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Journal of the Physical Society of Japan

Spin Depolarization of a Quantum Particle on a Liner Chain with Alternating Larmor Frequencies

K. W. Kehr, Kazuo Kitahara

Published Aug 15, 1988• 6 citations
Publisher

Abstract

The spin depolarization of a particle on a linear chain with alternating Larmor frequencies is considered. The particle is initially prepared at one site with polarized spin. A crossover from initially classical behavior to an asymptotic polarization is found, as a consequence of quantum-mechanical tunneling. The influence of dynamic fluctuations on the spin depolarization is studied in the frame of the Haken-Strobl model.

DOI
10.1143/jpsj.57.2819

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The spin depolarization of a particle on a linear chain with alternating Larmor frequencies is considered. The particle is initially prepared at one site with polarized spin. A crossover from initially classical behavior to an asymptotic polarization is found, as a consequence of quantum-mechanical tunneling. The influence of dynamic fluctuations on the spin depolarization is studied in the frame of the Haken-Strobl model.
The spin depolarization of a particle in quantum states is considered using a model of two sites, having different transverse magnetic fields, and between which the particle can tunnel. The ensemble average is performed with random distributions of the magnetic fields. A Gaussian decay law is obtained with the exponent reduced by a factor 2, for all times when the system is prepared in suitable eigenstates and for longtimes with arbitrary preparation. The apparent contradiction to van Vleck's theorem is resolved.
We extend the picture of a transfer of nuclear spin-1/2 polarization along a homogeneous one-dimensional chain with the XY Hamiltonian to the inhomogeneous chain with alternating nearest neighbor couplings and alternating Larmor frequencies. To this end, we exactly calculate the spectrum of the spin-1/2 XY Hamiltonian of the alternating chain with an odd number of sites. The exact spectrum of the XY Hamiltonian is also applied to study the multiple quantum (MQ) NMR dynamics of the alternating spin-1/2 chain. MQ NMR spectra are shown to have the MQ coherences of zero and ± second orders just as in the case of a homogeneous chain. The intensities of the MQ coherences are calculated.
Abstract We theoretically describe the phenomenon of non-adiabatic spin dynamics, which occurs in a gas cell filled by alkali vapor in the presence of a strong alternating magnetic field and pump light. Steep increase of the spin polarization occurs if the frequency of the magnetic field is equal to the certain value. The observable effect relies on the periodic field that consists of two perpendicular components defined by harmonics with the same amplitudes and different frequencies. The considered effect of the coherent spin motion cannot be explained by a resonance, because the Larmor precession is absent without a constant component of magnetic field. Moreover, there are some clearly visible peaks in the excitation spectrum of spin polarization, which are narrow in comparison to the relaxation rate. Detailed analysis according to proposed quantum model results in the reasoning of the effect via qualitative properties of non-adiabatic dynamics of atomic spin.
We theoretically describe the phenomenon of non-adiabatic spin dynamics, which occurs in a gas cell filled by alkali vapor in presence of a strong alternating magnetic field and pump light. Steep increase of the spin polarization occurs if frequency of the magnetic field is equal to the certain value. Although, the observable effect relies on the periodic field that consists of two perpendicular components defined by harmonics with the same amplitudes and different frequencies. Considered spin effect cannot be explained by a resonance, because the own Larmor frequency of spin precession is absent without a constant component of magnetic field. Moreover, there are some clearly visible peaks in the excitation spectrum of spin polarization, and they are super narrow in comparison to relaxation rate. Detailed analysis according to proposed quantum model results in the reasoning of the effect via qualitative properties of non-adiabatic dynamics of atomic spin.
We numerically study two methods of measuring tunneling times using a quantum clock. In the conventional method using the Larmor clock, we show that the Larmor tunneling time can be shorter for higher tunneling barriers. In the second method, we study the probability of a spin-flip of a particle when it is transmitted through a potential barrier including a spatially rotating field interacting with its spin. According to the adiabatic theorem, the probability depends on the velocity of the particle inside the barrier. It is numerically observed that the probability increases for higher barriers, which is consistent with the result obtained by the Larmor clock. By comparing outcomes for different initial spin states, we suggest that one of the main causes of the apparent decrease in the tunneling time can be the filtering effect occurring at the end of the barrier.
Abstract Spin relaxation of spin‐1/2 quantum particles on linear chains with random Larmor frequencies is studied. Wave packets are prepared with initial spin polarization in the propagation direction and with either zero, or finite group velocity. The discrete Schrödinger‐Pauli equation is solved numerically. Exponential spin relaxation is observed in a restricted time range. The decay constant depends on the width of the distribution of the Larmor frequencies and on the group velocity. No dependence on the initial halfwidth of the wave packet is found.