The Schrödinger cat state of trapped ions in harmonic and anharmonic oscillator traps
S. Shelly Sharma, Naresh Kumar Sharma · Journal of Physics B Atomic Molecular and Optical Physics · 2002
We examine the time evolution of a two-level ion interacting with a light field in a harmonic oscillator trap and in a trap with anharmonicities. The anharmonicities of the trap are quantified in terms of the deformation parameter τ characterizing the q -analogue of the harmonic oscillator trap. Initially the ion is prepared in a Schrödinger cat state. The entanglement of the centre-of-mass motional states and the internal degrees of freedom of the ion results in a characteristic collapse and revival pattern. We numerically calculate the population inversion I ( t ), quasi-probabilities Q ( t ) and partial mutual quantum entropy S ( P ) for the system as a function of time. Interestingly, small deformations of the trap enhance the contrast between population inversion collapse and revival peaks as compared to the zero-deformation case. For β = 3 and 4 (β determines the average number of trap quanta linked to centre-of-mass motion) the best collapse and revival sequence is obtained for τ = 0.0047 and 0.004, respectively. For large values of τ, decoherence sets are accompanied by loss of amplitude of population inversion, and for τ ~0.1 the collapse and revival phenomenon disappear. Each collapse or revival of population inversion is characterized by a peak in the S ( P ) versus t plot. During the transition from collapse to revival and vice-versa, we have a minimum mutual entropy value that is S ( P ) = 0. Successive revival peaks show a lowering of the local maximum point indicating a dissipative irreversible change in the ionic state. An improved definition of the collapse and revival pattern as the anharmonicity of the trapping potential increases is also reflected in the quasi-probability versus t plots.