Superpositions of SU(3) coherent states via a nonlinear evolution

We show that a nonlinear Hamiltonian evolution can transform an SU(3) coherent state into a superposition of distinct SU(3) coherent states, with a superposition of two SU(2) coherent states presented as a special case. A phase-space representation is depicted by projecting the multi-dimensional Q-symbol for the state to a spherical subdomain of the coset space. We discuss realizations of this nonlinear evolution in the contexts of nonlinear optics and Bose-Einstein condensates.

[1]  Barry C. Sanders,et al.  Entangled coherent states for systems with SU(2) and SU(1,1) symmetries , 2000 .

[2]  K. Nemoto.  Generalized coherent states for SU(n) systems , 2000, quant-ph/0004087.

[3]  Cornish,et al.  Stable 85Rb bose-einstein condensates with widely tunable interactions , 2000, Physical review letters.

[4]  Anders O. Wistrom,et al.  Evaluation of the Coulomb force via the Fredholm integral equation , 2000 .

[5]  G. Milburn,et al.  Weak-force detection using a double Bose-Einstein condensate , 1998, cond-mat/9812189.

[6]  Sven Gnutzmann,et al.  Coherent states and the classical limit on irreducible representations , 1998 .

[7]  B. Sanders,et al.  Representations of the Weyl group and Wigner functions for SU(3) , 1998, math-ph/9811012.

[8]  D. Strekalov,et al.  Direct observation of growth and collapse of a Bose–Einstein condensate with attractive interactions , 1998, Nature.

[9]  Gerard J. Milburn,et al.  Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential , 1997 .

[10]  Wineland,et al.  Optimal frequency measurements with maximally correlated states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[11]  Gagen.  Phase-space-interference approaches to quantum superposition states. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[12]  B. Sanders,et al.  Entangled Coherent States with Variable Weighting , 1993 .

[13]  Ansari,et al.  Photon statistics of multimode even and odd coherent light. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[14]  Chai,et al.  Two-mode nonclassical state via superpositions of two-mode coherent states. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[15]  Sanders.  Erratum: Entangled coherent states , 1992, Physical review. A, Atomic, molecular, and optical physics.

[16]  Sanders,et al.  Entangled coherent states. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[17]  Sanders,et al.  Quantum dynamics of the nonlinear rotator and the effects of continual spin measurement. , 1989, Physical review. A, General physics.

[18]  Gerry.  Application of SU(1,1) coherent states to the interaction of squeezed light in an anharmonic oscillator. , 1987, Physical review. A, General physics.

[19]  A. Perelomov.  Generalized Coherent States and Their Applications , 1986 .

[20]  B. Yurke,et al.  Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion. , 1986, Physical review letters.

[21]  Klauder,et al.  SU(2) and SU(1,1) interferometers. , 1986, Physical review. A, General physics.

[22]  F. Arecchi,et al.  Atomic coherent states in quantum optics , 1972 .

[23]  J. M. Radcliffe.  Some properties of coherent spin states , 1971 .

[24]  Vladimír Bužek,et al.  I: Quantum Interference, Superposition States of Light, and Nonclassical Effects , 1995 .

[25]  Milburn,et al.  Quantum and classical Liouville dynamics of the anharmonic oscillator. , 1986, Physical review. A, General physics.