Nonlinear modes of a macroscopic quantum oscillator

Abstract We consider the Bose–Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe, analytically and numerically, its collective modes — a nonlinear generalisation of the (symmetric and antisymmetric) Hermite–Gauss eigenmodes of a harmonic quantum oscillator.

[1]  Bradley,et al.  Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions. , 1995, Physical review letters.

[2]  Physics Letters , 1962, Nature.

[3]  Yuri S. Kivshar,et al.  Coupled mode theory for Bose-Einstein condensates , 2000, QELS 2000.

[4]  H. Herrero,et al.  Bose-Einstein solitons in highly asymmetric traps , 1998 .

[5]  A. Forchel,et al.  Size Dependence of Confined Optical Modes in Photonic Quantum Dots , 1997 .

[6]  A. Messiah.  Quantum Mechanics , 1961 .

[7]  Johann Peter Reithmaier,et al.  Optical Modes in Photonic Molecules , 1998 .

[8]  W. Ketterle,et al.  Observation of Feshbach resonances in a Bose–Einstein condensate , 1998, Nature.

[9]  C. Wieman,et al.  Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor , 1995, Science.

[10]  Non-ground-state Bose-Einstein condensates of trapped atoms , 1997, cond-mat/9712069.

[11]  Clark,et al.  Collective Excitations of Atomic Bose-Einstein Condensates. , 1996, Physical review letters.

[12]  J. Linnett,et al.  Quantum mechanics , 1975, Nature.

[13]  S. Gaponenko.  Optical properties of semiconductor nanocrystals , 1998 .

[14]  K. B. Davis,et al.  Bose-Einstein Condensation in a Gas of Sodium Atoms , 1995, EQEC'96. 1996 European Quantum Electronic Conference.

[15]  Yuri S. Kivshar,et al.  Stability of multihump optical solitons , 1999, patt-sol/9905006.

[16]  David Landhuis,et al.  Bose–Einstein condensation of atomic hydrogen , 1998, physics/9809017.

[17]  F. Dalfovo,et al.  Theory of Bose-Einstein condensation in trapped gases , 1998, cond-mat/9806038.