Sensitivity and back action in charge qubit measurements by a strongly coupled single-electron transistor

Abstract

We consider charge-qubit monitoring (continuous-in-time weak measurement) by a single-electron transistor (SET) operating in the sequential-tunneling régime. We show that commonly used master equations for this régime are not of the Lindblad form that is necessary and sufficient for guaranteeing valid physical states. In this paper we derive a Lindblad-form master equation and a corresponding quantum trajectory model for continuous measurement of the charge qubit by a SET. Our approach requires that the SET-qubit coupling be strong compared to the SET tunnelling rates. We present an analysis of the quality of the qubit measurement in this model (sensitivity versus back-action). Typically, the strong coupling when the SET island is occupied causes back-action on the qubit beyond the quantum back-action necessary for its sensitivity, and hence the conditioned qubit state is mixed. However, in one strongly coupled, asymmetric régime, the SET can approach the limit of an ideal detector with an almost pure conditioned state. We also quantify the quality of the SET using more traditional concepts such as the measurement time and decoherence time, which we have generalized so as to treat the strongly responding régime.

Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect

“…How fast the ensemble of possible trajectories converge to one of the possible values z = ±1 is characterized by the conditional variance [46]. This measure is defined as…”

Non-Markovian dynamics and noise characteristics in continuous measurement of a solid-state charge qubit

“…Motivated by potential applications to quantum computation [1,2], as well as general interest in mesoscopic quantum phenomena, intensive experimental and theoretical effort has been devoted to the attempts to study these oscillations and measurement possibilities of individual qubits. One of the especially interesting methods of detecting coherent oscillations is to monitor them continuously with a mesoscopic electrometer, such as single electron transistor (SET) [3][4][5][6][7][8][9][10] or quantum point contact (QPC) [11][12][13][14][15], whose conductance depends on the charge state of a nearby qubit. From the readout of the detector, one is capable of gaining essential insight into the nontrivial correlation characteristics between the detector and the measured system.…”

Quantum Efficiency of Charge Qubit Measurements Using a Single Electron Transistor

“…(4e)-(4f). Since this definition ignores the weight of each exponentially decaying component, it breaks down as the weight of the slowest decay component is the smallest one.(ii) Borrowing a technique in quantum optics, Γ d can be defined better from the Glauber coherence function [18]is the operator in Heisenberg picture, and · · · ss means average with respect to the steady-state. Then, one defines Γ…”

“…(ii) Borrowing a technique in quantum optics, Γ d can be defined better from the Glauber coherence function [18]:…”

“…When the tunnel coupling between the charge states is quenched, the measurement falls into the scenario of QND type. Moreover, it is believed that the SET detector holds promising applications in solid-state quantum computation [11,12], whose measurement properties have been therefore received considerable attention in the past years [13][14][15][16][17][18][19]. While in the higher-order cotunneling regime the measurement can reach the quantum limit (η = 1) in principle [15,16], it was found that the quantum efficiency of the SET detector is rather poor in the weak response and sequential tunneling regime [12][13][14].…”