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Acta Physica Sinica

ANALYSIS OF THE NUCLEAR QUADRUPOLE RESONACEFOR A ROTATING SAMPLE IN TERMS OF THE QUANTUMADIABATIC-PERTUBATION THEORY

Jian‐Min Yuan

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

For the degenerate case, the quantum adiabatic pertubation theory proposed recently in Ref. [6] is further developed in connection with Tycko's experiment of nuclear quadrupole resonace testing the Berry's phase. Using this developed theory, we, analyse the resonace asorption of the radio frequency field by a rotating sample with a nuclear quadrupole in detail and point out the possible new phenomenon in the corresponding experiment.

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For the degenerate case, the quantum adiabatic pertubation theory proposed recently in Ref. [6] is further developed in connection with Tycko's experiment of nuclear quadrupole resonace testing the Berry's phase. Using this developed theory, we, analyse the resonace asorption of the radio frequency field by a rotating sample with a nuclear quadrupole in detail and point out the possible new phenomenon in the corresponding experiment.
The 35Cl^{35}\mathrm{Cl}35Cl nuclear quadrupole resonance spectrum of a single crystal of sodium chlorate [R. Tycko, Phys. Rev. Lett. 58, 2281 (1987)] rotating about two axes reflects a non-Abelian gauge potential. This gauge potential is an example of Wilczek and Zee's [Phys. Rev. Lett. 52, 2111 (1984)] generalization of Berry's phase to the adiabatic transport of degenerate states.
A high-order adiabatic-approximation method is proposed to study the time evolution of degenerate quantum-mechanical systems with slowly changing Hamiltonians. We not only discuss the quantum adiabatic theorem, induced gauge structure, and non-Abelian Berry's phase factors in the first-order approximation, but we also give nonadiabatic corrections for problems in the second-order approximation. With the nuclear quadrupole resonance as an explicit example, we analyze the above-mentioned questions in detail and point out the observable effects of non-Abelian Berry's phase factors for nonadiabatic transitions between two instantaneous states in an improvement of Tycko's experiment.
The concept of geometric phase is demonstrated in a nuclear gyroscope using 131Xe^{131}\mathrm{Xe}131Xe nuclear spins (I=3/2) as sensors for quantum-phase accumulation. By spatial rotation sub-Hertz splittings due to geometric phases are resolved in nuclear-quadrupole spectra. Deviations from Berry's adiabatic geometric phase appear in the regime of nonadiabatic rotation. The observed frequency splittings are no longer linear in the rotational frequency, as expected from adiabatic rotations, and all possible transitions, namely, six in this partially degenerate spin-3/3 system, are observed experimentally.
In this paper high-order adiabatic approximate method is proposed to study the evolution of degenerate quantum systums with slowly-changing parameters and varying symmetry. We not only prove the quantum adiabatic theorem for degenerate cases and discuss the corresponding non-abelian induced gauge structure, but also point out the non-adiabatic corrections resulting from higher-order approximations. With nuclear quadrupole resonance as an explicit example, we use this method to analyse observable effects of non-abelian Berry's phases in adiabatic and non-adiabatic experimental process.
It is shown theoretically that by the use of two radio-frequency fields of the same resonance frequency but with the different phases and directions the degeneracy of the energy spectrum of a spin system with I = 3/2 is removed. This leads to four non-degenerate spin states which can be used as a platform for quantum computing. The feasibility of quantum computing based on a pure (without DC magnetic fields) nuclear quadrupole resonance technique is investigated in detail. Various quantum logic gates can be constructed by using different excitation techniques allowing different manipulations with the spin system states. Three realizations of quantum logic gates are considered: the application of an additional magnetic field with the resonance frequency, the amplitude modulation of one of the applied RF fields by the resonance frequency field, and the level-crossing method. It is shown that the probabilities of the resonance transitions depend on the method of excitation and on the direction of the excitation field. Feasibility of quantum computing is demonstrated with the examples of constructing a controlled-NOT logic gate using the resonance excitation technique and SWAP and NOT2 logic gates using the level-crossing method.