Collapse and revival of entanglement in the system of trapped ions

Vladimir S. Malinovsky, Ignacio R. Solá

J. I. Cirac, R. Blatt, A. S. Parkins +1 more

Chi‐Fai Lo, K.M. Ng

Atle Svandal, J. P. Hansen

We study the long-time dynamics of two entangled ions coupled by a single vibrational mode and two lasers with different frequencies as proposed by M\o{}lmer and S\o{}rensen [Phys. Rev. Lett. 82, 1835 (1999)]. It is shown that the time development involves collapses and revivals well known from the dynamics of a single atom in a cavity or in a trap. The revival time is found to be insensitive to the details of the initial collective vibrational state. Therefore, revival and collapse phenomena are obtained for coherent, thermal as well as other vibrational states.

Christoph Becher, Jan Benhelm, D. Chek-al-kar +16 more

S. Shelly Sharma, Naresh Kumar Sharma

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.