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Physical Review A

Theory of two-photon adiabatic passage: Absorption to and emission fromNstates

Moshe Shapiro

Published Aug 1, 1996• 19 citations
Publisher

Abstract

An analytic theory of resonantly enhanced two-photon excitation of N states with laser light of an arbitrary field is developed. Closed-form expressions for the time evolution of the system are derived. The formulation is used to explore adiabatic passage to a level embedded amongst N other levels. ``Counterintuitive'' pulse sequence is shown to lead to complete population transfer under adiabatic conditions. The reverse case of stimulated emission from N initial states is also studied. Complete population transfer to the ground state from an initial state satisfying the two-photon resonance condition is shown to be possible. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.1504

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An analytic theory of resonantly enhanced two-photon excitation of N states with laser light of an arbitrary field is developed. Closed-form expressions for the time evolution of the system are derived. The formulation is used to explore adiabatic passage to a level embedded amongst N other levels. ``Counterintuitive'' pulse sequence is shown to lead to complete population transfer under adiabatic conditions. The reverse case of stimulated emission from N initial states is also studied. Complete population transfer to the ground state from an initial state satisfying the two-photon resonance condition is shown to be possible. \textcopyright{} 1996 The American Physical Society.
The theory of one- and two-photon dissociation processes with strong laser pulses for slowly varying multiple continua (‘‘direct’’ dissociation) is developed. Closed form expressions for the state preparation and evolution during and after the excitation pulse are derived. We show how saturation of the photodissociation process as a function of the laser power sets in. We also show that for direct dissociation, the fragment state distribution is independent of the laser power. The dependence of spontaneous emission during dissociation (continuum Raman and resonance fluorescence) on the pulse intensity is studied. The formulation is extended to treating resonantly enhanced two-photon dissociation with strong laser pulses. Closed-form expressions for slowly varying pulses and slowly varying continua are derived. Using these expressions, the existence of adiabatic passage to the continuum (APC) by which a system executes a complete population transfer from an initial bound state to the continuum by following two guiding light pulses is established. A simple iterative scheme for going beyond the adiabatic approximation is introduced.
Ongoing work aimed at developing highly efficient methods of populating a chosen sublevel of an energy level highlights the need to understand off-resonant effects in coherent excitation. This motivated us to re-examine some aspects of the theory of coherent excitation in a three-state system with a view to obtaining algebraic expressions for off-resonant eigenvalues and eigenvectors. Earlier work gives simple closed-form expressions for the eigenvalues this system, expressions applying even when the system is not on two-photon resonance. We present here expressions of similar simplicity for the components of the normalised eigenvectors. The analytic properties of these components explain the observed sensitivity of the stimulated-Raman-adiabatic-passage process (STIRAP) to the condition of two-photon resonance. None of the eigenstates is ‘trapped’ or ‘dark’ unless the system is on two-photon resonance; off resonance, all states have nonzero projections on the unperturbed intermediate state. A simple argument shows that no dressed state can be adiabatically connected to both the unperturbed initial and final states when the system is off two-photon resonance. That is, adiabatic transfer from initial to final state requires that these be degenerate before and after the STIRAP pulse sequence, and this implies zero two-photon detuning. However, substantial transfer probabilities are observed experimentally for very small two-photon detunings. We show that such systems are characterised by very sharp avoided crossings of two eigenvalues, and that the observed population transfer can be understood as an effect of non adiabatic transitions occurring at the avoided crossings.
We demonstrate that various properties of population transfer by delayed pulses in three-level systems on two-photon resonance can be deduced analytically and for general pulse shapes. We use the fact that the three-level system reduces to effective two-level problems at large intermediate-level detuning \ensuremath{\Delta}, on resonance (\ensuremath{\Delta}=0) and for completely overlapping pulses. Special attention is paid to the effect of the pulse order on the population transfer efficiency. We show that on resonance the transfer efficiency depends substantially on the pulse order, while at large \ensuremath{\Delta} it does not. We also find that under some natural restrictions on the symmetry of the problem, the population of the initial level does not depend on the pulse order at any \ensuremath{\Delta}. Furthermore, we demonstrate that the population transfer in the three-level system can be viewed as a level-crossing problem in an equivalent two-level system not only at large \ensuremath{\Delta} (which is known) but also on resonance, \ensuremath{\Delta}=0. The effective on-resonance two-level problem is interesting by itself as it shows that a level crossing and adiabatic evolution do not necessarily lead to complete population inversion. As examples throughout the paper, we present several analytically solvable models.
We discuss various theoretical issues that arise when one extends the conventional stimulated Raman adiabatic passage, involving a pump pulse preceded by a Stokes pulse, to situations in which the pump interaction involves a two-photon transition. As in the simpler cases, it is possible to obtain complete population transfer between an initial state and a targeted final state, if certain general conditions on the pulses are met. We point out important considerations, associated with dynamic Stark shifts and multiphoton ionization, which make successful population transfer more difficult in the multiphoton extension. We illustrate these problems and requirements by considering specific examples of excitation in metastable helium.
We present explicit analytic expressions for adiabatic dressed states which, in suitable limits, produce complete population transfer between initial and final states of a four-state excitation chain without ever placing appreciable population into intermediate states. The population-transfer scheme is a generalization of the three-state stimulated Raman adiabatic passage that makes use of counterintuitive pulse sequences. We demonstrate analytically and numerically that the four-state system differs in a very significant qualitative way from previously studied N-state systems with odd N. In particular, we find that the presence of modest detuning from single-photon resonance is critical to the success of population transfer.
In this paper we extend the existing theory of stimulated Raman adiabatic passage (StiRAP) in three-level systems to examine the nature of selective photoexcitation using counterintuitively ordered pulses. Our goal is to develop a version of StiRAP that permits control of product selectivity in a chemical reaction. We analyze the case of selective excitation to one state in a pair of degenerate target states in a four-level system, and find that one cannot control the ratio of the populations in the two states in a resonant two-photon process. However, the extension of the system to include a fifth state and a third laser field makes selective excitation to one of the degenerate states possible. It is found that, subject to reasonable restrictions, one may accomplish complete population transfer to a single target state of a degenerate pair of states in a five-level system.