INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF OPTICS B: QUANTUM AND SEMICLASSICAL OPTICS J. Opt. B: Quantum Semiclass. Opt. 4 (2002) 430–437 PII: S1464-4266(02)37373-7 The effect of a non-zero spontaneous decay rate on teleportation G Chimczak and R Tana´ s Nonlinear Optics Division, Institute of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Pozna´ n, Poland E-mail: tanas@kielich.amu.edu.pl Received 15 May 2002, in final form 9 October 2002 Published 6 November 2002 Online at stacks.iop.org/JOptB/4/430 Abstract We discuss the influence of the spontaneous decay rate of the excited state on teleportation of the atomic state via cavity decay in the scheme of Bose et al (Bose S, Knight P L, Plenio M B and Vedral V 1999 Phys. Rev. Lett. 83 5158). We show that even a small but non-zero decay rate of the excited state leads to significant effects such as lowering the probability of successful teleportation if the product of the saturation parameter and the spontaneous decay rate is not negligible in comparison with the cavity mode decay rate. We compare analytical results obtained using adiabatic elimination with the results calculated numerically. Keywords: Quantum teleportation, quantum information processing 1. Introduction Spontaneous decay can play a destructive role in quantum information processing. The decay is responsible for decoherence and loss of information stored in a quantum system. However, spontaneous decay can also be helpful in quantum information processing. Detection of the decay allows entanglement, which is essential for many quantum applications. Researchers usually consider decays from cavities in this way, but many systems consist of optical cavities containing one atom [1–3] or two atoms [4]. Research is motivated by the fact that atomic states are ideal for storing quantum information. Spontaneous emission by the atoms, which is in effect unwanted decay leading to decoherence, has to be dealt with. One can avoid the problem by using a three- level atom in the  configuration. There are two stable ground states and one excited state of the atom, as shown in figure 1. The whole information processing procedure can be performed in such a way that the excited state will always have a small population. Under this condition, the excited atomic states can be eliminated adiabatically. If the population of the excited state is small enough, we can also neglect the spontaneous decay rate from this state. A teleportation scheme working in this way has recently been proposed [1]. However, one has to be very careful, because even a very small population can produce significant effects. This is because of the fact that the probability for an emission during the whole quantum 0 1 a b ω ω ω ω 0 1 ∆ γ a las cav Figure 1. Atomic levels scheme. The |a 0 –|b transition is driven by a classical laser field of frequency ω las and the |a 1 –|b transition is driven by the quantized cavity mode of frequency ω las . The laser and quantized fields are both detuned from the upper atomic state by . teleportation process is proportional to the product of the mean population of the excited state, the spontaneous decay rate and the total operation time. In the scheme of teleportation via cavity decay, discussed here, the process time has to be long compared with the inverse of the cavity decay rate κ −1 . If the time turns out to also be long compared with the inverse of the product of the atomic decay rate γ multiplied by the mean population in the upper level, the probability for the emission can take significant values and cannot be neglected even if the population of the excited state is very small. 1464-4266/02/060430+08$30.00 © 2002 IOP Publishing Ltd Printed in the UK 430