Qubit quantum-dot sensors: Noise cancellation by coherent backaction, initial slips, and elliptical precession

Abstract

We theoretically investigate the backaction of a sensor quantum dot with strong local Coulomb repulsion on the transient dynamics of a qubit that is probed capacitively. We show that the measurement backaction induced by the noise of electron cotunneling through the sensor is surprisingly mitigated by the recently identified coherent backaction [M. Hell, M. R. Wegewijs, and D. P. DiVincenzo, Phys. Rev. B 89, 195405 (2014)] arising from quantum fluctuations. This indicates that a sensor with quantized states may be switched off better than naively expected. This renormalization effect is missing in semiclassical stochastic fluctuator models and typically also in Born-Markov approaches, which try to avoid the calculation of the nonstationary, nonequilibrium state of the qubit plus sensor. Technically, we integrate out the current-carrying electrodes to obtain kinetic equations for the joint, nonequilibrium detector-qubit dynamics. We show that the sensor current response, level renormalization, cotunneling broadening, and leading non-Markovian corrections always appear together and cannot be turned off individually in an experiment or ignored theoretically. We analyze the backaction on the reduced qubit state---capturing the full non-Markovian effects imposed by the sensor quantum dot on the qubit---by applying a Liouville-space decomposition into quasistationary and rapidly decaying modes. Importantly, the sensor cannot be eliminated completely even in the simplest high-temperature, weak-measurement limit since the qubit state experiences an initial slip depending on the initial preparation of qubit plus sensor quantum dot. The slip persists over many qubit cycles, i.e., also on the time scale of the qubit decoherence induced by the backaction. A quantum-dot sensor can thus not be modeled as usual as a ``black box'' without accounting for its dynamical variables; it is part of the quantum circuit. We furthermore find that the Bloch vector relaxes (rate $1/{T}_{1}$) along an axis that is not orthogonal to the plane in which the Bloch vector dephases (rate $1/{T}_{2}$), blurring the notions of relaxation and dephasing times. Moreover, the precessional motion of the Bloch vector is distorted into an ellipse in the tilted dephasing plane.