Quantum feedback experiments stabilizing Fock states of light in a cavity

The ubiquitous decoherence phenomenon is responsible for the lack of quantum superpositions at the macroscopic scale. It is increasingly difficult to isolate a quantum system from its environment when its size increases. Making use of the weird quantum properties of mesoscopic quantum states thus requires efficient means to combat decoherence. One option is real-time quantum feedback. It features the components of a conventional feedback: measurement of the system's state (sensor), analysis (controller), and feedback action (actuator) aiming to the target state. The random back-action of the measurements by the sensor makes quantum feedback much more difficult than its classical counterpart. Mesoscopic photon number (Fock) states feature a decoherence rate proportional to the photon number. They are thus a simple example of a fragile quantum resource. We demonstrated recently two quantum feedback schemes continuously stabilizing Fock state of a microwave field in a high-quality cavity. Sensitive atoms, crossing the field one at a time, are used as quantum nondemolition (QND) probes of its photon number. The feedback actuator is either a classical source [Sayrin et al., Nature (London) 477, 73 (2011)] or individual resonant atoms emitting or absorbing one photon each [Zhou et al., Phys. Rev. Lett. 108, 243602 (2012)]. Both schemes detect the quantum jumps of the photon number and efficiently correct their adverse effects, preparing and preserving a fragile quantum resource. We present an in-depth analysis of our methods, which sheds light onto the fundamental difficulties encountered in quantum feedback, in particular concerning the state estimation algorithm, and onto the ways to circumvent them. These results open the way to informationally optimal QND measurements or to the stabilization of mesoscopic field state superpositions. More generally, they can be cast in a variety of contexts to loosen the tight constraints set by decoherence in quantum metrology and quantum information processing. DOI: 10.1103/PhysRevA.87.042320