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Quantum Trajectories with Incompatible Decoherence Channels

Abstract : In contrast with its classical version, a quantum measurement necessarily disturbs the state of the system. The projective measurement of a spin-1/2 in one direction maximally randomizes the outcome of a following measurement along a perpendicular direction. In this thesis, we discuss experiments on superconducting circuits that allow us to investigate this measurement back-action. In particular, we measure the dynamics of a superconducting qubit whose three Bloch x, y and z components are simultaneously recorded. Two recent techniques are used to make these simultaneous recordings. The x and y components are obtained by measuring the two quadratures of the fluorescence field emitted by the qubit. Conversely, the z component is accessed by probing an offresonant cavity dispersively coupled to the qubit. The frequency of the cavity depends on the energy of the qubit and the strength of this last measurement can be tuned from weak to strong in situ by varying the power of the probe. These observations are enabled by recent advances in ultra-low noise microwave amplification using Josephson circuits. This thesis details all these techniques, both theoretically and experimentally, and presents various unpublished additional results. In the presence of the simultaneous measurements, we show that the state of the system diffuses inside the sphere of Bloch by following a random walk whose steps obey the laws of the backaction of incompatible measurements. The associated quantum trajectories follow a variety of dynamics ranging from diffusion to Zeno blockade. Their peculiar dynamics highlights the non-trivial interplay between the back-action of the two incompatible measurements. By conditioning the records to the outcome of a final projective measurement, we also measure the weak values of the components of the qubit state and demonstrate that they exceed the mean extremal values. The thesis discusses in detail the statistics of the obtained trajectories.
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Quentin Ficheux. Quantum Trajectories with Incompatible Decoherence Channels. Quantum Physics [quant-ph]. École normale supérieure - ENS PARIS, 2018. English. ⟨tel-02098804⟩

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