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Physical Review A

Resonant enhancement of generation of harmonics

Igor A. Ivanov, Anatoli S. Kheifets

Published Nov 11, 2008• 24 citations
Publisher

Abstract

We develop a Floquet based formalism which describes a process of the generation harmonics of in an atom driven by a laser field. Using this formalism, we show that several harmonics are strongly enhanced in the spectrum when the laser frequency is such that a multiphoton resonance occurs between the initial state and a quasienergy state. We illustrate these findings by a numerical calculation of the harmonics generation in the potassium and rubidium atoms driven by a laser in the near-infrared energy range. The present formalism is also applicable when the initial state is a coherent superposition of several field-free atomic states.

DOI
10.1103/physreva.78.053406

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We develop a Floquet based formalism which describes a process of the generation harmonics of in an atom driven by a laser field. Using this formalism, we show that several harmonics are strongly enhanced in the spectrum when the laser frequency is such that a multiphoton resonance occurs between the initial state and a quasienergy state. We illustrate these findings by a numerical calculation of the harmonics generation in the potassium and rubidium atoms driven by a laser in the near-infrared energy range. The present formalism is also applicable when the initial state is a coherent superposition of several field-free atomic states.
In the strong-field regime a single multiphoton resonance can enhance many harmonics of the fundamental laser frequency simultaneously. We demonstrate that an alkali-metal atom driven by an intense, ultrafast midinfrared pulse is an ideal system for observing this effect by calculating the response of potassium atoms to radiation that is nearly three or five photon resonant with the $4s\ensuremath{-}4p$ transition. We find that all the harmonics through at least the 17th are enhanced over a wide range of intensities, and that the resonance width of the enhanced harmonics is governed by the lifetime of the multiphoton resonance.
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.
The coherent scattering spectrum of a three-level atom driven by an intense laser field with multiphoton resonant excitation is considered. The spectrum corresponding to harmonic generation is investigated both analytically and numerically for different initial atomic states. The analytical calculations are based on the generalized rotating wave approximation, which allows one to explain obtained spectra containing in general both even and odd harmonics. The results applied to the hydrogen atom show that one can achieve efficient generation of moderately high harmonics using multiphoton resonant excitation by appropriate laser pulses.
Combining Floquet theory with the hierarchy of correlations (a method based on the formal expansion into inverse powers of the coordination number), we study the nonequilibrium dynamics of the Mott insulator state in the Fermi-Hubbard model under the influence of a harmonically oscillating electric field representing the pump laser. After deriving the associated Floquet exponents, we consider multiphoton resonances leading to the generation of higher harmonics. For weak electric field strengths, the strongest signal is obtained for the third harmonic when the driving frequency equals one-third of the Mott gap (because even harmonics are absent due to inversion symmetry). For stronger electric field strengths and lower driving frequencies, the higher-harmonic spectrum can also exhibit plateaulike structures extending over several harmonics (i.e., Floquet channels) below the resonance peak, which is consistent with previous findings.
We extend the many-mode Floquet theorem (MMFT) for the investigation of multiphoton resonance dynamics driven by intense frequency-comb laser fields. The frequency comb structure generated by a train of short laser pulses can be exactly represented by a combination of the main frequency and the repetition frequency. MMFT allows non-perturbative and exact treatment of the interaction of a quantum system with the frequency-comb laser fields. We observe simultaneous multiphoton resonance processes between a two-level system and frequency-comb laser. The multiphoton processes can be coherently controlled by tuning the laser parameters such as the carrier-envelope phase (CEP) shift. In particular, high-order harmonic generation shows immense enhancement by tuning the CEP shift, due to simultaneous multiphoton resonances.
We consider harmonics generation and wave mixing by two-color multiphoton resonant excitation of three-level atoms and molecules in strong laser fields. The coherent part of the spectra corresponding to multicolor harmonics generation is investigated. The obtained analytical results on the basis of a generalized rotating wave approximation are in a good agreement with numerical calculations. The results applied to the hydrogen atoms and homonuclear diatomic molecular ions show that one can achieve efficient generation of moderately high multicolor harmonics via multiphoton resonant excitation by appropriate laser pulses.