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Physical Review Letters

Complete Control of Population Transfer between Clusters of Degenerate States

Ioannis Thanopulos, Petr Král, Moshe Shapiro

Published Mar 18, 2004• 47 citations
Publisher

Abstract

We present an analytic solution to the "degenerate quantum control problem," which enables the transfer of any desired fraction of population between arbitrary initial and final pure wave packets, made up of nearly degenerate energy eigenstates. It consists of two two-photon adiabatic passage steps, in which the population of the initial wave packet is first transferred, via a number of nondegenerate intermediate states, to a single eigenstate and then returned to a different target superposition state. We demonstrate the approach by executing a stepwise isomerization of three Jahn-Teller states of the Al3O molecule, where a proper optical coupling can easily be established.

DOI
10.1103/physrevlett.92.113003

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We present an analytic solution to the "degenerate quantum control problem," which enables the transfer of any desired fraction of population between arbitrary initial and final pure wave packets, made up of nearly degenerate energy eigenstates. It consists of two two-photon adiabatic passage steps, in which the population of the initial wave packet is first transferred, via a number of nondegenerate intermediate states, to a single eigenstate and then returned to a different target superposition state. We demonstrate the approach by executing a stepwise isomerization of three Jahn-Teller states of the Al3O molecule, where a proper optical coupling can easily be established.
A five-level four-pulse phase-sensitive extended stimulated Raman adiabatic passage scheme is proposed to realize complete control of the population transfer branching ratio between two degenerate target states. The control is achieved via a three-node null eigenstate that can be correlated with an arbitrary superposition of the target states. Our results suggest that complete suppression of the yield of one of two degenerate product states, and therefore absolute selectivity in photochemistry, is achievable and predictable, even without studying the properties of the unwanted product state beforehand.
A five-level four-pulse phase-sensitive extended stimulated Raman adiabatic passage scheme is proposed to realize complete control of the population transfer branching ratio between two degenerate target states. The control is achieved via a three-node null eigenstate that can be correlated with an arbitrary superposition of the target states. Our results suggest that complete suppression of the yield of one of two degenerate product states, and therefore absolute selectivity in photochemistry, is achievable and predictable, even without studying the properties of the unwanted product state beforehand.
A simple theoretical solution to the design of a control field that generates complete population transfer from an initial state, via NNN nondegenerate intermediate states, to one arbitrary member of $M\phantom{\rule{0.3em}{0ex}}(M\ensuremath{\leqslant}N)$ degenerate states is constructed. The full control field exploits an $(M+N\ensuremath{-}1)$-node null adiabatic state, created by designing the relative phases and amplitudes of the component fields that together make up the full field. The solution found is universal in the sense that it does not depend on the exact number of the unwanted degenerate states or their properties. The results obtained suggest that a class of multilevel quantum systems with degenerate states can be completely controllable, even under extremely strong constraints, e.g., never populating a Hilbert subspace that is only a few dimensions smaller than the whole Hilbert space.
The manipulation of population transfer and the creation of an arbitrary superposition between two atomic states in the framework of a closed inverse Y-type four-level system driven by a series of pulse pairs and an external control field is reported. It is shown that when the laser fields are tuned to resonance with respective transitions, the non-adiabatic coupling between two degenerate adiabatic states can be reduced tremendously and complete population transfer from the initial state to the target state can be achieved in a piecewise manner. Moreover, an arbitrary superposition between the initial state and target state can be created by suitably tuning the Rabi frequency of the control laser field, inter-pair time delay, pulse number or intra-pair time delay between the pump and Stokes pulses. This scheme combines stimulated Raman adiabatic passage and temporal coherent control, and may be useful for quantum information processing and control of chemical reactions.
We present a solution to the multichannel quantum control problem, where selective and complete population transfer from an initial bound state to MMM energetically degenerate continuum channels is achieved under loss-free conditions. The control is affected by adiabatic passage proceeding via NNN bound intermediate states, where even in the presence of real loss from these states, the control efficiency remains significant, about 40−−5040--50\phantom{\rule{0.2em}{0ex}}%40−−50. We illustrate the viability of the method by computationally controlling the ${\mathrm{CH}}_{3}(v)+{\mathrm{I}}^{*}(^{2}P_{1∕2})\ensuremath{\leftarrow}{\mathrm{CH}}_{3}\mathrm{I}\ensuremath{\rightarrow}{\mathrm{CH}}_{3}(v)+\mathrm{I}(^{2}P_{3∕2})$ multichannel photodissociation process.