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arXiv:0812.0361 · Journal of Physics B Atomic Molecular and Optical Physics

Stimulated Raman adiabatic passage analogues in classical physics

Andon A. Rangelov, Nikolay V. Vitanov, B W Shore

Published Feb 16, 2009• 10 citations
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Abstract

Stimulated Raman adiabatic passage (STIRAP) is a well-established technique for producing coherent population transfer in a three-state quantum system. We here exploit the resemblance between the Schrödinger equation for such a quantum system and the Newton equation of motion for a classical system undergoing torque to discuss several classical analogues of STIRAP, notably the motion of a moving charged particle subject to the Lorentz force of a quasistatic magnetic field, the orientation of a magnetic moment in a slowly varying magnetic field and the Coriolis effect. Like STIRAP, these phenomena occur for counterintuitive motion of the torque and are robustly insensitive to small changes in the interaction properties.

DOI
10.1088/0953-4075/42/5/055504

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Stimulated Raman adiabatic passage (STIRAP) is a well-established technique for producing coherent population transfer in a three-state quantum system. We here exploit the resemblance between the Schrödinger equation for such a quantum system and the Newton equation of motion for a classical system undergoing torque to discuss several classical analogues of STIRAP, notably the motion of a moving charged particle subject to the Lorentz force of a quasistatic magnetic field, the orientation of a magnetic moment in a slowly varying magnetic field and the Coriolis effect. Like STIRAP, these phenomena occur for counterintuitive motion of the torque and are robustly insensitive to small changes in the interaction properties.
The procedure of stimulated-Raman adiabatic passage (STIRAP), one of many well-established techniques for quantum-state manipulation, finds widespread application in chemistry, physics, and information processing. Numerous reviews discuss these applications, the history of its development, and some of the underlying physics. This tutorial supplies material useful as background for the STIRAP reviews as well as related techniques for adiabatic manipulation of quantum structures, with emphasis on the theory and simulation rather than on experimental results. It particularly emphasizes the picturing of behavior in various abstract vector spaces, wherein torque equations offer intuition about adiabatic changes. Appendices provide brief explanations of related coherent-excitation topics and useful evaluations of relative strengths of coherent transitions—the Rabi frequencies—involving Zeeman sublevels.
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 propose a method to improve the stimulated Raman adiabatic passage (STIRAP) via dissipative quantum dynamics, taking into account the dephasing effects. Fast and robust population transfer can be obtained with the scheme by the designed pulses and detuning, even though the initial state of the system is imperfect. With a concrete three-level system as an example, the influences of the imperfect initial state, variations in the control parameters, and various dissipation effects are discussed in detail. The numerical simulation shows that the scheme is insensitive to moderate fluctuations of experimental parameters and the relatively large dissipation effects of the excited state. Furthermore, the dominant dissipative factors, namely, the dephasing effects of the ground states and the imperfect initial state are no longer undesirable, in fact, they are the important resources to the scheme. Therefore, the scheme could provide more choices for the realization of the complete population transfer in the strong dissipative fields where the standard stimulated Raman adiabatic passage or shortcut schemes are invalid.
The stimulated Raman adiabatic passage (STIRAP) shows an efficient technique that accurately transfers population between two discrete quantum states with the same parity, in three-level quantum systems based on adiabatic evolution. This technique has widely theoretical and experimental applications in many fields of physics, chemistry, and beyond. Here, we present a generally robust approach to speed up STIRAP with invariant-based shortcut to adiabaticity. By controlling the dynamical process, we inversely design a family of Hamiltonians that can realize fast and accurate population transfer from the first to the third level, while the systematic error is largely suppressed in general. Furthermore, a detailed trade-off relation between the population of the intermediate state and the amplitudes of Rabi frequencies in the transfer process is illustrated. These results provide an optimal route toward manipulating the evolution of three-level quantum systems in future quantum information processing.
Stimulated Raman adiabatic passage is a quantum protocol that can be used for robust state preparation in a three-level system. It has been commonly employed in quantum optics, but recently this technique has drawn attention also in circuit quantum electrodynamics. The protocol relies on two slowly varying drive pulses that couple the initial and the target state via an intermediate state, which remains unpopulated. Here we study the detrimental effect of the parasitic couplings of the drives into transitions other than those required by the protocol. The effect is most prominent in systems with almost harmonic energy level structure, such as the transmon. We show that under these conditions in the presence of decoherence there exists an optimal STIRAP amplitude for population transfer.