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Physical Review A

Dramatic enhancement of high-order-harmonic generation via the quantum interference of dipole-transition paths

Di Zhao, Chenwei Jiang, Fuli Li

Published Mar 27, 2015• 2 citations
Publisher

Abstract

We present a theoretical study of the high-order-harmonic generation (HHG) from coherent superposition states of a three-level system driven by monochromatic cw laser fields. The HHG spectrum can be enhanced by about ${10}^{5}$ times via tuning the relative phase between the states which are initially prepared. Even if the ionization effects are taken into account, the enhancement factors are still up to about ${10}^{2}$ times. The enhancement is interpreted as the quantum constructive interference of different dipole transitions between quasienergy states. To realize the interference, the intensity of the driving laser field is chosen such that frequencies of the harmonics generated from the different dipole-transition paths, which are dependent on the ac Stark shifted energy separation of quasienergy states, are equal to each other. Moreover, the case studies of HHG spectra from a coherent superposition state of a three-level system show that the enhancement of harmonics is closely related to the harmonic strengths of the dipole transitions, as well as the parity of quasienergy states which are involved in the dipole-transition paths. The reduction of enhancement factors due to ionization effects is also qualitatively analyzed.

DOI
10.1103/physreva.91.033414

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We present a theoretical study of the high-order-harmonic generation (HHG) from coherent superposition states of a three-level system driven by monochromatic cw laser fields. The HHG spectrum can be enhanced by about 105{10}^{5}105 times via tuning the relative phase between the states which are initially prepared. Even if the ionization effects are taken into account, the enhancement factors are still up to about 102{10}^{2}102 times. The enhancement is interpreted as the quantum constructive interference of different dipole transitions between quasienergy states. To realize the interference, the intensity of the driving laser field is chosen such that frequencies of the harmonics generated from the different dipole-transition paths, which are dependent on the ac Stark shifted energy separation of quasienergy states, are equal to each other. Moreover, the case studies of HHG spectra from a coherent superposition state of a three-level system show that the enhancement of harmonics is closely related to the harmonic strengths of the dipole transitions, as well as the parity of quasienergy states which are involved in the dipole-transition paths. The reduction of enhancement factors due to ionization effects is also qualitatively analyzed.
This paper presents an analytical study of high-order harmonic generation (HHG) by quantum systems possessing permanent dipole moments (PDMs), such as atoms/molecules placed in a static electric field or polar molecules. HHG by conventional, non-PDM systems typically demonstrated a plateau in the envelope of harmonics followed by a steep fall in harmonic intensities when the harmonic number exceeds a certain threshold. This paper shows that the HHG by PDM systems results in a significant extension of the plateau to higher frequencies and a slower decline of intensities at frequencies higher than the end of the plateau . Moreover, there occurs a substantial growth of the total, summed intensity of all components of the scattering spectrum . Other physically interesting distinctive features of the HHG by PDM systems are: the presence of both odd and even harmonics of the laser frequency in the scattering spectrum; a triplet structure of both odd and even harmonics; and the appearance of a component at the doubled Rabi frequency (i.e. at a frequency much lower than the laser frequency). The results are obtained by using the adiabatic basis for the analysis of a multi-quantum resonance in a two-level system possessing PDMs.
Abstract Linearity is a fundamental postulate of quantum mechanics which is occasionally the subject of debate. This paper investigates the possibility of checking this assumption by using a laser field. We study the corrections caused by the presence of a small nonlinearity in the Hamiltonian of a quantum system. As a model we use a simplified two-level quantum system whose states are coupled by a small off-diagonal term proportional to the population of the upper level. The nonlinearity causes spontaneous decay of the upper level, shift and broadening of the line and the sensitive dependence of the final state on the initial condition. The presence of a strong laser field, resonant with the atomic transition, enhances the population transfer among the levels and introduces quantitative and qualitative modifications of the spectra of high order harmonic generation (HHG); these are cumulative effects which can be subject to experimental checks. Experiments are needed in order to set an upper limit to the nonlinear term.
High-harmonic generation (HHG) involves the up-conversion of a high-intensity driving field into its harmonic orders. This process is intrinsically nonclassical, requiring from quantum mechanics for a complete explanation as, under suitable conditions, involves phenomena such as particle tunneling through a potential barrier. When exposed to a high-intensity, low-frequency laser field, bound electrons ionize via tunneling, accelerate under the driving field, and recombine with the parent ion, emitting high-harmonic radiation. However, electrons can follow two distinct pathways, short and long trajectories, during these steps. In this work, we evaluate the signatures left by these trajectories on the quantum-optical state after HHG, and observe that they lead to entanglement between the driving field and the generated harmonics. By leveraging these correlations, we use harmonic generation to herald the creation of optical Schr\"odinger-cat-like states in the driving field. Additionally, using an ab initio approach, we examine how propagation effects, which spatially separate the harmonic contributions from short and long trajectories, influence the nonclassical characteristics of the emitted light.
We present a theoretical investigation of the multiphoton resonance dynamics driven by intense frequency-comb and cavity-mode fields inside a femtosecond enhancement cavity (fsEC). The many-mode Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and laser fields. The quasienergy structure driven by the frequency-comb laser field is modified by coupling the cavity-mode field and the multiphoton resonance processes between modified quasienergy states, resulting in the generation of even-order harmonics. The high-order harmonic generation (HHG) from a two-level system driven by the laser fields can be coherently controlled by tuning the laser parameters. In particular, the tuning intensity of the cavity-mode field allows one to coherently control the HHG power spectra without changing the absolute positions of comb frequencies.
Many-body environments are conventionally incorporated into quantum dynamics as heat baths, which induce a Lamb shift and quantum dissipation. In the traditional picture, such environmental coupling is expected to induce suppression and broadening of spectral signals. In this letter, we investigate high-order harmonic generation (HHG) in a two-level system coupled to a heat bath via dipole-dipole interactions using the Lindblad master equation. It is found that the environmental effect does not simply suppress the harmonic efficiency. Instead, when the cutoff frequency of the coupling spectral density exceeds the energy-level spacing, the environment can actually enhance the harmonic yield. Further analysis reveals that this enhancement originates from intense level fluctuations induced by the Lamb shift. Meanwhile, the environmental influence exhibits a distinct dependence on harmonic order, manifesting clearly different behaviors for lower and higher harmonics. Our results challenge the common relaxation-time picture of uniform damping and establish a microscopic, order-dependent mechanism for environmental control of HHG, with direct implications for solid-state attosecond spectroscopy and quantum material engineering.
We experimentally observe a new type of quantum-path interference, in two-dimensions (2D-QPI), in high-harmonic generation (HHG) driven by an orthogonally-polarised highly-bichromatic field. This regime is marked by comparable intensities of the two orthogonal colours. In this highly-bichromatic regime, we demonstrate that 2D-QPI is encoded in the measured harmonic intensity modulations with respect to the relative phase of the two-colour field. The modulations of the odd-order harmonics show a monomodal behaviour, whereas the even harmonics are modulated in a bimodal structure. Our calculations using the strong-field approximation and saddle-point method disentangle contributions from multiple quantum orbits in this HHG regime, revealing that the dipole response for both odd and even harmonics inherits the dynamic symmetry of the orthogonally-polarised driving field. This new type of 2D-QPI offers a novel route to HHG spectroscopy of attosecond electron dynamics by lifting up the dimensionality of the quantum paths involved in the interference.