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The geometric phase in two-level atomic systems

Ming Tian, Zeb W. Barber, Joe A. Fischer +1 more

Journal of LuminescenceJan 27, 20046 citations

Vacuum induced berry phase: Theory and experimental proposal

Sougato Bose, Angelo C. M. Carollo, Ivette Fuentes +2 more

We investigate quantum effects in geometric phases arising when a two-level system is interacting with a quantized electromagnetic field. When the system is adiabatically driven along a closed loop in the parameter space, signatures of the field quantization are observable in the geometric phase. We propose a feasible experiment to measure these effects in cavity QED and also analyse the semi-classical limit, recovering the usual Berry phase results.

Journal of Modern OpticsApr 1, 20037 citations

The Geometric Phase in Quantum Systems

Arno Böhm, Ali Mostafazadeh, Hiroyasu Koizumi +2 more

Springer eBooksJan 1, 2003426 citations

Geometric phases in quantum control disturbed by classical stochastic processes

David Viennot

We describe the geometric (Berry) phases arising when some quantum systems are driven by control classical parameters but also by outer classical stochastic processes (as, for example, classical noises). The total geometric phase is then divided into an usual geometric phase associated with the control parameters and a second geometric phase associated with the stochastic processes. The geometric structure in which these geometric phases take place is a composite bundle (and not an usual principal bundle), which is explicitly built in this paper. We explain why the composite bundle structure is the more natural framework to study this problem. Finally, we treat a very simple example of a two-level atom driven by a phase modulated laser field with a phase instability described by a Gaussian white noise. In particular, we compute the average geometric phase issued from the noise.We describe the geometric (Berry) phases arising when some quantum systems are driven by control classical parameters but also by outer classical stochastic processes (as, for example, classical noises). The total geometric phase is then divided into an usual geometric phase associated with the control parameters and a second geometric phase associated with the stochastic processes. The geometric structure in which these geometric phases take place is a composite bundle (and not an usual principal bundle), which is explicitly built in this paper. We explain why the composite bundle structure is the more natural framework to study this problem. Finally, we treat a very simple example of a two-level atom driven by a phase modulated laser field with a phase instability described by a Gaussian white noise. In particular, we compute the average geometric phase issued from the noise.

arXiv:1208.0143Journal of Mathematical PhysicsAug 1, 20121 citation

Quantum Phase Properties of a State Driven by a Classical Field

Naveen Kumar, Arpita Chatterjee

arXiv:2407.00982International Journal of Theoretical PhysicsMay 13, 20240 citations

Information Geometry in Time Dependent Quantum Systems and the Geometric Phase

Anshuman Dey, Suvankar Paul, Pratim Roy +1 more

We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the XY spin chain in a transverse magnetic field, when driven across anisotropic criticality. Next, we comment upon the nature of the geometric phase from classical holonomy analyses of such parameter manifolds. In the context of the transverse XY model in the thermodynamic limit, our results are in contradiction to those in the existing literature, and we argue why the issue deserves a more careful analysis. Finally, we speculate on a novel geometric phase in the model, when driven across a quantum critical line.We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the XY spin chain in a transverse magnetic field, when driven across anisotropic criticality. Next, we comment upon the nature of the geometric phase from classical holonomy analyses of such parameter manifolds. In the context of the transverse XY model in the thermodynamic limit, our results are in contradiction to those in the existing literature, and we argue why the issue deserves a more careful analysis. Finally, we speculate on a novel geometric phase in the model, when driven across a quantum critical line.

arXiv:1605.01358May 4, 20160 citations

Geometric Phase of a Two-level System Driven by a Classical Field

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