A trapped ion with time-dependent frequency interaction with a laser field

We analyse the problem of a trapped ion with time-dependent frequency interacting with a laser field. By using a set of unitary time-dependent transformations we show that this system is equivalent to the interaction between a quantized field and a double level with time-dependent interaction parameters. In passing, we show that in the on-resonance case different vibrational transitions may be achieved by using time-dependent parameters.

[1]  W. Vogel,et al.  Quantum-state engineering of a trapped ion by coherent-state superpositions , 1999 .

[2]  Vogel,et al.  Nonlinear coherent states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[3]  R. L. de Matos Filho,et al.  Engineering the Hamiltonian of a trapped atom , 1998 .

[4]  M. F. Guasti,et al.  Analytic approximation to the harmonic oscillator equation with a sub-period time dependent parameter ☆ , 2004 .

[5]  S. Stenholm.  Quantum theory of electromagnetic fields interacting with atoms and molecules , 1973 .

[6]  Quantum-state protection in cavities , 1998, quant-ph/9803045.

[7]  Gerard J. Milburn,et al.  Controlling the decoherence of a ''meter'' via stroboscopic feedback , 1997 .

[8]  Kurizki,et al.  Preparation and detection of macroscopic quantum superpositions by two-photon field-atom interactions. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[9]  Knight,et al.  Generation and detection of nonclassical field states by conditional measurements following two-photon resonant interactions. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[10]  H. Yuen.  Two-photon coherent states of the radiation field , 1976 .

[11]  Leonard Susskind,et al.  Quantum mechanical phase and time operator , 1964 .

[12]  Vogel,et al.  Even and odd coherent states of the motion of a trapped ion. , 1996, Physical review letters.

[13]  Zheng,et al.  Strong-coupling series for Abelian lattice gauge models in 3+1 dimensions. , 1994, Physical Review D, Particles and fields.

[14]  G. J. Milburn,et al.  DECOHERENCE IN ION TRAPS DUE TO LASER INTENSITY AND PHASE FLUCTUATIONS , 1998 .

[15]  Vogel,et al.  Quantum state engineering of the radiation field. , 1993, Physical review letters.

[16]  H. Moya-Cessa,et al.  Coherent states for the time dependent harmonic oscillator: the step function , 2003 .