arXiv quant-ph/04041142004-04-20quant-ph

椭圆磁场中的磁共振

Magnetic resonance in an elliptic magnetic field

E. A. Ivanchenko

备注：: 11 pages, Latex2e, no figures; submitted to Physica B
发表信息：: Physica B 358 (2005) 308-313
DOI：: 10.1016/j.physb.2005.01.466

摘要：

本文研究了自旋为1/2且具有偶极磁矩的粒子在$(h_0 cn(ωt,k), h_0 sn(ωt,k), H_0 dn(ωt,k))$形式的时变磁场中的行为，其中$ω$是驱动场频率，$t$是时间，$h_0$和$H_0$是场振幅，$cn$，$sn$，$dn$是Jacobi椭圆函数，$ k$是椭圆函数的模。从零到1的变化参数$k$产生从三角形形状到调制场的指数脉冲形状的广泛的函数集合。将问题归结为一般Heun方程的解。在任何$ k$的共振波函数的精确解。它已被证明，在这种情况下的转移概率不依赖于$k$。本研究对分析干涉实验、改进磁谱仪和量子计算等领域有一定的参考价值。

英文摘要：

The behaviour of a particle with a spin 1/2 and a dipole magnetic moment in a time-varying magnetic field in the form $(h_0 cn(ωt,k), h_0 sn(ωt,k), H_0 dn(ωt,k))$, where $ω$ is the driving field frequency, $t$ is the time, $h_0$ and $H_0$ are the field amplitudes, $cn$, $sn$, $dn$ are Jacobi elliptic functions, $ k$ is the modulus of the elliptic functions has been considered. The variation parameter $k$ from zero to 1 gives rise to a wide set of functions from trigonometric shapes to exponential pulse shapes modulating the field. The problem was reduced to the solution of general Heun' equation. The exact solution of the wave function was found at resonance for any $ k$. It has been shown that the transition probability in this case does not depend on $k$. The present study may be useful for analysis interference experiments, improving magnetic spectrometers and the field of quantum computing.

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摘要：

英文摘要：

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