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Physical review. B./Physical review. B

Generalized cluster correlation expansion theory for stimulated Raman adiabatic passage processes in the presence of a spin bath

Tommaso Fazio, Anna Napoli, Benedetto Militello

Published Jun 12, 2024• 1 citation
Publisher

Abstract

The stimulated Raman adiabatic passage (STIRAP) is applied to a system coupled to a bath made of fully interacting two-level systems whose dynamics is studied by exploiting the generalized cluster correlation expansion (gCCE) theory. We specialize our analysis to a negatively charged silicon vacancy (${\mathrm{V}}_{\mathrm{Si}}^{\ensuremath{-}1}$) in nonpurified 4H-SiC to assess the possibility of transferring population between two states of the ground manifold, also taking into account the interaction with a spherical nuclear-spin bath formed by nuclei of $^{29}\mathrm{Si}$ and $^{13}\mathrm{C}$. For this system, it is demonstrated that the presence of a small- or medium-sized bath has no effect on the protocol, finding in particular a set of parameter values for an efficient STIRAP process.

DOI
10.1103/physrevb.109.224305

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Physical Review A•Sep 10, 2014•19 citations
The stimulated Raman adiabatic passage (STIRAP) is applied to a system coupled to a bath made of fully interacting two-level systems whose dynamics is studied by exploiting the generalized cluster correlation expansion (gCCE) theory. We specialize our analysis to a negatively charged silicon vacancy (VSi\ensuremath−1{\mathrm{V}}_{\mathrm{Si}}^{\ensuremath{-}1}VSi\ensuremath−1​) in nonpurified 4H-SiC to assess the possibility of transferring population between two states of the ground manifold, also taking into account the interaction with a spherical nuclear-spin bath formed by nuclei of 29Si^{29}\mathrm{Si}29Si and 13C^{13}\mathrm{C}13C. For this system, it is demonstrated that the presence of a small- or medium-sized bath has no effect on the protocol, finding in particular a set of parameter values for an efficient STIRAP process.
The Stimulated Raman Adiabatic Passage (STIRAP) is applied to a system coupled to a bath made of fully-interacting two-level systems, whose dynamics is studied exploiting the generalized Cluster Correlation Expansion (gCCE) theory. We specialize our analysis to a negatively charged silicon vacancy (SiV-1) in non-purified 4H-SiC to assess the possibility of transferring population between two states of the ground manifold, also taking into account the interaction with a spherical nuclear spin bath formed by nuclei of 29Si and 13C. For this system, it is demonstrated that the presence of a small/medium sized bath has no effect on the protocol, finding in particular a set of parameter values for an efficient STIRAP process.
The Stimulated Raman Adiabatic Passage (STIRAP) on a three-state system interacting with a spin bath is considered, focusing on the efficiency of the population transfer. Our analysis is based on the perturbation treatment of the interaction term evaluated beyond the Rotating Wave Approximation, thus focusing on the limit of weak system–bath coupling. The analytical expression of the correction to the efficiency and the consequent numerical analysis show that, in most of the cases, the effects of the environment are negligible, confirming the robustness of the population transfer.
The prospect of employing the stimulated Raman adiabatic Passage (STIRAP) technique under the influence of pure dephasing is explored. A general analysis of how decoherence influences the performance of STIRAP is provided. Starting from a general and fully quantum-mechanical system–bath Hamiltonian, we derive a quantum master equation (QME) that describes the reduced dynamics of a dissipative STIRAP system. The derivation is based on the standard assumptions of (1) weak system–bath coupling; (2) Markovity, in the sense that the relaxation times are long in comparison to the bath correlation time, τc; and (3) weak field–matter interaction, in the sense that the Rabi period of the driving laser fields, Ω−1, is longer than τc. The dissipative term in this QME is the same as it would have been in the absence of the driving fields, because of the assumption of weak field–matter interaction. This type of uncontrollable dephasing is seen to diminish the efficiency of STIRAP, although the actual loss strongly depends on the specific dephasing mechanism. We also derive a more general QME, which is applicable to driving fields of arbitrary intensity. The dissipative term in the new QME is explicitly dependent on the driving fields, and therefore controllable. Intense fields are shown to effectively slow down the dephasing when Ωτc>1, which suggests that it may be possible to use STIRAP in order to transfer population between the quantum states of a solute molecule embedded in a solvent.
We examine the conditions needed to accomplish stimulated Raman adiabatic passage (STIRAP) when the three levels (ground ggg, excited eee, and final fff) are degenerate, with arbitrary couplings contributing to the pump-pulse interaction $(g\text{\ensuremath{-}}e)$ and to the Stokes-pulse interaction $(e\text{\ensuremath{-}}f)$. We show that in general a sufficient condition for complete population removal from the ggg set of degenerate states for arbitrary, pure or mixed, initial state is that the degeneracies should not decrease along the sequence ggg, eee, and fff. Using a sequence of unitary transformations we demonstrate that when this condition holds it is possible to achieve the degenerate counterpart of conventional STIRAP, whereby adiabatic passage produces complete population transfer. Indeed, the system is equivalent to a set of independent three-state systems, in each of which a STIRAP procedure can be implemented. We also examine the cases when this degeneracy constraint does not hold and show what can be accomplished in those cases. For example, for angular momentum states when the degeneracy of the ggg and fff levels is less than that of the eee level we show how a special choice for the pulse polarizations and phases can produce complete removal of population from the ggg set. Our scheme can be a powerful tool for coherent control in degenerate systems, because of its robustness, when selective addressing of the states is not required or impossible. We illustrate the analysis with several analytically solvable examples, in which the degeneracies originate from angular momentum orientation, as expressed by magnetic sublevels.
Stimulated Raman scattering involving adiabatic passage (STIRAP) is a proven technique for population transfer in three-level systems with strong oscillator strengths. We show that the STIRAP process should also yield high transfer efficiencies when the densities of states near the intermediate and final levels are high, provided certain criteria for the experimentally controllable parameters are met. We also show that high transfer efficiencies may even be possible when the pump and Stokes lasers can access levels outside of the three-level system. The criteria are derived with an approach that emphasizes the adiabatic nature of the transfer process in an eigenvector of the interaction Hamiltonian that resembles a trapped state. The results are compared to density matrix calculations.
This paper begins with the premise that stimulated Raman adiabatic passage (STIRAP) from one state to another by coupling to an intermediate state necessarily requires some population of that intermediate state. The usual view of the process depends on having no population in the intermediate state, but a simple argument from the time-dependent Schr\"odinger equation shows that such adiabatic transfer cannot occur. From another perspective, removing the time dependence of the Hamiltonian by making the rotating frame transformation cancels the optical frequency oscillations but does not account for the envelopes of the pulses commonly used for STIRAP. By assuming a small but finite intermediate state amplitude ${\ensuremath{\varepsilon}}_{1}$ in the wave function, the propagator for the evolution between initial and final states is derived. Applying the propagator to the initial state produces a single compact formula for the final intermediate-state population that is readily evaluated for an arbitrary choice of laser pulse parameters. Several plots for various experimental conditions show that under the conditions normally used for STIRAP experiments the effects are typically a few percent or less, but in the end this effect puts an ultimate limit on total efficiency.