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Physical Review A

Adiabatic transition histories of population transfer in the Λ system

M. Elk

Published Nov 1, 1995• 36 citations
Publisher

Abstract

The superadiabatic basis scheme developed by Berry [Proc. R. Soc. London 429, 61 (1990)] is used to analyze adiabatic population transfer in the \ensuremath{\Lambda} system in what is known as the counterintuitive pulse scheme. For a specific choice of pulses, we find that the diabatic loss is given by the exponentially small (8-4\ensuremath{\surd}2)exp(-2/\ensuremath{\epsilon}), where \ensuremath{\epsilon} is a small parameter describing the adiabaticity of the process. We thus establish the connection between population transfer in the \ensuremath{\Lambda} system and general adiabatic transition theory. We project numerical solutions onto superadiabatic basis states for the real three-level system and show how the history of population transfer has a very compact and universal history in one particular superadiabatic basis.

DOI
10.1103/physreva.52.4017

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The superadiabatic basis scheme developed by Berry [Proc. R. Soc. London 429, 61 (1990)] is used to analyze adiabatic population transfer in the \ensuremath{\Lambda} system in what is known as the counterintuitive pulse scheme. For a specific choice of pulses, we find that the diabatic loss is given by the exponentially small (8-4\ensuremath{\surd}2)exp(-2/\ensuremath{\epsilon}), where \ensuremath{\epsilon} is a small parameter describing the adiabaticity of the process. We thus establish the connection between population transfer in the \ensuremath{\Lambda} system and general adiabatic transition theory. We project numerical solutions onto superadiabatic basis states for the real three-level system and show how the history of population transfer has a very compact and universal history in one particular superadiabatic basis.
Two approaches of achieving population transfer and coherence are investigated for the three-level Λ system in the adiabatic limit. The effects of the laser pulse sequence on the population transfer efficiency and coherence are studied. Coherent control of quantum state and population is studied by numerical simulation based on self-consistent set of density matrix equations. It can be seen that the counterintuitive pulse sequence is more efficient in population transfer and coherence than the intuitive one.
A generalized adiabatic approximation is formulated for a two-state dissipative Hamiltonian which is valid beyond weak dissipation regimes. The history of the adiabatic passage is described by superadiabatic bases as in the nondissipative regime. The topology of the eigenvalue surfaces shows that the population transfer requires, in general, a strong coupling with respect to the dissipation rate. We present, furthermore, an extension of the Davis-Dykhne-Pechukas formula to the dissipative regime using the formalism of Stokes lines. Processes of population transfer by an external frequency-chirped pulse-shaped field are given as examples.
Abstract The way in which the transition amplitude to an initially unoccupied state increases to its exponentially small final value is studied in detail in the adiabatic approximation, for a 2-state quantum system. By transforming to a series of superadiabatic bases, clinging ever closer to the exact evolving state, it is shown that transition histories renormalize onto a universal one, in which the amplitude grows to its final value as an error function (rather than via large oscillations as in the ordinary adiabatic basis). The time for the universal transition is of order √ (ћ/δ) where δ is the small adiabatic (slowness) parameter. In perturbation theory the pre-exponential factor of the final amplitude renormalizes superadiabatically from the incorrect value ⅓π (for the ordinary adiabatic basis) to the correct value unity. The various histories could be observed in spin experiments.
Abstract In many quantum technologies adiabatic processes are used for coherent quantum state operations, offering inherent robustness to errors in the control parameters. The main limitation is the long operation time resulting from the requirement of adiabaticity. The superadiabatic method allows for faster operation, by applying counterdiabatic driving that corrects for excitations resulting from the violation of the adiabatic condition. In this article we show how to construct the counterdiabatic Hamiltonian in a system with forbidden transitions by using two-photon processes and how to correct for the resulting time-dependent ac-Stark shifts in order to enable population transfer with unit fidelity. We further demonstrate that superadiabatic stimulated Raman passage can realize a robust unitary NOT-gate between the ground state and the second excited state of a three-level system. The results can be readily applied to a three-level transmon with the ladder energy level structure.
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.
To achieve the selective population transfer to the specific excited state of molecules, the delayed-pulse method developed in the three-level system is more attractive and effective than the ordinary π-pulses method. However, two pulses in this adiabatic method are in a counterintuitive order and are significantly overlapped, so that it is very difficult to understand the physical meanings of the dynamical process. Here we develop the effective method to understand the adiabatic processes in a pictorial and easy way by using the concept of the Hückel molecular orbital theory. Then we investigate the complete population transfer in the four-level system in detail. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 511–522, 1999