Trapped and laser-cooled ions are increasingly used for a variety of modern high-precision experiments, frequency standard applications and quantum information processing. Therefore, in this communication we present a comprehensive analysis of the pattern of information entropy arising in the time evolution of an ion interacting with a laser field. A general analytic approach is proposed for a three-level trapped-ion system in the presence of the time-dependent couplings. By working out an exact analytic solution, we conclusively analyse the general properties of the von Neumann entropy and quantum information entropy. It is shown that the information entropy is affected strongly by the time-dependent coupling and exhibits long time periodic oscillations. This feature attributed to the fact that in the time-dependent region Rabi oscillation is time dependent. Using parameters corresponding to a specific three-level ionic system, a single beryllium ion in a RF-(Paul) trap, we obtain illustrative examples of some novel aspects of this system in the dynamical evolution. Our results establish an explicit relation between the exact information entropy and the entanglement between the multi-level ion and the laser field. We show that different nonclassical effects arise in the dynamics of the ionic population inversion, depending on the initial states of the vibrational motion/field and on the values of Lamb–Dicke parameter η.Trapped and laser-cooled ions are increasingly used for a variety of modern high-precision experiments, frequency standard applications and quantum information processing. Therefore, in this communication we present a comprehensive analysis of the pattern of information entropy arising in the time evolution of an ion interacting with a laser field. A general analytic approach is proposed for a three-level trapped-ion system in the presence of the time-dependent couplings. By working out an exact analytic solution, we conclusively analyse the general properties of the von Neumann entropy and quantum information entropy. It is shown that the information entropy is affected strongly by the time-dependent coupling and exhibits long time periodic oscillations. This feature attributed to the fact that in the time-dependent region Rabi oscillation is time dependent. Using parameters corresponding to a specific three-level ionic system, a single beryllium ion in a RF-(Paul) trap, we obtain illustrative examples of some novel aspects of this system in the dynamical evolution. Our results establish an explicit relation between the exact information entropy and the entanglement between the multi-level ion and the laser field. We show that different nonclassical effects arise in the dynamics of the ionic population inversion, depending on the initial states of the vibrational motion/field and on the values of Lamb–Dicke parameter η.

Journal of Physics A Mathematical and GeneralSep 21, 200549 citations

Motional macroscopic quantum superposition states of a trapped three-level ion

Özgür Esat Müstecaplıoğlu

We investigate quantum dynamical properties of a trapped three-level ion interacting with two laser beams in $\ensuremath{\Lambda}$ configuration. A unitary transformation method is developed to study the interaction of the ion with its vibrational phonons, quanta of ion's own center-of-mass motion. Under certain conditions on laser parameters, this interaction is shown to be unitarily equivalent to two-phonon cascade transitions. Complicated temporal behaviors of level populations and mean number of phonons are described clearly by identifying dynamical variables of the cascade model as building blocks. Furthermore, analyzing quantum states of vibrational phonons by Husimi- $Q$ function, we find that at times, determined by the underlying cascade dynamics, two- and three-component macroscopic quantum superposition states can be obtained depending on the Lamb-Dicke parameter and the initial conditions of the system. A wide range of initial conditions and experimental parameters are discussed using both exact and analytical solutions. Alternative routes to reach the target states are found.We investigate quantum dynamical properties of a trapped three-level ion interacting with two laser beams in $\ensuremath{\Lambda}$ configuration. A unitary transformation method is developed to study the interaction of the ion with its vibrational phonons, quanta of ion's own center-of-mass motion. Under certain conditions on laser parameters, this interaction is shown to be unitarily equivalent to two-phonon cascade transitions. Complicated temporal behaviors of level populations and mean number of phonons are described clearly by identifying dynamical variables of the cascade model as building blocks. Furthermore, analyzing quantum states of vibrational phonons by Husimi-$Q$ function, we find that at times, determined by the underlying cascade dynamics, two- and three-component macroscopic quantum superposition states can be obtained depending on the Lamb-Dicke parameter and the initial conditions of the system. A wide range of initial conditions and experimental parameters are discussed using both exact and analytical solutions. Alternative routes to reach the target states are found.

Physical Review AAug 27, 200319 citations

Dynamics of a two-level trapped ion in a cavity

Emmanouil George Thrapsaniotis

Annals of PhysicsJan 17, 20070 citations

Dynamics of two-level ions in a laser beam

Luis G. Reyna, JORGE R. SOBEHART

Computers & Mathematics with ApplicationsFeb 1, 19936 citations

Fidelity and concurrence of entangled qudits between a trapped ion and two laser beams

Rasim Dermez, S. Abdel‐Khalek, Eied Mahmoud Khalil

A quantum scheme is presented by which a three-level trapped ion interacts with a two laser beams in the absence and presence of the e®ect of classical field. We analyze the impact of the classical ¯eld and the Lamb-Dicke parameter (LDP) on the dynamical behavior of entanglement quanti¯er, population probabilities and the geometric phase. Based on four different variations of these two effects, LDP = 0.1, LDP=0.01 and ¯ = 0.0, ¯ = 0.49, the time dependence of geometric phase and populations probabilities are shown. The ¯nding emphasizes that both the time-dependent and LDP play an important role in the development of the entanglement, the geometric phase, ¯delity, and populations probabilities. This in-sight may be very useful in various applications in quantum optics and information processing.A quantum scheme is presented by which a three-level trapped ion interacts with a two laser beams in the absence and presence of the e®ect of classical field. We analyze the impact of the classical ¯eld and the Lamb-Dicke parameter (LDP) on the dynamical behavior of entanglement quanti¯er, population probabilities and the geometric phase. Based on four different variations of these two effects, LDP = 0.1, LDP=0.01 and ¯ = 0.0, ¯ = 0.49, the time dependence of geometric phase and populations probabilities are shown. The ¯nding emphasizes that both the time-dependent and LDP play an important role in the development of the entanglement, the geometric phase, ¯delity, and populations probabilities. This in-sight may be very useful in various applications in quantum optics and information processing.

Revista Mexicana de FísicaAug 18, 20211 citation

Q

function, we find that at times, determined by the underlying cascade dynamics, two- and three-component macroscopic quantum superposition states can be obtained depending on the Lamb-Dicke parameter and the initial conditions of the system. A wide range of initial conditions and experimental parameters are discussed using both exact and analytical solutions. Alternative routes to reach the target states are found.