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arXiv:quant-ph/0209004 · Physical Review A

Nonclassical effects in cold trapped ions inside a cavity

F. L. Semião, A. Vidiella-Barranco, José Antonio Roversi

Published Dec 10, 2002• 12 citations
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Abstract

We investigate the dynamics of a cold trapped ion coupled to the quantized field inside a high-finesse cavity, considering exact resonance between the ionic internal levels and the field (carrier transition). We derive an intensity-dependent Hamiltonian in which terms proportional to the square of the Lamb-Dicke parameter $(\ensuremath{\eta})$ are retained. We show that different nonclassical effects arise in the dynamics of the ionic population inversion, depending on the initial states of the vibrational motion and field and on the values of $\ensuremath{\eta}.$

DOI
10.1103/physreva.66.063403

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Physical Review A•Dec 1, 1998•5 citations
We investigate the dynamics of a cold trapped ion coupled to the quantized field inside a high-finesse cavity, considering exact resonance between the ionic internal levels and the field (carrier transition). We derive an intensity-dependent Hamiltonian in which terms proportional to the square of the Lamb-Dicke parameter (\ensuremathη)(\ensuremath{\eta})(\ensuremathη) are retained. We show that different nonclassical effects arise in the dynamics of the ionic population inversion, depending on the initial states of the vibrational motion and field and on the values of \ensuremathη.\ensuremath{\eta}.\ensuremathη.
We analyze the quantum motion of a cold, trapped two-level ion interacting with a quantized light field in a single-mode cavity. We show that in the nonclassical Lamb-Dicke limit the time evolution of the vibrational mode representing the quantized motion of the center of mass of the trapped ion is very sensitive to the quantum statistics of the light field. We also show that the system under consideration may evolve into the maximally entangled three-particle Greenberger-Horne-Zeilinger state. We briefly discuss the dynamics of a cluster of two-level ions trapped in a cavity and interacting with a quantized light field.
Following the path of Bužek et al. in [Phys. Rev. A 56 2352 1997], we investigate the full intensity-dependent interaction between a motional two-level ion which is trapped in a f-deformed oscillator (so possessing vibrational modes too) with a single-mode nonlinear quantized field in the Lamb-Dicke limit. After finding the explicit form of the entire ion-field state vector in a general framework, we particularly restrict ourselves to an appropriate nonlinearity function (describing intensity-dependent interaction) corresponding to the center-of-mass motion of a trapped ion which explicitly depends on the Lamb-Dicke parameter as well as another well-known nonlinearity function in the form n. Then, we evaluate the effects of two different initial quantized field states as well as the considered nonlinearity function (via varying the Lamb-Dicke parameter) on a few physical properties of the system. For this purpose, we pay attention to the amount of entanglement, mean number of vibrational quanta (phonons), population inversion of the two-level ion and Q-distribution function. Finally, by comparing our results with the previously considered “linear” one which is pointed in the above Ref., we establish that, by tuning the Lamb-Dicke parameter, one can adjust the mentioned nonclassical properties of the system appropriately.
The interaction of a cold trapped ion with a strong laser field is studied in a configuration in which quasienergetic levels become important but heating of the system is unessential. Absorption spectroscopy of the quasienergetic states of a strongly confined and laser-driven trapped ion is analyzed by probing vibrational transitions. Calculations are carried out analytically by using the master equation in quasienergetic state representation. We consider a V\mathsf{V}V-level scheme for the ion with a resonant strong pump field and a weak probe field. The steady-state and time-evolution behavior of the system is discussed and the probe-field absorption spectrum for various initial population distributions of the motional state is calculated. It is found that the absorption spectrum displays vibrational sidebands with multipeak splitting due to the nonlinear dependence of the Rabi frequencies on both the Lamb-Dicke parameter and the trap occupation number. This multipeak splitting has interesting consequences and can be useful for the measurement of the initial trap number population distribution.