Homotrinuclear Spin Cluster with Orbital Degeneracy in a Magnetic Field: Algebraic Dynamic Studies of the Geometric Phase January 25, 2008

2008 ◽  
Vol 63 (7-8) ◽  
pp. 405-411
Author(s):  
Ji-Wen Cheng ◽  
Qin-Sheng Zhu ◽  
Xiao-Yu Kuang ◽  
Shi-Xun Zhang ◽  
Cai-Xia Zhang
Keyword(s):  
Magnetic Field ◽  
Geometric Phase ◽  
Berry Phase ◽  
Energy Levels ◽  
Rotating Magnetic Field ◽  
Algebraic Dynamics ◽  
Orbital Degeneracy ◽  
Spin Cluster ◽  
Dynamic Studies ◽  
Adiabatic Energy

Based on the homotrinuclear spin cluster having SU(2)⊗SU(2) symmetry with twofold orbital degeneracy τ = 1/2) and the SU(2) algebraic structures of both ŝ and τˆ subspaces in the external magnetic field, we calculate exactly the non-adiabatic energy levels and the cyclic and non-cyclic non-adiabatic geometric phase of the homotrinuclear spin cluster by making use of the method of algebraic dynamics. The solution will show that the Berry phase is much influenced by the parameters N =γs/γτ (γs and γτ are the magnetic momentums of ŝ and τ̂ subspaces, respectively) in addition to ω/Ω in a rotating magnetic field. The change of the Berry phase in the basis state of the system is demonstrated from the changing diagram.

Algebraic dynamic study of geometric phase for a homonuclear linear spincluster

2007 ◽  
Vol 85 (8) ◽  
pp. 879-885
Author(s):  
X -X Chen ◽  
J Xue
Keyword(s):  
Magnetic Field ◽  
Coupling Strength ◽  
Geometric Phase ◽  
Time Dependent ◽  
Algebraic Dynamics ◽  
Spin Cluster ◽  
Alternative Expression ◽  
Linear Formula ◽  
External Time ◽  
The Magnetic Field

A homonuclear linear [Formula: see text] coupling spin cluster with the middle particle driven by an external time-dependent magnetic field is investigated by using the method of algebraic dynamics. The exact analytical solutions of the time-dependent Schrodinger equation of the spin cluster system are derived and employed to study the geometric phase. An alternative expression of the geometric phase in each eigenstate is obtained. It is shown that the geometric phase is related to the external magnetic-field parameter θ (the angle between the magnetic field and the Z axis) and the effective coupling strength Jn. Based on the relation, how the geometric phase depends on the coupling strength Jn in different reducible subspace is discussed.PACS Nos.: 33.20.Wr, 03.65.Fd, 03.65.Vf

scholarly journals SHOT NOISE FOR ENTANGLED ELECTRONS WITH BERRY PHASE

2007 ◽  
Vol 21 (07) ◽  
pp. 399-406
Author(s):  
HUI ZHAO ◽  
XUEAN ZHAO ◽  
YOU-QUAN LI
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Shot Noise ◽  
Beam Splitter ◽  
Berry Phase ◽  
Scattering Matrix ◽  
Rotating Magnetic Field ◽  
Matrix Approach ◽  
Rotating Magnetic Fields ◽  
New Approach

We study shot noise for entangled electrons in a 4-lead beam-splitter with one incoming lead driven by adiabatically rotating magnetic fields. We propose a setup of an adiabatically rotating magnetic field which is appropriate for an electron beam to transport through. Using the scattering matrix approach, we find that shot noise for the singlet and that for the entangled triplet oscillates between bunching and antibunching due to the influence of the Berry phase. It provides us with a new approach for testing the Berry phase in electron transport on the basis of entanglement.

scholarly journals Design of geometric phase gates and controlling the dynamic phase for a two-qubit Ising model in magnetic fields

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120743 ◽  
Author(s):  
M. Amniat-Talab ◽  
H. Rangani Jahromi
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Static Magnetic Field ◽  
Geometric Phase ◽  
Rotation Axis ◽  
Interaction Constant ◽  
Rotating Magnetic Field ◽  
Initial State ◽  
Geometric Phases ◽  
Phase Gate

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.

Geometric phase in quantum mechanics and calculation for spin one-half in a rotating magnetic field

2012 ◽  
Vol 90 (7) ◽  
pp. 605-609
Author(s):  
Paul Bracken
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Quantum System ◽  
Geometric Phase ◽  
Rotating Magnetic Field ◽  
Mathematical Formalism ◽  
Geometric Phases

A mathematical formalism for describing geometric phases is presented. A development of the geometric phase is given, which is valid for noncyclic nonadiabatic processes. The result is used to calculate exactly the geometric phase for a quantum system that is made up of a spin one-half system in a rotating magnetic field.

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