TWO-MODE PHOTON PHASE OPERATORS AND SCHWINGER ANGULAR MOMENTUM REPRESENTATION

Masashi Ban

Heng Fan

The angular momentum theory in the schwinger boson representation is developedto derive a new normal product expression for the commutator [e~(iαJx), e~(iβJy] by meansof the integral technique within normal product, and the effect on the coherent statecaused by two rotations which are in different seqences. Some new normal productexpressions for exponential operators, sueh as e~(σJ)-e~(λJ)+ etc, are also derived and theirapplications in atomic coherent states are presented.

Abir Bandyopadhyay, Jagdish Rai

Atkins and Dobson [Proc. R. Soc. London Ser. A 321, 321 (1971)] have constructed coherent angular-momentum states using the Schwinger bosonic representation and operating the displacement (coherent) operator on both of the bosonic vacuum states. By performing a squeezing transformation on the bosonic coherent states we generalize the idea of Schwinger angular-momentum coherent (SAMC) states to Schwinger angular-momentum squeezed (SAMS) states. We show that these SAMS states, which are constructed from the bosonic squeezed coherent states, exhibit squeezing of Schwinger angular-momentum operators under a certain range of parameters. The properties of these states are studied and compared with their single-mode bosonic counterpart. Application of these states in increasing the accuracy of an interferometer is discussed.

A.S. Shumovsky

I. A. Deryugin, A. A. Vishenskii, Vitaliy N. Kurashov

Abir Bandyopadhyay, Jagdish Rai

A simple, and elegant geometrical representation is developed to describe the concept of coherence and squeezing for angular momentum operators. Angular momentum squeezed states were obtained by applying Bogoliubov transformation on the angular momentum coherent states in Schwinger representation [Phys. Rev. {\bf{A 51}} (1995)]. We present the geometrical phase space description of angular momentum coherent and squeezed states and relate with the harmonic oscillator. The unique feature of our geometric representation is the portraying of the expectation values of the angular momentum components accompanied by their uncertainties. The bosonic representation of the angular momentum coherent and squeezed states is compared with the conventional one mentioning the advantages of this representation of angular momentum in context of coherence and squeezing. Extension of our work on single mode squeezing to double mode squeezing is presented and compared with the single mode one. We also point out the possible applications of the geometrical representation in analyzing the accuracy of interferometers and in studying the behavior, dynamics of an ensemble of quantum-mechanical two-level systems and its interaction with radiation.