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Chinese Physics Letters

Spin Switch and Qubit Register from a Spin Particle Controlled by a Time-Dependent Magnetic Field

Shun-Jin Wang, Jia Cheng-Long, Jun‐Hong An, Hong‐Gang Luo

Published May 1, 2004• 5 citations
Publisher

Abstract

A spin particle subjected to any time-dependent magnetic field is investigated in detail at different magnetic field configurations. Spin flip probability, spin alignment, cyclic and noncyclic nonadiabatic geometric phases are calculated exactly and their analytical expressions are presented. Our theoretical study shows that a spin particle controlled by a resonant time-dependent magnetic field can be used as efficient controllable devices of spin switch or qubit register.

DOI
10.1088/0256-307x/21/5/004

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A spin particle subjected to any time-dependent magnetic field is investigated in detail at different magnetic field configurations. Spin flip probability, spin alignment, cyclic and noncyclic nonadiabatic geometric phases are calculated exactly and their analytical expressions are presented. Our theoretical study shows that a spin particle controlled by a resonant time-dependent magnetic field can be used as efficient controllable devices of spin switch or qubit register.
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We derive a formula of the nonadiabatic noncyclic Pancharatnam phase for a quantum spin-12\frac{1}{2}21​ particle subject to an arbitrary magnetic field. The formula is applied to three specific kinds of magneic fields. (i) For an orientated magnetic field, the Pancharatnam phase is derived exactly. (ii) For a rotating magnetic field, the evolution equation is solved analytically. The Aharonov-Anandan phase is obtained exactly and the Pancharatnam phase is computed numerically. (iii) We propose a kind of topological transition in one-dimensional mesoscopic ring subject to an in-plane magnetic field, and then address the nonadiabatic noncyclic effect on this phenomenon.
It is well known that any cyclic solution of a spin 1/2 neutral particle moving in an arbitrary magnetic field has a nonadiabatic geometric phase proportional to the solid angle subtended by the trace of the spin. For neutral particles with higher spin, this is true for cyclic solutions with special initial conditions. For more general cyclic solutions, however, this does not hold. As an example, we consider the most general solutions of such particles moving in a rotating magnetic field. If the parameters of the system are appropriately chosen, all solutions are cyclic. The nonadiabatic geometric phase and the solid angle are both calculated explicitly. It turns out that the nonadiabatic geometric phase contains an extra term in addition to the one proportional to the solid angle. The extra term vanishes automatically for spin 1/2. For higher spin, however, it depends on the initial condition. We also consider the valence electron of an alkaline atom. For cyclic solutions with special initial conditions in an arbitrary strong magnetic field, we prove that the nonadiabatic geometric phase is a linear combination of the two solid angles subtended by the traces of the orbit and spin angular momenta. For more general cyclic solutions in a strong rotating magnetic field, the nonadiabatic geometric phase also contains extra terms in addition to the linear combination.
We investigate how to obtain a non-trivial geometric phase gate for a two-qubit spin chain, with Ising interaction in different magnetic fields. Indeed, one of the spins is driven by a time-varying rotating magnetic field, and the other is coupled with a static magnetic field in the direction of the rotation axis. This is an interesting problem both for the purpose of measuring the geometric phases and in quantum computing applications. It is shown that the static magnetic field does not change the adiabatic states of the system, and it does not affect the geometric phases, whereas it may be used to control the dynamic phases. In addition, by considering the exact two-spin adiabatic geometric phases, we find that a non-trivial two-spin unitary transformation, purely based on Berry phases, can be obtained by using two consecutive cycles with opposite directions of the magnetic fields, opposite signs of the interaction constant and the phase shift of the rotating magnetic field. In addition, in the non-adiabatic case, starting with a certain initial state, a cycle can be achieved and thus the Aharonov–Anandan phase is calculated.