Controlling the Decoherence of a “Meter” via Stroboscopic Feedback

Decoherence is the rapid destruction of the phase relation between two quantum states of a system caused by the entanglement of these two states with two different states of the environment [1]. The progressive decoherence of a mesoscopic Schrödinger cat has been observed for the first time in the experiment of Brune et al. [2], where the linear superposition of two coherent states of the electromagnetic field in a cavity with classically distinct phases has been generated and detected. In this Letter we describe a scheme in which decoherence due to spontaneous emission can be significantly mitigated by coherent feedback. In Ref. [2], a Schrödinger cat state for the microwave field in a superconducting cavity C has been generated using circular Rydberg atoms crossing a cavity prepared in a coherent state. All the atoms have an appropriately selected velocity and the relevant levels are two adjacent Rydberg states which we denote as jgl and jel. The atoms are initially prepared in the state jel. The high-Q superconducting cavity is sandwiched between two low-Q cavities R1 and R2, in which classical microwave fields can be applied and which are resonant with the transition between the state jel and the nearby lower circular state jgl. The intensity of the field in the first cavity R1 is then chosen so that, for the selected atom velocity, a py2 pulse is applied to the atom as it crosses R1. As a consequence, the atomic state before entering the cavity C is jcatoml ­ 1 p2 sjel 1 jgld . The high-Q cavity C is off resonance with respect to the e ! g transition. However we will allow for a strong field pulse to shift the excited state into resonance with the cavity C. In the off-resonant case, the atom and the field cannot exchange energy but only undergo dispersive frequency shifts depending on the atomic level [3]. The field undergoes an equal and opposite phase shift for the ground and excited states. However as only the relative phase of the two components matters we may attribute all