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Chinese Physics

Realization of adiabatic population transfer in a three-level system by using LR Hermitian invariants theory

Zhao Hua, Gao Ying‐Fang, Liang Jiu-Qing

Published May 27, 2004• 2 citations
Publisher

Abstract

We have studied the population transfer in a three-state system driven by laser beams in terms of the theory of Lewis–Riesenfeld Hermitian invariants for explicitly time-dependent Hamiltonian. The exact solutions obtained allow us to recover two existing schemes producing complete population transfer in the literature, i.e. the π-pulse and stimulated Raman adiabatic passage methods in our unified description. We present a strict formulation of adiabatic conditions and a more accurate expression of the π-pulse method according to the exact time-evolution of state vector.

DOI
10.1088/1009-1963/13/6/014

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We have studied the population transfer in a three-state system driven by laser beams in terms of the theory of Lewis–Riesenfeld Hermitian invariants for explicitly time-dependent Hamiltonian. The exact solutions obtained allow us to recover two existing schemes producing complete population transfer in the literature, i.e. the π-pulse and stimulated Raman adiabatic passage methods in our unified description. We present a strict formulation of adiabatic conditions and a more accurate expression of the π-pulse method according to the exact time-evolution of state vector.
ABSTRACT In this study, nonadiabatic population transfer was successfully achieved in a two‐level non‐Hermitian system with non‐conjugation complex Rabi frequencies and a real geometric phase along the superposition of ancillary basis states, by means of the ancillary picture and Lewis‐Riesenfeld (LR) invariant theory. Compared with the quantum adiabatic process, the core advantage of this scheme lies in that the inherent high‐speed characteristic of nonadiabatic evolution can avoid non‐targeted transitions, thus overcoming the limitations of traditional nonadiabatic processes. The Hamiltonian of the system was derived based on the laws of non‐unitary evolution. Time‐dependent complex pulses can be effectively regulated by adjusting control parameters; in the nonadiabatic population transfer process, the target pulses can be obtained simply by determining the relevant parameters in the non‐unitary evolution. Through the analysis of system dynamics via the ancillary picture and LR invariant theory, and verification by numerical simulations, it is shown that population inversion (the core characteristic of nonadiabatic population transfer) exhibits strong anti‐interference ability against system errors. In conclusion, this scheme provides a feasible approach for realizing high‐fidelity nonadiabatic population transfer in the aforementioned two‐level non‐Hermitian system.
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.
It introduced several methods to transfer population,including two-level system and three-level system, and gave some comparisons on transfer efficiency and transfer velocity of them in theory. It is shown that population transfer by coherent pulse sequence is better than incoherence one. Numerical simulation results showed that when using Stimulated Raman Adiabatic Rapid Passage (STIRAP), in which the pump laser pulse fully overlaps the Stokes pulse with the Stokes preceding the pump, population can be transferred completely and rapidly. Robust control of population transfer among Zeeman sublevels in the ground states of three-level system is investigated using adiabatic rapid passage in theory. The laser pulse widths are supposed to be short compared to the lifetime of the excited level, which means adiabatic. We demonstrated that techniques of STIRAP can be found to optimize population transfer in the ground states of three-level Λ system.
We show that the physical mechanism of population transfer in a three-level system with a closed loop of coherent couplings is not equivalent to an adiabatic rotation of the dark state of the Hamiltonian, but corresponds to a rotation of a higher-order trapping state in a generalized adiabatic basis. The concept of generalized adiabatic basis sets is used as a constructive tool to design pulse sequences for stimulated Raman adiabatic passage, which also give maximum population transfer under conditions when the usual condition of adiabaticty is only poorly fulfilled. Under certain conditions for the pulses (generalized matched pulses), there exists a higher-order trapping state, which is an exact constant of motion, and analytic solutions for the atomic dynamics can be derived.