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Journal of Shaanxi Normal University

Quantum beats in ladder three-level-system

Yongfang Li

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

The population of excited state in ladder three-level-system which probe field has a delay(-time) between two pulses is studied by utilizing the perturbation theory. The analysis results show that population of the excited state becomes oscillating with the increase of the delay time and the oscillation period can reach femto-second order.

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Physical Review A•Nov 1, 1994•99 citations
The population of excited state in ladder three-level-system which probe field has a delay(-time) between two pulses is studied by utilizing the perturbation theory. The analysis results show that population of the excited state becomes oscillating with the increase of the delay time and the oscillation period can reach femto-second order.
The delay time dependence of photoelectron spectra and state populations of three-level ladder K 2 molecule is investigated by pump-probe pulses via time-dependent wave packet approach. The periodical motion of the wave packet with oscillating period 500 fs results in the periodical variation of photoelectron spectra. The photoelectron spectra show Autler-Townes double splitting at zero delay time, and no splitting at positive delay time. The periodical change of state populations with delay time can be ascribed to the coupling effect between the two pulses. It is found that the selectivity of the state populations may be attained by regulating the delay time. The results can provide some important basis for realizing the optical control of molecules experimentally.
Recent femtosecond transmission-correlation measurements1 of large organic dye molecules revealed surprising details concerning the ultrafast relaxation dynamics of such dyes. Superposed on simple exponential decays, the observation of damped sinusoidal oscillations with a period of ~ 150 fs has been puzzling. We theoretically and numerically demonstrate that such oscillatory behavior could be due to quantum beats of closely spaced two levels, whose coherent superposition state is optically prepared and monitored by a pair of femtosecond pulses. Although studies of quantum beats have been developed in both fluorescence-type2 and nonfluorescence-type measurements, such as those based on photon echoes3 or polarization spectroscopy,4 this simple method gives a new approach to femtosecond time domain spectroscopy. The generalized perturbation theory5 of optical coherent transients is extended to the case of optical transmission-correlation or pump-probe-type experiments. The model used is a three-level system which has split levels in either the ground or optically excited states. Especially, if the ground state has sublevels, the system becomes quite similar to the case of coherent Raman beats. Both cases are shown to give quantum beats when the excitation pulses are short compared with the inverse sublevel splitting. The period and decay time of the damped sinusoid represent the separation energy and the dephasing time between the sublevels, respectively. Using third-order perturbation theory, the transmission-correlation signal STC(τ) as a function of the first-to-second pulse delay time Is derived for arbitrary-shaped excitation pulses and is given in the form of fourfold integrals with many terms.
This work explores the effect of spontaneous emission on coherence generation and population transfer in a three-level ladder atomic system driven by two pulses in counterintuitive order. With adiabatic evolution and the weak-dephasing approximation, we find that a large coherence and population transfer can be achieved even with spontaneous decay rate. The maximum coherence and population transfer decrease with the increase of spontaneous decay rate from the highest state to intermediate state. But this effect can be compensated by shortening the pulse width and enlarging the delay time. Results show that the coherence generation and population transfer never depend on the spontaneous decay rate from the intermediate state to ground state. The validity of the analytic solution is examined by numerical calculation.
In a recent publication we have studied counterintuitive pulse sequence applied to a three level ladder scheme, utilizing rectangular-shaped pulses. In this research we investigate amplification without population inversion in a three level ladder system interacting with two electromagnetic fields, namely, the probe and coupling fields. We take both probe and drive fields in the form of Gaussian shaped pulses. In a counterintuitive sequence scheme, the short probe pulse is introduced prior to the application of the coupling field, in contrast to a regular sequence scheme, where both fields are introduced at the same time. The influence of varying the probe pulse width and time delay between the initiation times of the probe and coupling fields on transient probe gain is investigated. It is found that the system exhibits a kind of memory about previously applied weak probe pulse. This may allow for detection of the past event by applying a strong drive pulse in the future.
The effect of delay time on photoelectron spectra and state populations of a four-level ladder K 2 molecule is investigated by a pump1–pump2–probe pulse via the time-dependent wave packet approach. The periodical motion of the wave packet leads to the periodical change of the photoelectron spectra. The Autler–Townes triple splitting appears at zero delay time, double splitting appears at nonzero delay time between pump1 and pump2 pulses, and no splitting appears at nonzero delay time between pump2 and probe pulses. The periodical change of the state populations with the delay time may be due to the coupling effect between the two pulses. It is found that the selectivity of the state populations may be attained by regulating the delay time. The results can provide an important basis for realizing the optical control of molecules experimentally.
Excitation of a quantum ladder system by frequency-swept (-chirped) laser pulses has been investigated by studying an atomic model system, the 5s-5p-5d ladder of rubidium. The population transfer is significantly enhanced when the frequency is swept such that it follows the spacing of the ladder. At intermediate intensities we observe oscillations in the population transfer to the upper level (5d), which can be attributed to interference between two routes of excitation: sequential transfer and direct two-photon excitation via a virtual intermediate state. We determine simultaneously the population transfer to the upper level (5d) and the direct three-photon ionization, the latter corresponding to a three-step ladder with the final state being in the continuum: 5s-5p-5d-\ensuremath{\varepsilon}p/\ensuremath{\varepsilon}f. Experiments were performed, using 100 fs pulses at \ensuremath{\sim}780 nm from a self-mode-locked Ti:Al2{\mathrm{Al}}_{2}Al2​O3{\mathrm{O}}_{3}O3​ oscillator amplified at 10 Hz.