|
| related topics |
| {phase, path, phys} |
| {time, decoherence, evolution} |
| {operator, operators, space} |
| {let, theorem, proof} |
| {states, state, optimal} |
| {level, atom, field} |
| {state, algorithm, problem} |
| {error, code, errors} |
| {group, space, representation} |
| {cos, sin, state} |
| {information, entropy, channel} |
| {equation, function, exp} |
|
Abelian and non-Abelian geometric phases in adiabatic open quantum
systems
M. S. Sarandy, D. A. Lidar
abstract: We introduce a self-consistent framework for the analysis of both Abelian and
non-Abelian geometric phases associated with open quantum systems, undergoing
cyclic adiabatic evolution. We derive a general expression for geometric
phases, based on an adiabatic approximation developed within an inherently
open-systems approach. This expression provides a natural generalization of the
analogous one for closed quantum systems, and we prove that it satisfies all
the properties one might expect of a good definition of a geometric phase,
including gauge invariance. A striking consequence is the emergence of a finite
time interval for the observation of geometric phases. The formalism is
illustrated via the canonical example of a spin-1/2 particle in a
time-dependent magnetic field. Remarkably, the geometric phase in this case is
immune to dephasing and spontaneous emission in the renormalized Hamiltonian
eigenstate basis. This result positively impacts holonomic quantum computing.
- oai_identifier:
- oai:arXiv.org:quant-ph/0507012
- categories:
- quant-ph cond-mat.mes-hall
- comments:
- v3: 10 pages, 2 figures. Substantially expanded version. Includes a
proof of gauge invariance of the non-Abelian geometric phase, and an appendix
on the left and right eigenvectors of the superoperator in the Jordan form
- doi:
- 10.1103/PhysRevA.73.062101
- arxiv_id:
- quant-ph/0507012
- journal_ref:
- Phys. Rev. A 73, 062101 (2006)
- created:
- 2005-07-01
- updated:
- 2006-04-28
Full article ▸
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