Monte Carlo Method for a Quantum Measurement Process by a Single-Electron Transistor

Abstract

We derive the quantum trajectory or stochastic (conditional) master equation for a single superconducting Cooper-pair box (SCB) charge qubit measured by a single-electron transistor (SET) detector. This stochastic master equation describes the random evolution of the measured SCB qubit density matrix which both conditions and is conditioned on a particular realization of the measured electron tunneling events through the SET junctions. Hence it can be regarded as a Monte Carlo method that allows us to simulate the continuous quantum measurement process. We show that the master equation for the "partially" reduced density matrix [Y. Makhlin et.al., Phys. Rev. Lett. 85, 4578 (2000)] can be obtained when a "partial" average is taken on the stochastic master equation over the fine grained measurement records of the tunneling events in the SET. Finally, we present some Monte Carlo simulation results for the SCB/SET measurement process. We also analyze the probability distribution P(m,t) of finding m electrons that have tunneled into the drain of the SET in time t to demonstrate the connection between the quantum trajectory approach and the "partially" reduced density matrix approach.

7 pages, to appear in Phys. Rev. B

References in corpus (10)

• Quantum Computation with Quantum Dots
• Quantum state engineering with Josephson-junction devices
• Continuous quantum measurement of a double dot
• Selective quantum evolution of a qubit state due to continuous measurement
• Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach
• Quantum Measurements Performed with a Single-Electron Transistor
• Dynamics of a mesoscopic qubit under continuous quantum measurement
• Quantum feedback control of a solid-state qubit
• Statistics and noise in a quantum measurement process
• Quantum measurement of coherence in coupled quantum dots

Cited by in corpus (14)

• High fidelity measurement and quantum feedback control in circuit QED
• Non-Markovian finite-temperature two-time correlation functions of system operators: beyond the quantum regression theorem
• Quantum mechanical approach to decoherence and relaxation generated by fluctuating environment
• Sensitivity and back-action in charge qubit measurements by a strongly coupled single-electron transistor
• Quantum Noise in the Electromechanical Shuttle
• Quantum trajectories for the realistic measurement of a solid-state charge qubit
• Spin-detection in a quantum electromechanical shuttle system
• Non-Markovian dynamics of a nanomechanical resonator measured by a quantum point contact
• Model for monitoring of a charge qubit using a radio-frequency quantum point contact including experimental imperfections
• Quantum coherence control of solid-state charge qubit by means of a suboptimal feedback algorithm
• Electron spin tomography through counting statistics: a quantum trajectory approach
• Decoherence and the retrieval of lost information
• Conditional counting statistics of electrons tunneling through quantum dot systems measured by a quantum point contact
• Conductance of a SET with a retarded dielectric layer in the gate capacitor