The length of time that a quantum system can exist in a superposition stateis determined by how strongly it interacts with its environment. Thisinteraction entangles the quantum state with the inherent fluctuations of theenvironment. If these fluctuations are not measured, the environment can beviewed as a source of noise, causing random evolution of the quantum systemfrom an initially pure state into a statistical mixture-a process known asdecoherence. However, by accurately measuring the environment in real time, thequantum system can be maintained in a pure state and its time evolutiondescribed by a quantum trajectory conditioned on the measurement outcome. Weemploy weak measurements to monitor a microwave cavity embedding asuperconducting qubit and track the individual quantum trajectories of thesystem. In this architecture, the environment is dominated by the fluctuationsof a single electromagnetic mode of the cavity. Using a near-quantum-limitedparametric amplifier, we selectively measure either the phase or amplitude ofthe cavity field, and thereby confine trajectories to either the equator or ameridian of the Bloch sphere. We perform quantum state tomography at discretetimes along the trajectory to verify that we have faithfully tracked the stateof the quantum system as it diffuses on the surface of the Bloch sphere. Ourresults demonstrate that decoherence can be mitigated by environmentalmonitoring and validate the foundations of quantum feedback approaches based onBayesian statistics. Moreover, our experiments suggest a new route forimplementing what Schrodinger termed "quantum steering"-harnessing action at adistance to manipulate quantum states via measurement.
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