.

High Photon Number Entangled States and Coherent State Superposition from the Extreme Ultraviolet to the Far Infrared.

We present a theoretical demonstration on the generation of entangled coherent states and of coherent state superpositions, with photon numbers and frequencies orders of magnitude higher than those provided by the current technology. This is achieved by utilizing a quantum mechanical multimode description of the single- and two-color intense laser field driven process of high harmonic generation in atoms. It is found that all field modes involved in the high harmonic generation process are entangled, and upon performing a quantum operation, lead to the generation of high photon number optical cat states spanning from the far infrared to the extreme ultraviolet spectral region. This provides direct insights into the quantum mechanical properties of the optical field in the intense laser matter interaction. Finally, these states can be considered as a new resource for fundamental tests of quantum theory, quantum information processing, or sensing with nonclassical states of light.

Conservation laws for electron vortices in strong-field ionisation.

ABSTRACT: We investigate twisted electrons with a well-defined orbital angular momentum, which have been ionised via a strong laser field. By formulating a new variant of the well-known strong field approximation, we are able to derive conservation laws for the angular momenta of twisted electrons in the cases of linear and circularly polarised fields. In the case of linear fields, we demonstrate that the orbital angular momentum of the twisted electron is determined by the magnetic quantum number of the initial bound state. The condition for the circular field can be related to the famous ATI peaks, and provides a new interpretation for this fundamental feature of photoelectron spectra. We find the length of the circular pulse to be a vital factor in this selection rule and, employing an effective frequency, we show that the photoelectron OAM emission spectra are sensitive to the parity of the number of laser cycles. This work provides the basic theoretical framework with which to understand the OAM of a photoelectron undergoing strong field ionisation.

Effective super-bandwidth in laser pulses.

We present here a theoretical analysis of the interaction between an ideal two-level quantum system and a super-oscillatory pulse, like the one proposed and successfully synthesized in [J. Opt.23, 075604 (2021)JOOPDB0150-536X10.1088/2040-8986/abfedf; arXiv:2106.09192 (2021)]. As a prominent feature, these pulses present a high efficiency of the central super-oscillatory region in relation to unavoidable sidelobes. Our study shows an increase in the effective bandwidth of the pulse in the super-oscillatory region, and not only the appearance of a local frequency higher than its highest Fourier-frequency component, as in the usual description of the phenomenon of super-oscillations. Beyond introducing the concept of effective super-bandwidth, the presented results could be relevant for experimental applications and opening new perspectives for laser-matter interaction.

Three-electron correlations in strong laser field ionization.

Strong field processes involving several active electrons reveal unambiguous dynamical signatures of the Pauli principle importance even in the nonrelativistic regime. We exemplify this statement studying three active electrons model atoms interacting with strong pulsed radiation, using an ab-initio time-dependent Schrödinger equation on a grid. In our restricted dimensionality model we are able to analyze momenta correlations of the three outgoing electrons using Dalitz plots. The different symmetries of the electronic wavefunctions, directly related to the initial state spin components, appear clearly visible.

A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation.

A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrödinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one- or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from 5 × 1013 W/cm2 to 5 × 1014 W/cm2. We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.

Extraction of higher-order nonlinear electronic response in solids using high harmonic generation.

Nonlinear susceptibilities are key to ultrafast lightwave driven optoelectronics, allowing petahertz scaling manipulation of the signal. Recent experiments retrieved a 3rd order nonlinear susceptibility by comparing the nonlinear response induced by a strong laser field to a linear response induced by the otherwise identical weak field. The highly nonlinear nature of high harmonic generation (HHG) has the potential to extract even higher order nonlinear susceptibility terms. However, up till now, such characterization has been elusive due to a lack of direct correspondence between high harmonics and nonlinear susceptibilities. Here, we demonstrate a regime where such correspondence can be clearly made, extracting nonlinear susceptibilities (7th, 9th, and 11th) from sapphire of the same order as the measured high harmonics. The extracted high order susceptibilities show angular-resolved periodicities arising from variation in the band structure with crystal orientation. Our results open a door to multi-channel signal processing, controlled by laser polarization.

Symphony on strong field approximation.

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagiellonski, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum-continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60.

Optical Control of Young's Type Double-slit Interferometer for Laser-induced Electron Emission from a Nano-tip.

Interference experiments with electrons in a vacuum can illuminate both the quantum and the nanoscale nature of the underlying physics. An interference experiment requires two coherent waves, which can be generated by splitting a single coherent wave using a double slit. If the slit-edge separation is larger than the coherence width at the slit, no interference appears. Here we employed variations in surface barrier at the apex of a tungsten nano-tip as slits and achieved an optically controlled double slit, where the separation and opening-and-closing of the two slits can be controlled by respectively adjusting the intensity and polarization of ultrashort laser pulses. Using this technique, we have demonstrated interference between two electron waves emitted from the tip apex, where interference has never been observed prior to this technique because of the large slit-edge separation. Our findings pave the way towards simple time-resolved electron holography on e.g. molecular adsorbates employing just a nano-tip and a screen.

Strong-Field Resonant Dynamics in Semiconductors.

We predict that a direct band gap semiconductor (GaAs) resonantly excited by a strong ultrashort laser pulse exhibits a novel regime: kicked anharmonic Rabi oscillations. In this regime, Rabi oscillations are strongly coupled to intraband motion, and interband transitions mainly take place when electrons pass near the Brillouin zone center where electron populations undergo very rapid changes. The asymmetry of the residual population distribution induces an electric current controlled by the carrier-envelope phase of the driving pulse. The predicted effects are experimentally observable using photoemission and terahertz spectroscopies.

Suppression of photoionization by a static field.

The dc field Stark effect is studied theoretically for atoms in high intensity laser fields. We prove that the first-order perturbation corrections for the energy and photoionization rate vanish when the dc field strength serves as a perturbational strength parameter. Our calculations show that by applying a dc field in the same direction as the polarization direction of the ac field, the photoinduced ionization rate is almost entirely suppressed. This suppression is attributed to changes in the phase shift of the continuum atomic wave functions which can be controlled by the dc field.