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The Journal of Physical Chemistry A

Adiabatic Population Transfer with Control Fields

Mustafa Demirplak, Stuart A. Rice

Published Oct 29, 2003• 759 citations
Publisher

Abstract

This paper explores the benefit of using time dependent basis sets in the description of adiabatic population transfer between molecular states. Using a time dependent basis set formalism, we develop a counter-diabatic field paradigm that generates adiabatic population transfer for apparently unfavorable conditions. We also describe a time dependent perturbation approach to account for the effect of stochastic dephasing on adiabatic population transfer.

DOI
10.1021/jp030708a

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This paper explores the benefit of using time dependent basis sets in the description of adiabatic population transfer between molecular states. Using a time dependent basis set formalism, we develop a counter-diabatic field paradigm that generates adiabatic population transfer for apparently unfavorable conditions. We also describe a time dependent perturbation approach to account for the effect of stochastic dephasing on adiabatic population transfer.
We report the results of studies of various aspects of the counter diabatic field paradigm, a recipe that generates adiabatic population transfer between levels by assisting a given field so that the total field generates the population transfer that the adiabatic approximation suggests for the given field. The sensitivity of this recipe to the pulse parameters and to Gaussian stochastic phase fluctuations between the fields has been investigated. Ladder-climbing population transfer between the vibrational levels of a nonrotating Morse oscillator is examined, and a numerical demonstration of the efficiency of the scheme is given.
In the past two decades many schemes to actively control the dynamical evolution of a quantum system have been proposed and established. We focus attention on the use of assisted adiabatic processes to generate selected target states with high efficiency. Specific control protocols that fall in this category are sometimes called shortcuts to adiabaticity. We review two assisted adiabatic population transfer schemes, the counter-diabatic and fast-forward protocols, with the intent of calling attention to their conceptual basis and applications to real systems, specifically vibrational energy transfer in polyatomic molecules and manipulation of Bose-Einstein (BEC) condensates. The particular applications of the counter-diabatic and fast-forward protocols to improving the efficiency of population transfer between vibrational states of a polyatomic molecule that we have studied are (i) selective vibrational energy transfer in the nonrotating thiophosgene (SCCl2) molecule and (ii) enhancing the yield of HNC in the driven rotation free isomerization reaction HCN→CNH. A major component of our considerations concerns reduction of the degradation of population transfer efficiency within a subset of states that is generated by coupling of the subset of states to a manifold of background states. We have examined the influence of a manifold of background vibrational states on population transfer within a subset of embedded vibrational states, and on how that influence can be suppressed. We emphasize that any control protocol must be designed to minimize interference between the background states and excitations within the selected subset of states that are used to define initial and target states. We have also examined the application of the fast-forward protocol to the transport of population between sites of a BEC in an optical lattice. Through the applications we illustrate how the theoretical framework of an assisted adiabatic process depends on the character of the system studied, on the available control parameters, on the constraints imposed by the experimental setting, on the efficiency of population transfer (fidelity) to be achieved, and on the stability of the control process with respect to the variation of the external control fields.
The feasibility of efficient population transfer between an initial state and a decaying target state of the same parity without populating an intermediate state, in the presence of large-amplitude stochastic energy level fluctuations that mimic the dephasing in a solute molecule due to the influence of a solvent, is demonstrated theoretically. In particular, it is shown that a decaying target state, whose decay rate constant is large compared with the band width of picosecond laser pulses but small compared with the associated peak Rabi frequencies, can dramatically suppress the dephasing-induced nonadiabaticity associated with the dynamics of population transfer, resulting in, irrespective of the correlation time of stochastic energy level fluctuations, negligible population in the intermediate state and complete population transfer to the decaying target state. These results should further motivate experimental studies of optical control of molecular dynamics in a liquid. An interesting connection between our results and the quantum Zeno and anti-Zeno effects is also discussed.
The control of population transfer can be affected by the adiabatic evolution of a system under the influence of an applied field. If the field is too rapidly varying or too weak, the conditions for adiabatic transfer are not satisfactorily met. We report the results of an analysis of properties of counterdiabatic fields (CDFs) that restore the adiabatic dynamics of a system by suppressing diabatic effects as they are generated. We observe that a CDF is not unique and find the one that has minimum intensity, and we provide natural upper and lower bounds to the integrated intensity of a CDF in terms of integrals of the eigenvalues of the system Hamiltonian. For Hamiltonians that are separable with respect to their parameters, we prove that the time integral of an associated CDF is path independent. Finally we explain why and when, in the neighborhood of an avoided crossing, a CDF can be approximated by Lorentzian pulses.
The superadiabatic basis scheme developed by Berry [Proc. R. Soc. London 429, 61 (1990)] is used to analyze adiabatic population transfer in the \ensuremath{\Lambda} system in what is known as the counterintuitive pulse scheme. For a specific choice of pulses, we find that the diabatic loss is given by the exponentially small (8-4\ensuremath{\surd}2)exp(-2/\ensuremath{\epsilon}), where \ensuremath{\epsilon} is a small parameter describing the adiabaticity of the process. We thus establish the connection between population transfer in the \ensuremath{\Lambda} system and general adiabatic transition theory. We project numerical solutions onto superadiabatic basis states for the real three-level system and show how the history of population transfer has a very compact and universal history in one particular superadiabatic basis.
We report studies of state-to-state vibrational energy transfer in an isolated polyatomic molecule driven by combined stimulated Raman adiabatic passage (STIRAP) and counter-diabatic fields (CDFs). The goal of these studies is development of a method for improving the efficiency of level-to-level population transfer under conditions that degrade the efficiency of conventional STIRAP-generated population transfer. The vehicles for our studies are selective population of one of a pair of near-degenerate states in nonrotating SCCl 2 and enhancing the yield of nonrotating HNC in the HCN → HNC isomerization reaction. The efficiency of the population transfer within a subset of states embedded in a manifold of states is examined for the cases in which the transition dipole moments between the initial and target states are much smaller than and comparable to the transition dipole moments between background states and for the case in which the subset states have large transition dipole moments with the background states. We show that, in a subset of states that is coupled to background states, a combination of STIRAP fields and CDFs that do not individually generate processes that are competitive with the desired population transfer can generate population transfer efficiency greater than can ordinary STIRAP with field strength and/or pulse duration similarly restricted and that the exact CDF for an isolated three-level system is a useful approximation to the exact CDF for three- and five-state systems embedded in background states. We report a study of the stability of the STIRAP and approximate CDF control protocol to variation of the CDF intensity, the relative phase between the STIRAP and CDFs, and the pulse duration.