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.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.

arXiv:quant-ph/0011090Journal of Physics B Atomic Molecular and Optical PhysicsMar 26, 200210 citations

Single two-level ion in an anharmonic-oscillator trap: Time evolution of the Q function and population inversion

S. Shelly Sharma, Naresh Kumar Sharma, L. Zamick

We investigate the time evolution of the population inversion as well as the $Q$ function for center-of-mass motion for a two-level ion, interacting with single-mode laser light field, in an anharmonic-oscillator trap. The anharmonicities of the trap are quantified in terms of the deformation parameter of the $q$ -analog trap. For $\ensuremath{\tau}=0.003$ ${(q=e}^{\ensuremath{\tau}})$ the collapses and revivals of population inversion become well-defined facilitating experimental observation, but for large $\ensuremath{\tau}\ensuremath{\sim}0.1$ the time dependence of population inversion is completely wiped out. The quasiprobability function shows an atypical behavior with a single peak at $t=0$ splitting up into as many as seven fragments (at $t=130$ ) during collapse and at a later time these segments come together to signal the revival of population inversion. A small degree of anharmonicity is seen to enhance the coherence of the ion-trap system, whereas for large $\ensuremath{\tau}$ ($\ensuremath{\sim}0.1$ in the present context) the coherence is completely lost.We investigate the time evolution of the population inversion as well as the $Q$ function for center-of-mass motion for a two-level ion, interacting with single-mode laser light field, in an anharmonic-oscillator trap. The anharmonicities of the trap are quantified in terms of the deformation parameter of the $q$-analog trap. For $\ensuremath{\tau}=0.003$ ${(q=e}^{\ensuremath{\tau}})$ the collapses and revivals of population inversion become well-defined facilitating experimental observation, but for large $\ensuremath{\tau}\ensuremath{\sim}0.1$ the time dependence of population inversion is completely wiped out. The quasiprobability function shows an atypical behavior with a single peak at $t=0$ splitting up into as many as seven fragments (at $t=130$) during collapse and at a later time these segments come together to signal the revival of population inversion. A small degree of anharmonicity is seen to enhance the coherence of the ion-trap system, whereas for large $\ensuremath{\tau}$ ($\ensuremath{\sim}0.1$ in the present context) the coherence is completely lost.

Physical Review AJul 1, 199715 citations

We investigate the time evolution of the population inversion as well as the

Q

function for center-of-mass motion for a two-level ion, interacting with single-mode laser light field, in an anharmonic-oscillator trap. The anharmonicities of the trap are quantified in terms of the deformation parameter of the

q

-analog trap. For $\ensuremath{\tau}=0.003$ ${(q=e}^{\ensuremath{\tau}})$ the collapses and revivals of population inversion become well-defined facilitating experimental observation, but for large $\ensuremath{\tau}\ensuremath{\sim}0.1$ the time dependence of population inversion is completely wiped out. The quasiprobability function shows an atypical behavior with a single peak at

t=0

splitting up into as many as seven fragments (at

t=130

) during collapse and at a later time these segments come together to signal the revival of population inversion. A small degree of anharmonicity is seen to enhance the coherence of the ion-trap system, whereas for large $\ensuremath{\tau}$ ($\ensuremath{\sim}0.1$ in the present context) the coherence is completely lost.