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Chinese journal of atomic and molecular physics

Quantum coherence in the vibration state of a trapped ion

Zhong Wang

Published Jan 1, 2000• 0 citations
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Abstract

In this paper the dynamics of the two level trapped ion which acts with standing light field is investigated analytically. Evolution of the quantum mean energy of the ion with time displays the characteristic of collapse revival which implies the vibration states of the system have squeezing effect. The collapse revival of the quantum mean energy of the ion will become irregular because of the higher term in Hamiltonian of the system. The higher term will suppress coherence of the vibration state of the ion.

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In this paper the dynamics of the two level trapped ion which acts with standing light field is investigated analytically. Evolution of the quantum mean energy of the ion with time displays the characteristic of collapse revival which implies the vibration states of the system have squeezing effect. The collapse revival of the quantum mean energy of the ion will become irregular because of the higher term in Hamiltonian of the system. The higher term will suppress coherence of the vibration state of the ion.
The quantum dynamics of a trapped ion which acts with two standing light fields with different frequency is investigated on the condition of high detuning. Evolution of the quantum mean energy of the ion with time displays the characteristic of collapse revival which implies the vibration states of the ion have squeezing effect. The higher the value of the squeezing parameter G 3 . The higher the degree of squeezing of the vibration states of the ion can be observed. If G 3 is greater than a particular value, the degree of squeezing will become smaller.
In this paper the quantum dynamics of the trapped atom which acts with a standing light field and a travelling light field is investigated. Evolution of the quantum mean energy of the ion with time displays the characteristic of collapse-revival which implies that the vibration states of the system have squeezing effect. The larger the nonlinearity of the system, the higher the frequency of collapse-revival of the system, and the smaller the quantum mean energy of the ion. The higher the intensity of the travelling light field, the higher the degree of squeezing of the vibration states of the system can be observed.
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.
We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C. A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.