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Physical Review A

Generalization of the Rabi population inversion dynamics in the sub-one-cycle pulse limit

Nađa Došlić

Published Jul 13, 2006• 34 citations
Publisher

Abstract

We consider the population inversion in a two-level system generated by a sub-one-cycle pulse excitation. Specifically, we explore the effect that the time derivative of the pulse envelope has on the Rabi dynamics. Our analysis is based on a combination of analytical, perturbative, and nonperturbative treatments and is complemented by numerical simulations. We find a shortening of the Rabi inversion period and show that complete inversion is unobtainable under resonant, ultrashort pulse conditions. The impact of nonresonant and carrier-envelope phase-dependent effects on the dynamics of two-level and multilevel systems is studied numerically, and conditions for complete population inversion are derived.

DOI
10.1103/physreva.74.013402

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We consider the population inversion in a two-level system generated by a sub-one-cycle pulse excitation. Specifically, we explore the effect that the time derivative of the pulse envelope has on the Rabi dynamics. Our analysis is based on a combination of analytical, perturbative, and nonperturbative treatments and is complemented by numerical simulations. We find a shortening of the Rabi inversion period and show that complete inversion is unobtainable under resonant, ultrashort pulse conditions. The impact of nonresonant and carrier-envelope phase-dependent effects on the dynamics of two-level and multilevel systems is studied numerically, and conditions for complete population inversion are derived.
We theoretically study the carrier-envelope phase-dependent inversion generated in a two-level system by excitation with a few-cycle pulse. On the basis of the invariance of the inversion under time reversal of the exciting field, parameters are introduced to characterize the phase sensitivity of the induced inversion. Linear and nonlinear phase effects are numerically studied for rectangular and sinc-shaped pulses. Furthermore, analytical results are obtained in the limits of weak fields, as well as strong dephasing, and by nearly degenerate perturbation theory for sinusoidal excitation. The results show that the phase-sensitive inversion in the ideal two-level system is a promising route for constructing carrier-envelope phase detectors.
The response of a two-level system to a few-cycle pulse pair has been investigated with a special focus on the relation between population inversion and the carrier-envelope phases (CEPs) of the two pulses. The goal is to explore possible schemes of coherent control based on sequential ultrafast pulses. Simulation results indicate a close CEP-inversion relation, which stems from the coherent nature of the interaction. The impact of the pulse amplitudes is evaluated and is shown to create weak-field and strong-field interaction regions with drastically different characteristics. The important role of carrier-wave Rabi flopping in defining these characteristics is also analyzed. Finally, advantages of the method and experimental realization are discussed.
Dynamic multiphoton resonances in ultra-short super-intense laser pulses consisting of 50-200 field periods are considered numerically for a two-level system. The impact of non-resonant (Bloch-Siegert) and carrier-envelope effects on the dynamics of a two-level system was studied numerically, and conditions for complete population inversion were derived. The widths of multiphoton resonances increase with the increasing of the laser field. Results do not depend practically on the pulse duration. Effective resonance frequencies for multiphoton resonances increases strongly in a super-intense field. Multiphoton resonances are shifted and unified with each other in super-intense laser fields.
Here we use perturbation techniques based on the averaging method to investigate Rabi oscillations in cw and pulse-driven two-level systems (TLS's). By going beyond the rotating-wave approximation, especifically to second-order in perturbation, we obtain the Bloch-Siegert shift of the TLS resonant frequency, in which the resonant frequency increases with the driving field amplitude. This frequency shift implies that short resonant πππ-pulses in which the Rabi frequency is approximately 40\% or higher of the transition frequency do not achieve complete inversion in TLS's. Hence, guided by analytical results based on the averaging technique, we propose two methods for obtaining population inversions in the TLS driven by short πππ-pulses: one with chirping and the other with pulse shaping and near resonance blue-shifted detuning. Both methods minimize dephasing due to the Bloch-Siegert shift, reduce the dependance of the excitation of the TLS on the pulse phase, and are very effective in achieving complete population inversions.
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.
The interactions of sub-cycle and single-cycle pulses with two- or three-level quantum systems are studied, respectively. For the two-level quantum system, two cases in which the carrier frequency of pulses is in resonance and far from resonance with the atom are analysed. The ultrafast complete population transfer can be obtained. The sub-cycle pulse with a far off-resonant carrier frequency is found to be more suitable for the population transfer. The relation between the area of pulses and population transfer is clarified in the sub-cycle and single-cycle domain. For the Lambda-type three-level quantum system, more than 90% of population transfer can be achieved from one level to another. The scheme is insensitive to the variation of the laser parameters such as the peak Rabi frequency and the carrier frequency for both two- and three-level quantum systems.