Accuracy of a teleported cavity-field state

Abstract

We present a calculation of the fidelity of a cavity-field state teleported by means of a scheme that requires only two high-Q cavities. Based on current experimental capabilities, we demonstrate the feasibility of our scheme if the mean photon number of the cavity field is on the order of unity, allowing a reasonably accurate teleportation.PACS number͑s͒: 03.65. Bz, 03.67.Ϫa, 32.80.Rm, 42.50.Dv Quantum nonlocality has recently become the cornerstone of a set of striking proposals, which open the way to new quantum technologies: bit commitment ͓1͔, teleportation ͓2͔, computation ͓3͔, and communication ͓4͔. Inspired by these theoretical advances, experimentalists have developed techniques for the realization of teleportation ͓5͔ and to demonstrate quantum logic operations ͓6͔. However, the realization of all these proposals faces a crucial problem, intrinsic to the nature of entanglement: the decoherence of quantum states subjected to the action of the environment. This drastic process, transforming superpositions of quantum states into statistical mixtures, has been discussed by a number of authors ͓7,13͔ and, recently, observed experimentally ͓14͔. Since the coherence decays with a lifetime proportional to the inverse of the system excitation number ͓7͔, it becomes indispensable to estimate, from a given superposition, the fidelity of a resulting process. Recently, Braunstein and Kimble ͓8͔ have computed the fidelity of a teleported ''Schrödinger cat''-like state ͑SCLS͒ generated by parametric down-conversion as a running wave. Here, however, we focus on the specific problems of quantum-state engineering and teleportation in cavity quantum electrodynamics ͑CQED͒. In this realm, a SCLS teleportation protocol has recently been proposed, requiring three high-Q cavities ͓9͔. In the present paper, we advance computation of the fidelity of a trapped SCLS, teleported through a scheme based on only two high-Q cavities, whose feasibility we also analyze. The advantage of adopting our two-cavity scheme for teleporting a SCLS, as opposed to its alternative one in the literature ͓9͔, is twofold: it minimizes field dissipation through cavity damping mechanisms and also provides topological simplification of the experimental setup.Previously presented two-cavity schemes ͓10,11͔ have not envisaged teleportation of mesoscopic field states. In this work, the quantum channel employing a mixed atomic-field state, prepared through the interaction between a two-level atom and a cavity field, is more suitable to mesoscopic-state teleportation. Teleportation of N(Ͼ2)-dimensional states has also been proposed in the CQED domain ͓12͔.The teleportation apparatus is depicted in Fig. 1. The SCLS engineering consists of a two-level Rydberg atom A that crosses a Ramsey-type arrangement, i.e., a high-Q micromaser cavity C 1 located between two Ramsey zones R 1 and R 2 . After interacting with this arrangement, the atom is counted by detector D A , projecting the SCLS in C 1 . Subse-quently, this SCLS is teleported from Alice's cavity C 1 t...

Engineering arbitrary motional ionic states through realistic intensity-fluctuating laser pulses

“…In this connection, a phenomenological-operator approach developed recently to account for errors in complex quantum processes was applied [30,31].…”

“…We will also propose an alternative way of engineering an ionic motional state in the presence of noise, which consists in maximizing the fidelity of the experimentally achieved state. A phenomenological-operator approach, originally developed in the context of cavity QED [30,31], will be considered here to account for the evolution of the ionic states under the influence of the fluctuating-intensity laser pulses. The strategy is to provide a straightforward technique to incorporate the main results obtained by standard ab-initio methods for treating errors in trapped ions (in particular we consider the master equation calculations in Ref.…”

“…This approximation results in a non-unity fidelity for the sculpted state. Usually, the fidelity of a given quantum process is defined to account for the inevitable errors introduced by the environment due to dissipative mechanisms [30,31].…”

“…Through the phenomenological-operator approach, first developed in the domain of cavity QED [30,31], the effect of noise is introduced directly in the evolution of the state vector of the whole system, instead of turning to the evolution of the density operator as in the ab initio methods. In Sec.…”

“…IV, we calculate the fidelity of a sculpted state under the effects of noise. Here, a phenomenological-operator approach [30,31] will be applied to account for the presence of noise in the engineering process. This approach has been developed precisely to compute the effects of noise in complex processes such as quantum state engineering and teleportation of quantum states; processes where the protocol requires several steps of quantum interactions.…”