(2005) Ion trap transducers for quantum electromechanical oscillators. Physical Review A, 72 (4). 041405(R).

We demonstrate theoretically how photon-number statistics of a driven damped oscillator at finite temperature can be extracted by measuring the dephasing spectrum of a two-level system dispersively coupled to the oscillator; we thus extend the work of M. I. Dykman and M. A. Krivoglaz ͓Sov. Phys. Solid State 29, 210 ͑1987͔͒ and J. Gambetta et al. ͓Phys. Rev. A 74, 042318 ͑2006͔͒. We carefully consider the fidelity of this scheme-to what extent does the measurement reflect the initial number statistics of the mode? We also derive analytic results for the dephasing of a qubit by a driven thermal mode, and compare results obtained at different levels of approximation. Our results have relevance both to experiments in circuit cavity QED, as well as to nanoelectromechanical systems.

We describe the conditional and unconditional dynamics of two coupled quantum dots when one dot is subjected to a measurement of its occupation number by coupling it to a third readout dot via the Coulomb interaction. The readout dot is coupled to source and drain leads under weak bias, and a tunnel current flows through a single bound state when energetically allowed. The occupation of the quantum dot near the readout dot shifts the bound state of the readout dot from a low conducting state to a high conducting state. The measurement is made by continuously monitoring the tunnel current through the readout dot. We show that there is a difference between the time scale for the measurement-induced decoherence between the localized states of the dots, and the time scale on which the system becomes localized due to the measurement.

We describe a quantum electromechanical system comprising a single quantum dot harmonically bound between two electrodes and facilitating a tunneling current between them. An example of such a system is a fullerene molecule between two metal electrodes [Park et al., Nature 407, 57 (2000)]. The description is based on a quantum master equation for the density operator of the electronic and vibrational degrees of freedom and thus incorporates the dynamics of both diagonal (population) and off diagonal (coherence) terms. We derive coupled equations of motion for the electron occupation number of the dot and the vibrational degrees of freedom, including damping of the vibration and thermo-mechanical noise. This dynamical description is related to observable features of the system including the stationary current as a function of bias voltage.