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Physical Review A

Optimized adiabatic passage with dephasing

X. Lacour, S. Guérin, Hans Rudolf Jauslin

Published Sep 16, 2008• 22 citations
Publisher

Abstract

We study adiabatic population transfer with dephasing in two-level models driven by a chirped driving field. We show that the population transfer is maximized when the dynamics follows specific ellipses as trajectories in the parameter space. We determine the optimal parameters and estimate the losses in a closed form. These estimates show a similar robustness as for the standard lossless adiabatic processes with respect to variations of the parameters.

DOI
10.1103/physreva.78.033417

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We study adiabatic population transfer with dephasing in two-level models driven by a chirped driving field. We show that the population transfer is maximized when the dynamics follows specific ellipses as trajectories in the parameter space. We determine the optimal parameters and estimate the losses in a closed form. These estimates show a similar robustness as for the standard lossless adiabatic processes with respect to variations of the parameters.
We examine the adiabatic limit of population transfer in two-level models driven by a chirped laser field. We show that the nonadiabatic correction is minimized when the adiabatic eigenenergies associated to the dynamics are parallel. In the diagram of the difference of the eigenenergy surfaces as a function of the parameters, this corresponds to an adiabatic passage along a level line. The analytical arguments are based on the Dykhne-Davis-Pechukas treatment. We illustrate this behavior with various examples.
Abstract This study demonstrates complete adiabatic population transfer in a closed three-level atomic system using chirped laser pulses. By satisfying the three-photon resonance condition, we effectively mitigate the first-order Doppler effect. Under the assumption of weak coupling between the stable levels, we show that relative phase fluctuations of the lasers exert a negligible influence on the population dynamics during the transfer process. A comprehensive analysis of the system parameters is conducted to determine the optimal conditions for achieving 100% population transfer while minimizing the excited state population
We explore the efficiency and robustness of population transfer in two-state systems by adiabatic passage (i) when the driving pulse is optimally designed in order to lead to parallel adiabatic passage or (ii) with a linear chirping. We show how one could practically implement the corresponding designs of the pulses in the spectral domain. We analyze the robustness of the two shapings taking into account fluctuations of the phase, amplitude, and the area of the pulse. We show the overall superiority of the parallel adiabatic passage especially when one faces the issue of a pulse area that is not well known. We show that the robustness of parallel adiabatic passage is not improved when it is complemented by a correcting field that cancels out the nonadiabatic losses.
Adiabatic rapid passage (ARP) is extensively used to achieve efficient transfer or inversion of populations in quantum systems. Landau and Zener accurately estimated the transfer probability of ARP for a closed system and showed that this probability improved with higher drive amplitude. Recently, we found that, in open quantum systems, applying a strong drive can give rise to significant drive-induced dissipation (DID). Here, we investigate the effect of DID on the performance of ARP that is implemented using a linearly chirped pulse on a two-level system. From the Landau-Zener formula, the population transfer was known to be enhanced with increasing drive amplitude. However, here we show that, beyond a threshold value of the drive amplitude, the transfer probability is reduced because of the detrimental effect of DID. We show that the competition between the two processes results in an optimal behavior of the population transfer. We also propose a phenomenological model that helps explain such nonmonotonic behavior of the transfer. Using this model, we estimate the optimum time at which the maximum population transfer occurs. We extend the analysis for rectangular as well as Gaussian pulse profiles and conclude that a Gaussian pulse outperforms a rectangular pulse.
Adiabatic passage induced by chirped laser pulses in three-level $\ensuremath{\Lambda}$ systems is investigated. Two different strategies for efficient population transfer (equal and opposite sign of the chirp) are analyzed. The role of detuning, crucial for the attempt to reduce the population of the intermediate state, is demonstrated. The scheme of adiabatic passage by laser pulses with chirps of different sign is not symmetric with respect to the sign of the one-photon detuning. Blue detuning results in a smaller transient population of the intermediate state than does red detuning. The results are explained on the basis of dressed states. Numerical results for a fully off-resonant adiabatic passage scheme, based on two pulses with the same sign of the chirps, are also considered. The robustness of the schemes in terms of the Rabi frequency, chirp rate, detuning, and time delay of the pulses is explored.
Population transfer via chirped rapid adiabatic passage is studied using open quantum and semiclassical models, with and without the rotating-wave approximation. A time-dependent variational approach based on the multiple-Davydov D2_22​ trial state is employed to simulate the quantum models with an arbitrary finite mean photon number. We examine the accuracy of both the semiclassical field description and the rotating-wave approximation. Robust population transfer is identified over a wide parameter regime controlled by the laser spectral chirp and is found to be insensitive to the spin--phonon coupling strength, Gaussian pulse area, and energy gap of the two-level system.