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.
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.
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.
Carrier-envelope-phase-dependent effects of high-harmonic generation for two-level atoms interacting with Gaussian shape few-cycle pulses (with $\ensuremath{\phi}=0$ and $\ensuremath{\phi}=\ensuremath{\pi}/2$) have been investigated theoretically by using a time-frequency analysis. The differences in energies and populations of the two adiabatic states and the harmonic spectra in the cutoff region are illustrated. We find that, by tuning the carrier-envelope phase, the high-harmonic generation in the cutoff region can be controlled. Our results also show that the model of two-level atoms driven by few-cycle pulses can be used to study carrier-envelope phase effects.
The influence of ultrashort low-frequency laser pulses of different intensities and pulse lengths on the dynamics of a resonantly driven atomic system is investigated theoretically. We demonstrate the periodical dependence of the total ionization rate on the appearance time of a strong few-cycle laser pulse. By depleting the excited state, the intense short pulse not only resets the Rabi oscillations, but also introduces a time shift that is proportional to the pulse length. This time shift can be employed to determine the ultrashort pulse length. In the case of ultrashort pulses with lower intensities, we observe side-bands in the two-photon ionization spectrum, whose intensities vary periodically with the appearance time of the pulse. This can be utilized to measure the period of Rabi oscillations. We have developed an S-matrix theory of two-colour ionization which can explain some of the observations of our numerical calculations. Furthermore, we have studied the high harmonic generation spectra as well as the attosecond pulses generated from the high harmonics. We show that the Rabi oscillation can be used to alter the ionization rate within laser sub-cycles and therefore select different quantum trajectories in the high harmonics generation.
We study the field-ionization threshold behavior when a Rydberg atom is ionized by a short single-cycle pulse field. Both hydrogen and sodium atoms are considered. The required threshold field amplitude is found to scale inversely with the binding energy when the pulse duration becomes shorter than the classical Rydberg period, and, thus, more weakly bound electrons require larger fields for ionization. This threshold scaling behavior is confirmed by both three-dimensional classical trajectory Monte Carlo simulations and numerically solving the time-dependent Schr\"odinger equation. More surprisingly, the same scaling behavior in the short pulse limit is also followed by the ionization thresholds for much lower bound states, including the hydrogen ground state. An empirical formula is obtained from a simple model, and the dominant ionization mechanism is identified as a nonzero spatial displacement of the electron. This displacement ionization should be another important mechanism beyond the tunneling ionization and the multiphoton ionization. In addition, an ``ionization window'' is shown to exist for the ionization of Rydberg states, which may have potential applications to selectively modify and control the Rydberg-state population of atoms and molecules.
Currently, the Magnus expansion method is widely used in studying Rydberg atoms in intense laser fields. In these studies, pulse lengths are usually set as an integer multiple of wavelength, at the same time, the initial phase of the laser pulse are usually set as zero, i.e. , without considering the effect of the initial phase in the calculation. However, this will result in some items multiplied by zero. Then, contributions from these items will be lost. Herein, we investigated the effects of the non-integer-cycle pulse and laser initial phase in the calculation of the transition probability of Rydberg atoms in intense laser fields. Our calculation result shows that these effects are trivial when the nondipole approximation is adopted. In dipole approximation i.e. , when the wavelength of the laser field exceeds the characteristic size of atomic or molecular orbitals, these effects are trivial only in the case of a long pulse duration and a large principal quantum number, however in the case of ultrashort laser pulses, these effects are obvious.
Stimulated by a recent experiment [L. D. Noordam et al., Phys. Rev. Lett. 68, 1496 (1992)], we present a model of Rydberg-atom photoionization whose essential feature is the resonance between the initially populated Rydberg state and an additional state lying below Rydberg quasicontinuum. Despite the infinite number of discrete states involved in our model we have obtained the expressions for photoionization yield and discrete-state populations in completely analytical form. These expressions cover both short- and long-time scales, i.e., when laser-pulse duration is shorter or longer than the classical round-trip time of the Rydberg electron. The short-time scale corresponds to the conditions met in the experiment of Noordam et al. and, on the basis of our expressions, we have gained at least qualitative understanding of their observations. In the case of long pulses, which in our considerations are never longer than 54 ps, near resonance is shown to be the origin of a profound ionization suppression, particularly for some specific frequencies, which we identify as those ensuring the formation of a perfectly dark dressed state of zero width and thus unionizable. This dark state is shown to be populated with a probability increasing when laser gets stronger. We discuss the connection between stabilization and formation of this perfectly dark state as well as of additional dressed states, which are dark in the sense that they have the property of becoming very narrow as laser intensity increases. The undamped perfectly dark state, created at specific laser frequencies, has given us rise to introduce what we call the zero-pole approximation for ionization yield, which, as we have shown, works well if duration and intensity of laser pulse are appropriately combined.