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arXiv:2305.08209 · Symmetry

Adiabatic Manipulation of a System Interacting with a Spin Bath

Benedetto Militello, Anna Napoli

Published Nov 8, 2023• 2 citations
arXivHTMLPDF

Abstract

The Stimulated Raman Adiabatic Passage, a very efficient technique for manipulating a quantum system based on the adiabatic theorem, is analyzed in the case where the manipulated physical system is interacting with a spin bath. The exploitation of the rotating wave approximation allows for the identification of a constant of motion, which simplifies both the analytical and the numerical treatment, which allows for evaluating the total unitary evolution of the system and bath. The efficiency of the population transfer process is investigated in several regimes, including the weak and strong coupling with the environment and the off-resonance. The formation of appropriate Zeno subspaces explains the lowering of the efficiency in the strong damping regime.

DOI
10.3390/sym15112028

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The Stimulated Raman Adiabatic Passage, a very efficient technique for manipulating a quantum system based on the adiabatic theorem, is analyzed in the case where the manipulated physical system is interacting with a spin bath. The exploitation of the rotating wave approximation allows for the identification of a constant of motion, which simplifies both the analytical and the numerical treatment, which allows for evaluating the total unitary evolution of the system and bath. The efficiency of the population transfer process is investigated in several regimes, including the weak and strong coupling with the environment and the off-resonance. The formation of appropriate Zeno subspaces explains the lowering of the efficiency in the strong damping regime.
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.
A master equation approach to the study of environmental effects in the adiabatic population transfer in three-state systems is presented. A systematic comparison with the non-Hermitian Hamiltonian approach [Vitanov and Stenholm, Phys. Rev. A 56, 1463 (1997)] shows that, in the weak-coupling limit, the two treatments lead to essentially the same results. In contrast, in the strong-damping limit the predictions are quite different: In particular, the counterintuitive sequences in the STIRAP scheme turn out to be much more efficient than expected before. This point is explained in terms of quantum Zeno dynamics.
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.
The stimulated Raman adiabatic passage 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 general approach to robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control. By controlling the dynamical process, we inversely design a family of Hamiltonians with non-divergent Rabi frequencies that can realize fast and accurate population transfer from the first to the third level, while the systematic errors are 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.
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.
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.