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Modern Physics Letters B

High-order harmonic and attosecond pulse generations from Rydberg state driven by the spatially inhomogeneous field

Liqiang Feng, Yi Li, Fan-Shun Meng, Hang Liu, R. S. Castle

Published Feb 8, 2017• 8 citations

Abstract

High-order harmonic spectra and attosecond pulse generation from Rydberg atom (He[Formula: see text]) driven by the spatially inhomogeneous field have been theoretically investigated. (i) Firstly, with an electron initially in a single excited Rydberg state (nth), the harmonic yield can be enhanced due to the decreased ionization potential, and a maximum enhancement can be obtained when the initial state is prepared as the third excited state (n = 3). However, the low cutoff energy from the excited state is unbeneficial to the generation of the higher photon pulse. Thus, with the further introduction of the laser chirp, not only the harmonic cutoff is extended, but also the harmonic modulation is reduced. As a result, five super-bandwidths from 63 eV to 267 eV can be found. (ii) Secondly, by preparing the initial state as a coherent superposition of excited state, the harmonic yield can be further enhanced, especially for the coherent superposition of the first and the third (n = 1 + 3) and the second and the fourth (n = 2 + 4) excited states, the harmonic yield is enhanced by 4–8 orders of magnitude compared with the case of the single ground initial state. Furthermore, by properly adding the laser pulse into the spatially inhomogeneous region (gap center [Formula: see text] a.u.) from left [Formula: see text] to right [Formula: see text], much higher cutoff energies can be obtained in the left region. As a consequence, two super-bandwidths of 248 eV and 496 eV can be obtained. Finally, by properly superposing the harmonics, a series of sub-25-as pulses with intensity enhancement of 5–8 orders of magnitude can be produced.

DOI: 10.1142/s0217984917500294

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High-order harmonic spectra and attosecond pulse generation from Rydberg atom (He[Formula: see text]) driven by the spatially inhomogeneous field have been theoretically investigated. (i) Firstly, with an electron initially in a single excited Rydberg state (nth), the harmonic yield can be enhanced due to the decreased ionization potential, and a maximum enhancement can be obtained when the initial state is prepared as the third excited state (n = 3). However, the low cutoff energy from the excited state is unbeneficial to the generation of the higher photon pulse. Thus, with the further introduction of the laser chirp, not only the harmonic cutoff is extended, but also the harmonic modulation is reduced. As a result, five super-bandwidths from 63 eV to 267 eV can be found. (ii) Secondly, by preparing the initial state as a coherent superposition of excited state, the harmonic yield can be further enhanced, especially for the coherent superposition of the first and the third (n = 1 + 3) and the second and the fourth (n = 2 + 4) excited states, the harmonic yield is enhanced by 4–8 orders of magnitude compared with the case of the single ground initial state. Furthermore, by properly adding the laser pulse into the spatially inhomogeneous region (gap center [Formula: see text] a.u.) from left [Formula: see text] to right [Formula: see text], much higher cutoff energies can be obtained in the left region. As a consequence, two super-bandwidths of 248 eV and 496 eV can be obtained. Finally, by properly superposing the harmonics, a series of sub-25-as pulses with intensity enhancement of 5–8 orders of magnitude can be produced.

Two-electron processes can generate high harmonics beyond the conventional single-active-electron cutoff. Motivated by recent experimental evidence of an extended secondary plateau in the helium high-harmonic spectrum [S. Wang et al, Optica, (2023); S. Wang et al, In Print in Nature Photon., (2026)], we present a two-electron generalisation of the strong-field approximation. We analyse the resulting expressions using the saddle-point method and determine the extended cutoff. We find good agreement with classical predictions of cutoff scalings of

4.7

and

5.5

times the ponderomotive energy, which significantly exceed the established single-electron scaling of 3.17. We calculate high-harmonic spectra generated via a two-electron process in helium atoms driven by an intense few-cycle infrared laser pulse. Our results demonstrate that the harmonic spectrum extends far beyond the water window, reaching photon energies up to

\approx 1.2\,\mathrm{keV}

in the soft x-ray region. The large spectral bandwidth can support the generation of sub-attosecond soft x-ray pulses, which are of particular interest for probing ultrafast dynamics across matter, including applications in core-level spectroscopy and biological imaging.

We theoretically investigate the wavelength scaling of high-order harmonic yield from a Rydberg atom driven by a few-cycle pulse. It is found that the harmonic yield decreases with a slow scaling λ−2.8 as the increase of the laser wavelength for a Rydberg atom compared with λ−4.6 for a ground atom though the traveling time of the electron in the continuum state is longer for a Rydberg atom. Further analysis reveals that the initial large spatial width of the Rydberg atom is responsible for the slow wavelength scaling of the high-order harmonic yield.

The amplification of ultrashort extreme-ultraviolet (XUV) pulses in argon in high-order harmonic generation processes is studied by using the time-dependent Schr\"odinger equation in the spin-free one-active-electron and single-atom approximation. We consider a neutral argon atom initially in the valence 3p state and a sufficiently intense two-cycle driving infrared (IR) pulse for the atom to be mainly ionized after the first laser cycle. The correlated dynamics and transitions from the valence 3p to a virtual subvalence 3s state and in the ionized regions are examined by synchronizing a 1.5-fs XUV pulse to the IR pulse. The calculated single-atom gain spectrum (26--45 eV) agrees with recent experimental measurements. We discuss different channels that can be present in the gain process as a function of pulse parameters and through an analysis of the dynamics of the populations in terms of field-free eigenstates. When the XUV pulse is considered at the end of the driving IR field the amplification is due to contributions of stimulated recombination from excited Rydberg and low energy continuum states to the 3s and 3p states of argon. In regions where the IR field is intense, high energy and angular momentum states are populated and the medium can interact with the pulses through bound and continuum states involving parametric transitions, which is further confirmed by studying classical electron trajectories. We discuss how these parametric interactions might be suitable for amplification of photon energies far from the ionization threshold as observed in the experiments.

Using a linearly polarized, phase-stabilized 3-fs driving pulse of 800 nm central wavelength shape-optimized on its ascending edge by its an amplitude-reduced pulse irradiating on a superposition state of the helium atom, we demonstrate theoretically the generation of a super strong isolated 176-attosecond pulse in the spectral region of 93–124 eV. The unusually high intensity of this attosecond pulse is marked by the Rabi-like oscillations emerging in the time-dependent populations of the ground state and the continuum during the occurrence of the electron recombination, which is for the first time observed in this work.

We theoretically investigate the isolated attosecond pulse generation from pre-excited medium with a chirped and chirped-free two-color field. It is found that the large initial population of the excited state can lead to the high density of the free electrons in the medium and the large distortion of the driving laser field after propagation, though it benefits large enhancement of harmonic intensity in single atom response. These effects can weaken the phase-match of the macroscopic supercontinuum. On the contrary, the small initial population of 4% can generate well phase-match intense supercontinuum. We also investigate an isolated attosecond pulse generation by using a filter centered on axis to select the harmonics in the far field. Our results reveal that the radius of the spatial filter should be chosen to be small enough to reduce the duration of the isolated attosecond pulse due to the curvature effect of spatiotemporal profiles of the generated attosecond pulses in the far field.

In this Rapid Communication we present a method of extending the harmonic generation plateau to high energies with very high conversion efficiencies using moderate intensities. Preparing the initial state as a coherent superposition of the ground state and an excited state we can induce dipole transitions between the continuum and the ground state via the intermediate (excited) state responsible for the ionization. We solve numerically the Schr\"odinger equation and show that the spectrum contains two distinct plateaus, with cutoffs at

{U}_{e}+3{U}_{p}

and

{U}_{g}+3{U}_{p}

. Using an essential states method we demonstrate that the plateaus are due to recombination into the excited and ground states. We briefly discuss possible experimental realizations of the scheme we present.