Geometric phases in two-level atoms excited by pulses propagating without loss

Journal Article · Sat Feb 01 00:00:00 EST 1992 · Physical Review A. General Physics; (United States)

DOI:https://doi.org/10.1103/PhysRevA.45.1371· OSTI ID:7234500

Sen, T ^[1]; Milovich, J L ^[2]

---

1. Superconducting Super Collider Laboratory, MS-1042, 2550 Beckleymeade Avenue, Dallas, Texas 75237 (United States)
2. Lawrence Livermore National Laboratory, L-630, P.O. Box 5511, Livermore, California 94550 (United States)

We consider the geometrical phases arising in the state vector of two-level atoms due to their interaction with a self-consistently generated classical electrical field propagating without loss through the atomic medium. Three conservation laws are shown to exist generally and are used to solve for the individual quantum amplitudes, phases, and the electric field. We calculate the geometrical phases in two situations: (a) where the atoms are initially in the ground state and (b) where the initial state is a coherent superposition of the ground and excited states. In both cases the geometrical phase is the Aharonov-Anandan phase resulting from the atomic state vector tracing out a closed curve on the projective Hilbert space--here the Bloch sphere. We show that geometric quantities associated with the curve on the Bloch sphere are directly related to physical observables. The solid angle subtended by the closed curve (shown to equal twice the geometric phase) is a measure of the maximum atomic inversion, while the speed with which the curve is traced is related to the energy uncertainty in the state. An experimental method to observe the total phase change in a two-level subsystem is outlined, using photon echoes in a three-level medium.

• DOE Contract Number: AC35-89ER40486
• OSTI ID: 7234500
• Journal Information: Physical Review A. General Physics; (United States), Vol. 45:3; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
EXCITATION
ABSORPTION
CONSERVATION LAWS
ELECTROMAGNETIC RADIATION
ENERGY LOSSES
HILBERT SPACE
PHOTON-ATOM COLLISIONS
RESONANCE
WAVE PROPAGATION
ATOM COLLISIONS
BANACH SPACE
COLLISIONS
ENERGY-LEVEL TRANSITIONS
LOSSES
MATHEMATICAL SPACE
PHOTON COLLISIONS
RADIATIONS
SORPTION
SPACE
664200* - Spectra of Atoms & Molecules & their Interactions with Photons- (1992-)