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arXiv:1010.0138 · Physical Review A

Coherent control of atomic excitation using off-resonant strong few-cycle pulses

Pankaj K. Jha, Hichem Eleuch, Yuri V. Rostovtsev

Published Oct 20, 2010• 52 citations
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Abstract

We study the dynamics of a two-level system driven by an off-resonance few-cycle pulse which has a phase jump $\ensuremath{\phi}$ at $t={t}_{0}$, in contrast to many-cycle pulses, under the nonrotating-wave approximation (NRWA). We give a closed form analytical solution for the evolution of the probability amplitude $|{C}_{a}(t)|$ for the upper level. Using the appropriate pulse parameters like the phase jump $\ensuremath{\phi}$, jump time ${t}_{0}$, pulse width $\ensuremath{\tau}$, frequency $\ensuremath{\nu}$, and Rabi frequency ${\ensuremath{\Omega}}_{0}$ the population transfer after the pulse is gone can be optimized and, for the pulse considered here, an enhancement factor of ${10}^{6}--{10}^{8}$ was obtained.

DOI
10.1103/physreva.82.045805

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We study the dynamics of a two-level system driven by an off-resonance few-cycle pulse which has a phase jump \ensuremathϕ\ensuremath{\phi}\ensuremathϕ at t=t0t={t}_{0}t=t0​, in contrast to many-cycle pulses, under the nonrotating-wave approximation (NRWA). We give a closed form analytical solution for the evolution of the probability amplitude ∣Ca(t)∣|{C}_{a}(t)|∣Ca​(t)∣ for the upper level. Using the appropriate pulse parameters like the phase jump \ensuremathϕ\ensuremath{\phi}\ensuremathϕ, jump time t0{t}_{0}t0​, pulse width \ensuremathτ\ensuremath{\tau}\ensuremathτ, frequency \ensuremathν\ensuremath{\nu}\ensuremathν, and Rabi frequency \ensuremathΩ0{\ensuremath{\Omega}}_{0}\ensuremathΩ0​ the population transfer after the pulse is gone can be optimized and, for the pulse considered here, an enhancement factor of 106−−108{10}^{6}--{10}^{8}106−−108 was obtained.
Abstract Developing an analytical theory for atomic coherence driven by ultrashort laser pulses has proved to be challenging due to the breakdown of the rotating wave approximation (RWA). In this paper, we present an approximate analytical solution that describes a two-level atom under the excitation of a far-off-resonance, few-cycle pulse of arbitrary shape without invoking the RWA. As an example of its applicability, a closed-form solution for Gaussian pulses is explicitly given, and the result is used to analyse the impact of carrier envelope phase on atomic population ratios. Comparisons with numerical solutions validate the accuracy our solution within the scope of the approximation. Finally, we outline an alternative approach that can lead to a more accurate solution by capturing the nonlinear behaviors of the system. The work lays out feasible theoretical paths toward analytically describing two-level atoms driven by ultrashort pulses.
Developing an analytical theory for atomic coherence driven by ultrashort laster pulses has proved to be challenging due to the breakdown of the rotating wave approximation (RWA). In this paper, we present an approximate, closed-form solution to the Schrodinger equation that describes a two-level atom under the excitation of a far-off-resonance, few-cycle pulse of arbitrary shape without invoking the RWA. As an example of its applicability, an analytical solution for Gaussian pulses is explicitly given. Comparisons with numerical solutions validate the accuracy our solution within the scope of the approximation. Finally, we outline an alternative approach that can lead to a more accurate solution by capturing the nonlinear behaviors of the system.
Abstract By using the exact analytical solution and exploring the effect of ultra-short strong pulses in the presence of an external classical field for a two-level atom, we discuss the influence of the phase jump on the behavior of the atomic inversion, coherence and squeezing entropy during the time evolution of various pulse shapes. We show the optimal conditions to attain the phenomenon of coherence trapping. Moreover, we identify the range of physical parameters required for squeezing and its enhancement. The few-cycle pulses present new interesting features for controlling the physical quantities and are a good candidate to perform quantum optics tasks.
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.