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Journal of Optics B Quantum and Semiclassical Optics

Induced transitions between Wannier ladders

Markus Glück, Marlies Hankel, Andrey R. Kolovsky, H. J. Korsch

Published Oct 1, 2000• 10 citations
Publisher

Abstract

We study the transitions between the ground and excited Wannier states induced by a weak ac field. Because the upper Wannier states are several orders of magnitude less stable than the ground states, these transitions decrease the global stability of the system characterized by the rate of probability leakage or decay rate. Using non-Hermitian resonant perturbation theory we obtain an analytical expression for this induced decay rate. The analytical results are compared with exact numerical calculations of the system decay rate.

DOI
10.1088/1464-4266/2/5/308

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We study the transitions between the ground and excited Wannier states induced by a weak ac field. Because the upper Wannier states are several orders of magnitude less stable than the ground states, these transitions decrease the global stability of the system characterized by the rate of probability leakage or decay rate. Using non-Hermitian resonant perturbation theory we obtain an analytical expression for this induced decay rate. The analytical results are compared with exact numerical calculations of the system decay rate.
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Density matrix formalism is used to model two-photon free-induction decay from a ladder-type, three-level scheme with a resonant intermediate state. Counterpropagating light beams are assumed. Only the upper transition is frequency shifted out of resonance with the injected field. Results indicate departure from single-photon behavior; in particular, there is a π phase shift in the oscillations when the Rabi frequencies associated with each transition are comparable in magnitude. The theory is applied to the 32S1/2 (F = 1) − 32P1/2 − 42D3/2 excitation scheme of sodium.
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In this thesis two questions of equilibrium and non-equilibrium properties in many-body quantum mechanical systems are investigated. The first part is focused on probability distributions of quantum observables in many-body quantum systems. After an introduction to probability distributions, full counting statistics and the transverse field Ising model we give a brief overview over related experiments and then derive an expression for the probability distribution of the transverse field magnetization of a finite subsystem in any Gaussian state. We study the probability distribution in ground and thermal states as well as in a non-equilibrium setting after a quantum quench. We find an analytic expression for the time evolution after the quench and compare to numerics. The second part of the thesis is concerned with the stability of exact quasi-particle excitations of an integrable model after weak integrability breaking perturbations are introduced. For this we first discuss the stability of excitations in integrable systems and then give an introduction to the Heisenberg XXX-model in a magnetic field. After constructing exact excitations we calculate the decay rate in leading order perturbation theory using methods of integrability.