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.
Carrier-envelope-phase-dependent effects of high-harmonic generation for two-level atoms interacting with Gaussian shape few-cycle pulses (with \ensuremathϕ=0 and \ensuremathϕ=\ensuremathπ/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.
A lot of experimental and theoretical studies of a system in cavity quantum electrodynamics (cavity QED), which consists of two spatially separated quantum emitters strongly coupled to a single optical cavity mode, have recently attracted much interest in the quantum optics community for various quantum information applications. Here, we propose a method for high-order harmonic generation in a photonic crystal microcavity coupled to single semiconductor quantum dots (QDs). The system is coherently driven by a bichromatic laser consisting of the control and signal fields at low input power (a few nanowatts) and the cavity output power via the cavity loss channel is monitored. Via numerical simulations, we thoroughly explore the difference of the generated high-order harmonic spectra between two QDs, one QD, and zero QDs in microcavity. The results clearly indicate that harmonic generation can be significantly enhanced via collective coherent coupling in the case of two spatially separated QDs coupled to the same photonic crystal microcavity mode. In addition, we present a study of the carrier-envelope phase (CEP) effect on high-order harmonic spectra, which may provide the insight of CEP effect in a new regime. Beyond this, our obtained results also apply to other classes of single-mode cavity-QED setup incorporating two-level atoms or comparable solid-state emitters.
We study the carrier-envelope-phase (CEP) effect of a few-cycle laser pulse on bound-bound transitions in helium in the high-frequency region. Specifically, for the one-photon transition from the 11S to the 21P state, the CEP effect increases as the frequency increases; while for the two-photon transition from the 11S to the 31D state, the CEP effect shows a peak at a frequency that is almost equal to the energy difference between the 11S and 31D states. By using a four-level model, we find that the CEP effect on the 11S--21P transition is attributed to the quantum interference between the positive-frequency and negative-frequency subpaths of the one-photon transition; whereas the CEP effect on the 11S--31D transition is attributed to the interference between the sum-frequency and difference-frequency components of the two-photon transition. These results indicate that the CEP effect can occur not only due to the interference between neighboring multiphoton-transition paths, but also due to the interference between two components inside one multiphoton-transition path. Therefore, this work, together with our previous work for the low-frequency region [Peng et al., Phys. Rev. A 82, 053407 (2010)], may provide a complete picture of the CEP effect on bound-bound transitions in the whole range of laser frequency.
We present ab initio calculations using the R-matrix with time dependence (RMT) method for high-order harmonic generation (HHG) in argon in a short, intense pulse regime. The calculations employ a 6-cycle sin2 pulse at 850 nm with peak intensity 2.3×1014 W/cm2 and, for comparison with the experiment by Guo et al. [J. Phys. B: At. Mol. Opt. Phys. 51, 034006 (2018)], a Gaussian pulse with the same frequency and peak intensity. Both pulse shapes yield the expected harmonic structure in the region above the ionization threshold (approximately 15.82 eV in LS-coupling). The spectra exhibit strong carrier-envelope-phase (CEP) sensitivity. The energy region leading up to the ionization threshold contains spectral features arising from residual coherent dipole oscillations (free-induction decay) that strongly depend on spectral windowing and the post-pulse propagation time. We show that the HHG spectrum, particularly below the ionization threshold, is a defined quantity that depends on analysis choices rather than being a uniquely determined observable. Comparison between theoretical predictions and experimental observations in this energy regime, therefore, requires explicit specification of these parameters.
We present an experimental and theoretical study of carrier-envelope-phase (CEP) effects on the population transfer between two bound atomic states interacting with pulses consisting of many cycles. Using intense radio-frequency pulse with Rabi frequency of the order of the atomic transition frequency, we investigate the influence of the CEP on the control of phase-dependent multiphoton transitions between the Zeeman sublevels of the ground state of 87Rb. Our scheme has no limitation on the duration of the pulses. Extending the CEP control to longer pulses creates interesting possibilities to generate pulses with accuracy that is better than the period of optical oscillations.
We show that a simple nonperturbative two-level model of an atom driven by a very strong periodic field, results in a rich picture of very high harmonic generation and related phenomena. It reproduces experimentally observed plateau, yields for the first time simple analytic formulas for the plateau cutoff frequency, critical driving intensity, and saturation, and predicts intensity-induced multi-resonances. One of the most fascinating phenomenon discovered recently in nonlinear interaction of light with atoms and ions, is very high-order (up to 135) odd harmonic generation (HHG) by intense (∼ 1013 W/cm2 and higher) optical laser radiation in rare gasses and some ions [1], The spectra of generated harmonics drasticly deviate from the perturbation theory predictions [2], In particular, intensity of harmonics, falling monotonically with their orders only up to a certain point, levels off forming a so-called “plateau", and falls monotonically again beyond it. Generally, harmonte generation depends on phase-matching conditions and nonlinear response of individual atoms. It has recently become clear however [3,4] that the major features of HHG, in particular the plateau, result mainly from general properties of atomic nonlinear response. The most direct and apparently successful way so far to approach the problem theoretically has been numerical simulation of the Schrödinger [2,5-7] (including an empiric rule [6]) for many-electron atoms using Hartry-Slater approximation. This approach requires, however, tremendous amount of calculations and involves many processes, making it difficult to gain simple insights. An interesting simplified model [8] based on 3-D delta-potential with a single (ground) level [9] produces results in integration form. The idea of retaining a single energy scale (ionization energy) brings one close to an even simpler system: a two-level model atom. A two-level model of HHG [10], however, due to various complications introduced into it, failed to generate simple results, whereas an analytic solution [11] holds for a virtually degenerate two-level model only (see below) which is unapplicable to the experimental conditions [1-4,7,9]; besides, no relaxation was considered in [10,11].
We present an experimental and theoretical study of the carrier-envelope phase effects on population transfer between two bound atomic states interacting with intense ultrashort pulses. Radio frequency pulses are used to transfer population among the ground state hyperfine levels in rubidium atoms. These pulses are only a few cycles in duration and have Rabi frequencies of the order of the carrier frequency. The phase difference between the carrier and the envelope of the pulses has a significant effect on the excitation of atomic coherence and population transfer. We provide a theoretical description of this phenomenon using density matrix equations. We discuss the implications and possible applications of our results.