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Journal of Physics Communications

Few-cycle excitation of atomic coherence: an analytical solution beyond the rotating-wave approximation

Nazar Pyvovar, Bing Zeng, Lingze Duan

Published Jul 1, 2022• 1 citation
Publisher

Abstract

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.

DOI
10.1088/2399-6528/ac7eaf

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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.
We calculate analytically the error introduced by the rotating-wave approximation (RWA) to the description of a two-level-atom response to a resonant sufficiently intense femtosecond optical pulse of a few-cycle duration and any envelope. The analytically calculated non-RWA refinements to the RWA response are of the lowest order, i.e., linear in the small ratio of the Rabi to optical frequencies. One type of such refinements is small-amplitude rapid oscillations at nearly twice the optical frequency superimposed on the standard RWA population-inversion evolution. The other refinement is an extension of the spectrum of the induced atomic dipole moment in which the third harmonic of the transition frequency appears. The spectrum of this harmonic has an internal structure dependent on both strength and duration of the pulse. The analytically found non-RWA corrections are in qualitative agreement with the recent results of different numerical approaches by other authors and a recent experiment.
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=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 $\ensuremath{\phi}$, jump time t0{t}_{0}t0​, 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 106−−108{10}^{6}--{10}^{8}106−−108 was obtained.
We solve the problem of ultrashort pulse propagation in a two-level medium beyond the rotating-wave (RWA) and slowly varying-envelope approximations. The method of solution is based on the Maxwell-Bloch equations represented in the form that allows one to switch between RWA and general (non-RWA) cases in the framework of a single numerical algorithm. Using this method, the effect of a subcycle pulse (containing less than a single period of field oscillations) on the two-level medium was analyzed. It is shown that for such short pulses, the clear breakdown of the area theorem occurs for the pulses of large enough area. Moreover, deviations from the area theorem appear to be strongly dependent on the pulse shape that cannot be observed for longer few-cycle pulses.
The trapping states of a quantum system occupy a very special place in quantum optics. Here, we propose a method to realize the population trapping (PT) in a two-level atom driven by a carrier envelope phase (CEP) locked laser pulse. We present detailed numerical results on the influence of CEP in different detuned atoms beyond the rotating wave approximation and find the population is strongly dependent on CEP, the detuning and the Rabi frequency. This allows us to choose proper parameters to realize three specific trapping states: upper trapping state, half trapping state and lower trapping state. To explain the fantastic influence of CEP, we present an analytical solution under weak-field approximation, which is consistent with the numerical solution. We further define the action quantity of the pulse acting on the atom as the integral for the interaction Hamiltonian and find the population varies approximatively linearly with the action quantity. This investigation provides directive significance for achieving PT at arbitrary quantum states and insightful schemes to regulate and control the quantum dynamics of atoms via accurately controlled optical field, and the results could be beneficial for applications to laser cooling, isotope separation and so on.