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Chinese Journal of Quantum Electronics

Influence of laser intensity fluctuations on entanglement of two trapped ions

Zhongjie Wang

Published Jan 1, 2011• 0 citations
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Abstract

Entangled state of trapped ions has many very important applications in quantum computation and quantum information.Due to the characteristics of quantum systems,the occurrence of laser intensity fluctuations is inevitable,and it has significant influence to the entanglement of trapped ions.With the anti-model of J-C,the effect of intensity fluctuations on dynamics of entanglement of system was studied by computing concurrence and a rough comparison between the model of J-C and the anti-model of J-C was also discussed.The result shows that the noise caused by intensity fluctuation makes the entanglement of two ions weaken with time similarly in an exponential way.The difference of entanglement of system between the model of J-C and the anti-model of J-C is obvious in a weaker laser field.

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Entangled state of trapped ions has many very important applications in quantum computation and quantum information.Due to the characteristics of quantum systems,the occurrence of laser intensity fluctuations is inevitable,and it has significant influence to the entanglement of trapped ions.With the anti-model of J-C,the effect of intensity fluctuations on dynamics of entanglement of system was studied by computing concurrence and a rough comparison between the model of J-C and the anti-model of J-C was also discussed.The result shows that the noise caused by intensity fluctuation makes the entanglement of two ions weaken with time similarly in an exponential way.The difference of entanglement of system between the model of J-C and the anti-model of J-C is obvious in a weaker laser field.
The effect of intensity fluctuations on laser-induced coupling of electronic and vibrational states of a trapped ion is studied analytically. Different types of noise relevant to the experiments are considered. The resulting decoherence phenomenology is shown to present nontrivial characteristics. Noise color leads to nonexponential decay of the coherences: after the initial decay, determined by the probability distribution, a transient period specific to the noise spectrum is apparent; at large times, exponential decay sets in for widely different noise properties. The detection of these features in the evolution of an initial coherent state of the vibrational mode is discussed.
Summary form only given.To model the decoherence in ion traps resulting from laser intensity and phase fluctuations, we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. We discuss the effects those fluctuations have on gate operations in ion-trap quantum computation and briefly address possible detection and error correction mechanisms. The master equation is then averaged over the noise and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. We get solutions for the probability of the ion to be in the ground state for both intensity and phase fluctuations. Our results predict that the decoherence rate resulting from intensity fluctuations will depend on the vibrational quantum number in different ways depending on which vibrational excitation sideband is used. So the dependence of the decoherence rate for the second red sideband depends quadratically on the vibrational energy state |n> the ion is prepared in, whereas for the first sideband, this effect is linear in n. Due to this result, the second red (or any higher-order) sideband is a better choice for testing the dependence of decoherence on the excitation in the vibrational state experimentally than just the first-order sideband. Because those fluctuations in the exciting laser pulse are not the only source of decoherence, we briefly discuss fluctuations in the trap potential itself. These fluctuations lead to a wobbling trap center point, and we discuss the effects due to them.
In this paper, the interaction between two trap ions with laser beam and electromagnetic field containing the Stark shift terms has been investigated. The analytical solution for the differential equations which describes the system Hamiltonian is obtained. The dynamical behavior for the entanglement, entropy squeezing and purity of system are discussed. Some important physical characteristics such as revivals and collapses for the occupation of the trapped ion, entanglement sudden death (birth) and single trapped ion entropy squeezing are discussed. In addition, the influence of Lamb–Dicke parameter and the initial states on the evolution of the entanglement, linear entropy are studied. Finally, some remarks about the obtained results are given briefly.
The time evolution properties of the field quantum entropy in the system of a trapped ion interacting resonantly with a standing-wave laser field is studied by utilizing the Von Neumann reduced quantum entropy theory, and our attention focuses on the discussion of the influence of the Lamb-Dick parameter, the position of the ion in the standing-wave laser field and the initial state of the trapped ion on the evolution properties of the field quantum entropy. The results obtained from the numerical calculation indicate that: the value of the Lamb-Dick parameter effect the oscillation frequency and amplitude of the quantum entanglement between the trapped ion and the standing-wave laser field, the larger the Lamb-Dick parameter is, the weaker the average entanglement level between the ion and the field will be. When moving the tapped ion from the node of the standing-wave laser to the loop, the vibration frequency of the quantum entanglement between the field and the ion becomes slow gradually, and the entanglement degree gets weaker and weaker. With the decrease of the probability of the trapped ion being in the excited state, the quantum entanglement between the trapped ion and the stanging-wave laser field shows the tendency of increase first and then decrease. These properties have certain reference value for the preparation of entangled states and for the quantum communications with the thapped ion, and so on.
We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker–Planck equation and analytic expressions of the steady-state probability distribution function (SPD) of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that (i) the correlation strength λ of correlated noises always enhances the fluctuation of laser intensity; (ii) the correlation time τ of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but τ weakens it for the above-threshold case.