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Physical Review A

Nonadiabaticity in stimulated Raman adiabatic passage

Yuan Sun, Harold J. Metcalf

Published Sep 10, 2014• 19 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.90.033408

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arXiv:quant-ph/9811079•Nov 27, 1998•1 citation
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 \ensuremathε1{\ensuremath{\varepsilon}}_{1}\ensuremathε1​ 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.
This paper discusses a generalization of stimulated Raman adiabatic passage (STIRAP) in which the single intermediate state is replaced by N intermediate states. Each of these states is connected to the initial state ${\ensuremath{\psi}}_{i}$ with a coupling proportional to the pump pulse and to the final state ${\ensuremath{\psi}}_{f}$ with a coupling proportional to the Stokes pulse, thus forming a parallel multi-\ensuremath{\Lambda} system. It is shown that the dark (trapped) state exists only when the ratio between each pump coupling and the respective Stokes coupling is the same for all intermediate states. We derive the conditions for existence of a more general adiabatic-transfer state that includes transient contributions from the intermediate states but still transfers the population from state ${\ensuremath{\psi}}_{i}$ to state ${\ensuremath{\psi}}_{f}$ in the adiabatic limit. We present various numerical examples for success and failure of multi-\ensuremath{\Lambda} STIRAP, which illustrate the analytic predictions. Our results suggest that in the general case of arbitrary couplings, it is most appropriate to tune the pump and Stokes lasers either just below or just above all intermediate states.
This work explores the effect of phase relaxation on the population transfer efficiency in stimulated Raman adiabatic passage (STIRAP). The study is based on the Liouville equation, which is solved analytically in the adiabatic limit. The transfer efficiency of STIRAP is found to decrease exponentially with the dephasing rate; this effect is stronger for shorter pulse delays and weaker for larger delays, since the transition time is found to be inversely proportional to the pulse delay. Moreover, it is found that the transfer efficiency of STIRAP in the presence of dephasing does not depend on the peak Rabi frequencies at all, as long as they are sufficiently large to enforce adiabatic evolution; hence increasing the field intensity cannot reduce the dephasing losses. It is shown also that for any dephasing rate, the final populations of the initial state and the intermediate state are equal. For strong dephasing all three populations tend to 13\frac{1}{3}31​.
The technique of stimulated Raman adiabatic passage (STIRAP) is an efficient and robust technique for population transfer in three-state chain-wise connected quantum systems, 1-2-3. Here we analyze the transition time in STIRAP, that is the time it takes for the population to be transferred from state 1 to state 3. We derive a very simple formula for this transition time, which shows that it is inversely proportional to the nonadiabatic coupling $\mathrm{\ensuremath{\vartheta}\ifmmode \dot{}\else \.{}\fi{}}({t}_{c})$, estimated at the time tc{t}_{c}tc​ when the pump and Stokes couplings have the same value. Explicit formulas for several pulse shapes of the pump and Stokes fields are derived. Contrary to the naive expectation that the transition time might be proportional to the delay between the pump and Stokes pulses, or to the width of their overlap region, we find that the transition time is inversely proportional to the delay, i.e., larger delays produce faster transitions. We also calculate the transition time in two important variations of the STIRAP technique---bright-STIRAP and STIRAP in multistate systems---where similar features are found.
We explore theoretically the rovibrational dynamics of stimulated Raman adiabatic passage (STIRAP) in molecular electronic states including both the rotational and the vibrational degrees of freedom, with the LiH molecule as an example. By using a pure rovibrational state as initial state, we find that, under the condition of two-photon resonance, an efficient rovibrational population transfer can be achieved via STIRAP in molecular electronic states and the desired target state can be selected by adjusting laser-pulse parameters. Besides the interested rovibrational states, however, some unwanted rovibrational states may affect population transfer process, especially while the two-photon detuning is taken into account. By inspecting the evolution process of wave packet, we can easily search these unwanted rovibrational states and study their influences. Moreover, the effect of rotational temperature on the population transfer process is discussed using thermal mixed state as initial state.
We discuss the detrimental effect of small rapid random fluctuations of laser-field amplitude and phase upon the efficiency of stimulated Raman adiabatic passage (STIRAP). Such fluctuations typically accompany the laser stabilization procedures that produce nearly monochromatic light on top of a much broader bandwidth Lorentz-profile pedestal which may carry only a few percent or less of the total power. As we will show, their effects differ qualitatively from the fluctuations that have hitherto been considered (for example, phase diffusion). We present analytic expressions for the population transfer efficiency of STIRAP when limited by stochastic fluctuations of this type. These expressions show, in contrast to situations discussed in the past in which population transfer improves with increasing peak Rabi frequencies, that for the weak broadband noise that accompanies a strong narrow-spectral component, there is an optimum value for the peak Rabi frequency and that the effect of fluctuations, although small, cannot be entirely eliminated in practice. The mission of the current work is to point out that, under the given circumstances, efforts in experiments trying to overcome the detrimental consequences of fluctuations by increasing the intensity, which is the intuitively proper approach, will not be successful.
We discuss a simple scheme for preparing atoms and molecules in an arbitrary preselected coherent superposition of quantum states. The technique, which we call fractional stimulated Raman adiabatic passage ({\it f-STIRAP}), is based upon (incomplete) adiabatic population transfer between an initial state ψ1ψ_1ψ1​ and state ψ3ψ_3ψ3​ through an intermediate state ψ2ψ_2ψ2​. As in STIRAP, the Stokes pulse arrives before the pump pulse, but unlike STIRAP, the two pulses terminate simultaneously while maintaining a constant ratio of amplitudes. The independence of f-STIRAP from details of pulse shape and pulse area makes it the analog of conventional STIRAP in the creation of coherent superpositions of states. We suggest a smooth realization of f-STIRAP which requires only two laser pulses (which can be derived from a single laser) and at the same time ensures the automatic fulfillment of the asymptotic conditions at early and late times. Furthermore, we provide simple analytic estimates of the robustness of f-STIRAP against variations in the pulse intensity, the pulse delay, and the intermediate-state detuning, and discuss its possible extension to multistate systems.