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American Journal of Physics

Simple mechanical analogs of rapid adiabatic passage in atomic physics

B. W. Shore, M. V. Gromovyy, Леонід Петрович Яценко, V. I. Romanenko

Published Nov 17, 2009• 30 citations
Publisher

Abstract

We discuss two mechanical systems in which the approximate equations of motion are the same as the rapid adiabatic passage of a two-state quantum-mechanical system, such as that which occurs with quasistatic interactions and from the quasiperiodic action of a chirped-frequency laser pulse. We discuss a pair of masses on springs, weakly coupled by another spring, one of whose spring constants varies slowly, and a pair of coupled pendula, where the length of one pendulum slowly changes. In each example an approximation analogous to the rotating-wave approximation used in the corresponding quantum system brings the second-order macroscopic equations of motion into first-order form, and a slow variation in a system parameter characteristic leads to adiabatic change and rapid adiabatic passage.

DOI
10.1119/1.3231688

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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.
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An analytic theory of the adiabatic passage (AP) regime of interaction of short frequency chirped laser pulses with a two-level quantum system (QS) being initially in the superpositional quantum state is presented. We show that the initial value of the non-diagonal elements of the density matrix can influence the dynamics of the population transfer during the action of the laser pulse, but do not influence essentially the final populations of the states of the QS obtained at the end of the interaction near the AP regime. A novel solution to the Bloch equations is obtained in the form of a converging power series generalizing the ordinary AP solution.