Quantum Feedback Control of Non-classical Microwave Fields in Cavity Quantum Electrodynamics Experiments

In our Cavity Quantum Electrodynamics experiments, we use a beam of Rydberg atoms to manipulate and probe non-destructively microwave photons trapped in a very high Q superconducting cavity. In recent years, we have realized ideal quantum non-demolition (QND) measurements of photon numbers, observed the radiation quantum jumps due to cavity relaxation and prepared non-classical fields such as Fock and Schrödinger cat states. Combining QND photon counting with a homodyne mixing method, we have reconstructed the Wigner functions of these non-classical states and, by taking snapshots of these functions at increasing times, obtained movies of the decoherence process .

The next step in this research program was to demonstrate ways to protect these non-classical states against decoherence. One natural method is to implement a procedure analogous to the feedback strategies used to stabilize complex systems in classical physics. A probe measures the system state, a controller determines the action leading it towards the chosen operating point and an actuator realizes this action. Juggling, for instance, relies on feedback loops from the eye to the hands through the brain. Transferring the feedback concept to the quantum world faces a fundamental difficulty: quantum measurement changes randomly the state of the system and this change must be taken into account in the feedback procedure. In our first demonstration experiment, we have chosen as an operating point a fixed photon number in our cavity. The “eye” in this “photon juggling game” is the beam of Rydberg atoms which performs a weak QND measurement extracting a partial information about the photon number. The “brain” is a computer using this information to estimate in real time the state of the field in the cavity and the “hand” is a classical microwave source feeding the cavity. These operations are performed in successive loops bringing the field towards the desired photon number. Subsequent quantum jumps of the field are detected by the computer and their effect is reversed by the feedback procedure. In this way, a pre-determined photon number is maintained in a steady state. We hope to be able to extend soon these experiments to the protection of other non-classical states such as Schrödinger cats of radiation.