Section: New Results

Using Spontaneous Emission of a Qubit as a Resource for Feedback Control

Participants: Nathanael Cottet, Benjamin Huard, Sebastien Jezouin, François Mallet, Pierre Rouchon, Alain Sarlette, Pierre Six.

The results of this section were published in [15].

We performed an experiment that demonstrates the permanent stabilization of any state of a superconducting qubit despite decoherence using a feedback scheme based on the information leaking out by the relaxation channel itself when the qubit spontaneously emits a photon.

At first sight, it may seem that using the detection of the photon that a qubit emits during a relaxation event cannot allow to protect an arbitrary quantum state from decoherence. First, it is very hard to collect efficiently the photons emitted by a two-level system. Second, the information contained in the emitted photon alone does not seem to be sufficient to correct the effect of relaxation and stabilize an arbitrary qubit state.

However, as we recently showed experimentally (see previous paragraph), it is now possible to measure the spontaneously emitted field using heterodyne detection, and reconstruct the quantum trajectory of a qubit. The information is therefore indeed useful and accessible!

Here, we go well beyond this previous work by not only decoding but also using the information contained in the spontaneously emitted field in real time. Specifically, we use the information contained in fluorescence to stabilize permanently any chosen state of the qubit by measurement feedback.

Stabilizing qubits by a feedback protocol based on the measurement of their relaxation channel had been proposed about 20 years ago by Hofmann and coworkers. They had claimed that it is possible to stabilize any state in the Southern hemisphere of the Bloch sphere. Wang and Wiseman revisited this problem 15 years ago and proposed a scheme that stabilizes any state of the Bloch sphere except the equator. In our work, we devise a new scheme that stabilizes any state, even on the equator! We are also the first ones to implement any such scheme experimentally.

The experiment itself covers several premieres, which are of wider interest to the quantum information and quantum control communities. First, we reach an unprecedented $35\%$ of measurement efficiency for the spontaneously emitted photons out of a qubit (crucial parameter for feedback control). Second, this is the first multiple-input multiple-output feedback in the quantum regime. Finally, we devise a new feedback controller based on the ac-Stark effect to tune the qubit frequency as a function of one input analog signal.