Coherent back action of quantum dot detectors: Qubit spin precession

Hell, Michael; Wegewijs, Maarten Rolf; DiVincenzo, David

doi:10.1103/PhysRevB.89.195405

Journal Article

FZJ-2014-05506

Coherent back action of quantum dot detectors: Qubit spin precession

Hell, M. (Corresponding Author)FZJ* ; Wegewijs, M. R.FZJ* ; DiVincenzo, D.FZJ*

2014
APS College Park, Md.

Physical review / B 89(19), 195405 (2014) [10.1103/PhysRevB.89.195405]

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Please use a persistent id in citations: http://hdl.handle.net/2128/8049 doi:10.1103/PhysRevB.89.195405

Abstract: A sensitive technique for the readout of the state of a qubit is based on the measurement of the conductance through a proximal sensor quantum dot (SQD). Here, we theoretically study the coherent backaction of such a measurement on a coupled SQD-charge-qubit system. We derive Markovian kinetic equations for the ensemble-averaged state of the SQD-qubit system, expressed in the coupled dynamics of two charge-state occupations of the SQD and two qubit isospin vectors, one for each SQD charge state. We find that aside from introducing dissipation, the detection also renormalizes the coherent evolution of the SQD-qubit system. Basically, if the electron on the detector has time to probe the qubit, then it also has time to fluctuate and thereby renormalize the system parameters. In particular, this induces torques on the qubit isospins, similar to the spin torque generated by the spintronic exchange field in noncollinear spin-valve structures. Second, we show that for a consistent description of the detection, one must also include the renormalization effects in the next-to-leading order in the electron tunneling rates, especially at the point of maximal sensitivity of the detector. Although we focus on a charge-qubit model, our findings are generic for qubit readout schemes that are based on spin-to-charge conversion using a quantum dot detector. Furthermore, our study of the stationary current through the SQD, a test measurement verifying that the qubit couples to the detector current, already reveals various significant effects of the isospin torques on the qubit. Our kinetic equations provide a starting point for further studies of the time evolution in charge-based qubit readout. Finally, we provide a rigorous sum rule that constrains such approximate descriptions of the qubit isospin dynamics and show that it is obeyed by our kinetic equations.

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