Stability of the ground state of a harmonic oscillator in a monochromatic wave.

@article{Berman2001StabilityOT,
  title={Stability of the ground state of a harmonic oscillator in a monochromatic wave.},
  author={Gennady P. Berman and Daniel F. V. James and D. I. Kamenev},
  journal={Chaos},
  year={2001},
  volume={11 3},
  pages={
          449-463
        }
}
The stability of the ground state of a harmonic oscillator in a monochromatic wave is studied. This model describes, in particular, the dynamics of a cold ion in a linear ion trap, interacting with two laser fields with close frequencies. The stability of the "classical ground state"-the vicinity of the point (x=0,p=0)-is analyzed analytically and numerically. For the quantum case, a method for studying a stability of the quantum ground state is developed, based on the quasienergy… Expand
Tuneable interacting bosons for relativistic and quantum information processing
We study the full time evolution of a system of two modes of a bosonic quantum field that interact through quadratic hamiltonians. We specialise to a time dependent two-mode squeezing HamiltonianExpand
Time evolution of interacting bosons through squeezing Hamiltonians
We study the full time evolution of one- and two-mode bosonic quantum systems that interact through single- and two-mode squeezing Hamiltonians. We establish that the single- and two-mode cases areExpand

References

SHOWING 1-10 OF 17 REFERENCES
Symmetry of quantum phase space in a degenerate Hamiltonian system.
TLDR
The structure of the global "quantum phase space" is analyzed for the harmonic oscillator perturbed by a monochromatic wave in the limit when the perturbation amplitude is small, and the stochastic layers in the classical phase space are exponentially thin. Expand
QUANTUM WEAK CHAOS IN A DEGENERATE SYSTEM
Quantum weak chaos is studied in a perturbed degenerate system: a charged particle interacting with a monochromatic wave in a transverse magnetic field. The evolution operator for an arbitrary numberExpand
Localization of quantum states at the cyclotron resonance
Abstract Tunneling of a quantum particle to the classically inaccessible region in an intrinsically degenerate system is investigated here by means of quasienergy eignestates. The exact resonanceExpand
NONLINEAR COLLECTIVE OSCILLATIONS OF AN ION CLOUD IN A PAUL TRAP
In an experiment using a Paul trap, we create a ${\mathrm{H}}_{2}^{+}$ ion cloud by electron ionization of the background gas at ${10}^{\ensuremath{-}9}$-mbar residual pressure. Exciting the ionsExpand
Frequency-locked motion of two particles in a Paul trap.
TLDR
This work presents the first observations of frequency locking of two microspheres in a Paul trap, in close agreement with theoretical predictions, and reproduces the main features of earlier work on two-ion chaos. Expand
Radiofrequency Spectroscopy of Stored Ions I: Storage
Publisher Summary This chapter discusses the ways to develop techniques to isolate, contain in a trap, thermalize, and possibly refrigerate the atomic systems under observation. The electrons moveExpand
Dynamical stability and quantum chaos of ions in a linear trap
The realization of a paradigm chaotic system, namely, the harmonically driven oscillator, in the quantum domain using cold trapped ions driven by lasers is theoretically investigated. The simplestExpand
Fractional frequency collective parametric resonances of an ion cloud in a Paul trap
ion cloud ina Paul trap driven at simple fractions of twice the secular frequency of the trap by an additionally appliedquadrupole field. The fractional resonances are observable only if theExpand
Quantum Chaos: A Harmonic Oscillator in Monochromatic Wave
A review on transition from regular dynamics to quantum chaos in a quantum degenerate system - a harmonic oscillator perturbed by a monochromatic wave. It explains how the transition to quantum chaosExpand
On the spectrum of the system of interacting quantum nonlinear resonances
Abstract Correlation functions of the density matrix components and the frequency spectrum are numerically analysed in the system of two interacting quantum nonlinear resonances. For overlappingExpand
...
1
2
...