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Journal of Modern Optics

Physical properties of a trapped two-level ion decaying by thermal and squeezed vacuum reservoirs

Navid Yazdanpanah, Mohammad Kazem Tavassoly

Published Aug 7, 2015• 4 citations
Publisher

Abstract

In this paper, we first study the interaction between a trapped two-level ion with a field reservoir in a general form. Then, we use thermal and squeezed vacuum reservoirs to continue our investigation. We try to find the equation of motion for the whole system density operator by applying the Weisskopf theory. Next, we evaluate the explicit form of the density matrix elements analytically. In the obtained density matrix elements, we arrive at some physical parameters of the trapped ion system as well as the applied field reservoirs by which one can control the transition probabilities between the trapped ionic states. We also introduce some hermitian operators for the trapped ion system and calculate the expectation values of their time evolution by considering the mentioned two reservoirs. In the continuation, we design a system for measuring the hermitian trapped ion’s operators theoretically. Finally, we find a way to transport the information of the trapped ion system by our proposed quantum processor.

DOI
10.1080/09500340.2015.1071442

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In this paper, we first study the interaction between a trapped two-level ion with a field reservoir in a general form. Then, we use thermal and squeezed vacuum reservoirs to continue our investigation. We try to find the equation of motion for the whole system density operator by applying the Weisskopf theory. Next, we evaluate the explicit form of the density matrix elements analytically. In the obtained density matrix elements, we arrive at some physical parameters of the trapped ion system as well as the applied field reservoirs by which one can control the transition probabilities between the trapped ionic states. We also introduce some hermitian operators for the trapped ion system and calculate the expectation values of their time evolution by considering the mentioned two reservoirs. In the continuation, we design a system for measuring the hermitian trapped ion’s operators theoretically. Finally, we find a way to transport the information of the trapped ion system by our proposed quantum processor.
In this paper we study the full quantum approach to the interaction of NNN trapped two-level ions with NNN quantized fields in such a way that each of the trapped ions separately interacts with one of the quantized fields. A semiclassical model of this type of interaction has been already studied, using classical laser fields instead of quantized fields, by Cirac and Zoller [Phys. Rev. Lett. 74, 4091 (1995)]. During each interaction, the excitation of a trapped ion occurs due to the occurrence of resonance between the trapped ion and one of the modes of multimode quantized field. In this way, we are able to find the quantized radiation field, which propagates from each excited trapped ion after its deexcitation. It is demonstrated that such a propagated field is a function of the position of ion within the trap, ion number, trapping and ionic transition frequencies, spontaneous emission rate, and time evolution of trapped ionic operators. In the continuation, to achieve the explicit form of such a field we propose a method to evaluate the temporal evolution of operators of the system by utilizing the Heisenberg operator approach. Via the propagated field of each trapped ion, the spectral properties such as intensities as well as power spectra of their radiations are evaluated. Furthermore, the quantum statistics of field and in particular, its photon antibunching and sub-Poissonian statistical properties are investigated. Finally, resonance spectroscopy of the trapped ions is obtained by which one can allocate a characteristic spectrum to each of them.
The dissipative and decoherence properties of a two-level atom interacting with a squeezed vacuum field reservoir are investigated based on the nonautonomous master equation of the atomic density matrix in the framework of algebraic dynamics. The nonautonomous master equation is converted into a Schrödinger-like equation and its dynamical symmetry is found based on the left and right representations of the relevant algebra. The time-dependent solutions and the steady solutions are obtained analytically. The asymptotic behaviour of the solutions is examined and the approach to the equilibrium state is proved. Based on the analytic solution the response of the system to the squeezed vacuum field reservoir is studied numerically.
The dissipative and decoherence properties of the two-level atom interacting with the squeezed vacuum field reservoir are investigated based on the nonautonomous master equation of the atomic density matrix in the framework of algebraic dynamics. The nonautonomous master equation is converted into a Schr\\"{o}dinger-like equations and its dynamical symmetry is found based on the left and right representations of the relevant algebra. The time-dependent solution and the steady solution are obtained analytically. The asymptotic behavior of the solution is examined and the approach to the equilibrium state is proved. Based on the analytic solution the response of the system to the squeezed vacuum field reservoir is studied numerically.
We consider a system consisting of a single two-level ion in a harmonic trap, which is localized inside an optical cavity in contact with a thermal bath and subjected to the action of two external lasers. We are able to obtain an analytical solution for the total density operator of the system and show that squeezing in the motion of the ion and in the cavity field is generated. We also show that complete revivals of the states of the motion of the ion and of the cavity field occur periodically when the temperature is zero. The correlations and entanglement between the motion and the cavity field are studied. We found that for entanglement may either disappear completely for finite times or disappear and appear during finite intervals.
Abstract In this paper we consider a system consisting of a number of two-level atoms in a Bose–Einstein condensate (BEC) and a single-mode quantized field, which interact with each other in the presence of two different damping sources, i.e. cavity and atomic reservoirs. The reservoirs which we consider here are thermal and squeezed vacuum ones corresponding to field and atom modes. Strictly speaking, by considering both types of reservoirs for each of the atom and field modes, we investigate the quantum dynamics of the interacting bosons in the system. Then, via solving the quantum Langevin equations for such a dissipative BEC system, we obtain analytical expressions for the time dependence of atomic population inversion, mean atom as well as photon number and quadrature squeezing in the field and atom modes. Our investigations demonstrate that for modeling the real physical systems, considering the dissipation effects is essential. Also, numerical calculations which are presented show that the atomic population inversion, the mean number of atoms in the BEC and the photons in the cavity possess damped oscillatory behavior due to the presence of reservoirs. In addition, non-classical squeezing effects in the field quadrature can be observed especially when squeezed vacuum reservoirs are taken into account. As an outstanding property of this model, we may refer to the fact that one can extract the atom–field coupling constant from the frequency of oscillations in the mentioned quantities such as atomic population inversion.
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.