Geometric jphases in self-induced transparency

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We consider the geometric phases arising in the lossless propagation of light pulses through a medium composed of near resonant two-level atoms. A reformulation of the coupled Maxwell-Schroedinger equations allows us to construct conservation laws in a general context. There exist periodic solutions of these equations which lead to the possibility of cyclical evolution of the state vector and the appearance of a geometric phase. We first show that if the ground state is the initial state of the system, then it acquires a geometric phase after the passage of the soliton pulses of McCall and Hahn. More generally if ... continued below

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48 p.

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Sen, T. & Milovich, J. May 1, 1991.

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  • Sen, T. Superconducting Super Collider Lab., Dallas, TX (United States)
  • Milovich, J. Lawrence Livermore National Lab., CA (United States)

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Description

We consider the geometric phases arising in the lossless propagation of light pulses through a medium composed of near resonant two-level atoms. A reformulation of the coupled Maxwell-Schroedinger equations allows us to construct conservation laws in a general context. There exist periodic solutions of these equations which lead to the possibility of cyclical evolution of the state vector and the appearance of a geometric phase. We first show that if the ground state is the initial state of the system, then it acquires a geometric phase after the passage of the soliton pulses of McCall and Hahn. More generally if the initial state is a superposition of the two levels, continuous pulse trains can propagate without appreciable loss. We also find in this case that the state vector develops a geometric phase provided the parameters take on the particular values required for cyclical evolution. In both cases we exhibit the geometric character of the calculated phases by showing that they equal half the solid angle subtended by a closed curve traced by the Bloch, vector on the Bloch sphere. We verify a recent assertion of Anandan and Aharonov that the energy uncertainty in the state is directly related to the speed at which the tip of the Bloch vector moves along the curve on the Bloch sphere (or in more general terms the energy uncertainty is related to the speed in the projective Hilbert space).

Physical Description

48 p.

Notes

INIS; OSTI as DE95011143

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  • Other Information: PBD: May 1991

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  • Other: DE95011143
  • Report No.: SSCL--469
  • Grant Number: AC35-89ER40486
  • DOI: 10.2172/79722 | External Link
  • Office of Scientific & Technical Information Report Number: 79722
  • Archival Resource Key: ark:/67531/metadc742688

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • May 1, 1991

Added to The UNT Digital Library

  • Oct. 19, 2015, 7:39 p.m.

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  • April 29, 2016, 5:50 p.m.

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Sen, T. & Milovich, J. Geometric jphases in self-induced transparency, report, May 1, 1991; Dallas, Texas. (digital.library.unt.edu/ark:/67531/metadc742688/: accessed November 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.