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Physical Review Letters

Cyclic Population Transfer in Quantum Systems with Broken Symmetry

Petr Král, Moshe Shapiro

Published Oct 12, 2001• 178 citations
Publisher

Abstract

We show that quantum systems with broken symmetry can be selectively excited due to the coexistence of one- and two-photon transitions between the same states. Discrimination between two mirror-symmetric quantum wells or left- and right-handed chiral molecules can be accomplished by a ``cyclic population transfer'' process, in which one optically couples three system states $|1〉\ensuremath{\leftrightarrow}|2〉\ensuremath{\leftrightarrow}|3〉\ensuremath{\leftrightarrow}|1〉$, and completely transfers population from state $|1〉$ to state $|2〉$ and $|3{〉}_{M}$ (i.e., state $|3〉$ of the mirror imaged system) or state $|3〉$ and $|2{〉}_{M}$, depending on the laser phases.

DOI
10.1103/physrevlett.87.183002

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We show that quantum systems with broken symmetry can be selectively excited due to the coexistence of one- and two-photon transitions between the same states. Discrimination between two mirror-symmetric quantum wells or left- and right-handed chiral molecules can be accomplished by a ``cyclic population transfer'' process, in which one optically couples three system states ∣1〉\ensuremath↔∣2〉\ensuremath↔∣3〉\ensuremath↔∣1〉|1〉\ensuremath{\leftrightarrow}|2〉\ensuremath{\leftrightarrow}|3〉\ensuremath{\leftrightarrow}|1〉∣1〉\ensuremath↔∣2〉\ensuremath↔∣3〉\ensuremath↔∣1〉, and completely transfers population from state ∣1〉|1〉∣1〉 to state ∣2〉|2〉∣2〉 and ∣3〉M|3{〉}_{M}∣3〉M​ (i.e., state ∣3〉|3〉∣3〉 of the mirror imaged system) or state ∣3〉|3〉∣3〉 and ∣2〉M|2{〉}_{M}∣2〉M​, depending on the laser phases.
The Goos and Hänchen (GH) shifts in reflected and transmitted probe light through a cavity mixture of left- and right-handed chiral molecules into two enantiomer states are investigated. Due to the broken mirror symmetry of the left- and right-handed chiral molecules in the presence of cyclic population transfer, such quantum systems can be selectively excited because of the coexistence of one- and two-photon transitions. With the help of coupling Rabi frequency and damping effects due to scattering processes, the generated GH shifts accompanied by simultaneously negative and positive lateral shifts in reflected and transmitted probe lights are greatly enhanced. It is found that the large negative and positive GH shifts are available in the presence of multiphoton resonance and off-resonance conditions for two different enantiomers' chiral molecules. Moreover, the switching between superluminal and subluminal light propagation is extremely dependent on choosing the left- and right-handed chiral molecules. Furthermore, the effects of pulse shape and mode of Laguerre-Gaussian probe light on the GH shifts that lead to a switch between negative and positive shift are also studied. The negative and positive GH shifts in a reflected and transmitted probe beam for an incident Gaussian and different mode of Laguerre-Gaussian shaped beam with various widths by the use of two different enantiomers' chiral molecules are also discussed.
Abstract For quantum systems with broken parities, a transition can appear for any two different states, and cyclic transition structures can be generated for the lowest three levels. Based on these loop transitions, we discuss how to achieve high-precision localization effects for physical objects with broken parities, i.e . chiral molecules and asymmetric quantum wells. In a Δ-type three-level system interacting simultaneously with three external fields, one of which is a standing-wave field, the absorption spectrum carries information about the position of the objects. Moreover, we can achieve 100% probability of finding the objects at certain positions by choosing appropriate parameters. In addition, we present two possible implementations of the suggested scheme in a system comprising a mixture of left- and right-handed chiral molecules and asymmetric quantum wells and show how the phase-sensitive localization effect can be used to discriminate between enantiomeric molecules.
The optical bistability (OB) and multistability (OM) in chiral molecules are investigated by placing the sample into a unidirectional ring cavity. Because of broken mirror symmetry of the effective potential, the chiral molecules have a cyclic three-level Δ-configuration structure, in which one- and two-photon transitions can coexist. We find that the OB is achievable in this system on exact one-, two- and three-photon resonance conditions but absent in the three-level Λ-type system under the two-photon resonance. Moreover, the OM and the switching between OB and OM are also realized by choosing parameters properly. Interestingly, the left- and right-handed chiral molecules exhibit different bistable and multistable behaviors. It is shown that the threshold intensity of OB is strongly dependent on the percentage of the two enantiomers in the mixture. This provides an effective approach to probe molecular chirality and to determine enantiomer excess, which may find potential application in organic chemistry, pharmacology, biochemistry, etc..
We propose a streamlined method of fast enantiomer-specific state transfer (ESST) of chiral molecules in cyclic three-level systems. Such three-level enantiomers are chirality-dependent systems driven by one of the three Rabi frequencies differing with a sign for the left- and right-handed chiral molecules. When the Hamiltonian of the three-level chiral molecules possesses the specific SU(2) algebraic structure, the populations transferred to the two excited states are shown to be exchanged between the left- and right-handed chiral molecules if they are initially prepared in their ground states. By employing unitary SU(2) transformation and inversely engineering time-dependent Hamiltonians with designed Rabi frequencies, we can make the left- and right-handed chiral molecules evolve respectively to different excited states from their initial ground states simultaneously. Thus a fast ESST is achieved.