The 2008 experiments of Klein, Beil and Halfmann established stimulated Raman adiabatic passage (STIRAP) — and its detuned, intuitive-order variant, bright STIRAP (b-STIRAP) — as workable coherent population transfer between hyperfine ground states of Pr3+^{3+}:Y2_2SiO5_5, while explicitly leaving three linked issues open: unexplained deviations between the numerical model and the measured transfer data in weak-adiabaticity regimes (intuitive pulse ordering at large pulse delays), the sensitivity of bright STIRAP to common-mode laser frequency jitter and to radiative loss from the intermediate excited state, and the absence of systematic fidelity and scalability studies of STIRAP variants in doped solids under device-oriented constraints. The problem asks for the quantitative explanation of these deviations, for optimized and demonstrated strategies that extend coherent adiabatic transfer despite jitter and intermediate-state loss, and for the systematic characterization needed to assess adiabatic transfer in doped solids for quantum-information applications. Partial progress exists — composite STIRAP in the same material, robust-passage and shortcut-to-adiabaticity theory and experiments in other platforms — but none of the three strands has been resolved.

Background

Stimulated Raman adiabatic passage (STIRAP) is a coherent-control technique that transfers population between two long-lived quantum states ∣1⟩|1\rangle and ∣3⟩|3\rangle of a three-level 'Lambda' system by driving both to a short-lived intermediate state ∣2⟩|2\rangle with two lasers, called pump and Stokes. Its hallmark is the counterintuitive pulse order — the Stokes pulse (coupling the initially empty target state to ∣2⟩|2\rangle) precedes the pump pulse — under which the state vector adiabatically follows a 'dark' superposition of ∣1⟩|1\rangle and ∣3⟩|3\rangle that contains no amplitude of the lossy intermediate state. Transfer can then be complete and robust against variations of Rabi frequencies and pulse timing even when ∣2⟩|2\rangle decays rapidly. With both lasers detuned from single-photon resonance but kept on two-photon resonance, the reversed (intuitive, pump-first) ordering can also produce adiabatic transfer; it proceeds through a 'bright' adiabatic eigenstate that does contain a transient component of the decaying intermediate state. This variant is called bright STIRAP (b-STIRAP); its efficiency is intrinsically lower than dark-state STIRAP, and it depends on the value of the single-photon detuning.

Rare-earth ions doped into dielectric crystals at cryogenic temperature combine narrow optical transitions with long-lived hyperfine ground-state coherences, making them leading candidates for optical quantum memories and processors. The workhorse material Pr3+^{3+}:Y2_2SiO5_5 has hyperfine ground-state coherences of order hundreds of microseconds (extendable by magnetic-field tuning), an excited-state lifetime of about 164 μ\mus, and — because each dopant ion sees a slightly different crystal environment — inhomogeneous broadening of several GHz on the optical transitions, so that experiments must first carve out a 'spectral pit' by optical pumping and spectral hole burning (removing population from a selected frequency class of ions) before a well-defined Lambda system is addressed.

After the first demonstration of STIRAP in a doped solid by Goto and Ichimura (2006), Klein, Beil and Halfmann demonstrated robust STIRAP between hyperfine levels of Pr3+^{3+}:Y2_2SiO5_5 in 2007 and in 2008 published the detailed parameter study that underlies this problem: transfer efficiency versus Rabi frequencies, detunings, and pulse delay for both dark-state STIRAP and bright STIRAP, with numerical simulations that included a stochastic model of laser frequency jitter. An independent replication in Tm3+^{3+}:YAG (Alexander et al., 2008) confirmed the platform generality — roughly 90% efficiency for STIRAP but only about 45% for bright STIRAP — and the authoritative review by Vitanov, Rangelov, Shore and Bergmann (2017) codified the understanding that bright STIRAP's lower efficiency stems from the bright eigenstate's component of the decaying intermediate state. The 2008 paper closed by stating the limitations that define this problem: the numerical model deviated from the data in weak-adiabaticity regimes (intuitive pulse ordering at delays so large that the pulses barely overlap), with the origin not identified; bright STIRAP's viability is limited by common-mode laser frequency jitter (correlated frequency fluctuations of both lasers, which preserve two-photon resonance but fluctuate the single-photon detuning on which bright STIRAP relies) and by radiative loss from the intermediate state; and systematic studies of the scalability and fidelity of STIRAP variants in doped solids under realistic device-oriented constraints — larger inhomogeneous ensembles, integrated photonic geometries, longer experimental sequences — remained to be done before these techniques could be assessed for quantum-information applications.

Problem Statement

Establish adiabatic population transfer in rare-earth-ion-doped solids as a quantitatively understood, robust, and scalable tool for quantum-information applications, building on the Pr3+^{3+}:Y2_2SiO5_5 experiments of Klein, Beil and Halfmann (2008). This requires three jointly supporting results.

(1) Quantitative explanation of the weak-adiabaticity deviations: identify the physical mechanism(s) — residual experimental imperfections, additional decoherence channels, or inadequacy of the stochastic laser-jitter model — responsible for the reported deviations between the numerical simulations and the measured transfer data in weak-adiabaticity regimes, in particular for the intuitive (reversed) pulse ordering at pulse delays large enough that the pump and Stokes pulses barely overlap, and incorporate them into a model that predicts (not merely fits) the measured transfer efficiencies versus pulse delay, detuning, and Rabi frequency across the parameter range.

(2) Robustness strategies for coherent transfer, including bright STIRAP: determine and demonstrate optimized strategies — pulse shapes and composite phase sequences, choices of detuning and Rabi strength, improved laser coherence, engineered level structures — that extend high-fidelity coherent adiabatic population transfer in doped solids in the presence of the two mechanisms that limit bright STIRAP: common-mode laser frequency jitter, which fluctuates the single-photon detuning on which the bright-state transfer relies, and radiative loss from the intermediate excited state, which is transiently populated in the bright-STIRAP mechanism.

(3) Systematic fidelity and scalability characterization: measure and characterize the transfer fidelity and scalability of STIRAP and its variants in doped solids under realistic device-oriented constraints — larger inhomogeneously broadened ensembles, integrated photonic geometries, and longer or repeated experimental sequences — so that these adiabatic transfer protocols can be genuinely assessed for quantum-information applications.

The problem is resolved when these results jointly hold: the deviations are explained within a model validated across the experimental parameter range, the robustness strategies are demonstrated with fidelities quantified against the specific jitter and radiative-loss channels they are claimed to overcome, and the transfer fidelity and scalability under each of the device-oriented constraints — larger inhomogeneously broadened ensembles, integrated photonic geometries, and longer or repeated experimental sequences — are measured or rigorously bounded.

References

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