We present a quantum theory of cooling of a mechanical resonator using back-action with constant electron current. The resonator device is based on a doubly clamped nanotube, which mechanically vibrates and acts as a double quantum dot for electron t
ransport. Mechanical vibrations and electrons are coupled electrostatically using an external gate. The fundamental eigenmode is cooled by absorbing phonons when electrons tunnel through the double quantum dot. We identify the regimes in which ground state cooling can be achieved for realistic experimental parameters.
We assess proposals for entangling two distant atoms by measurement of emitted photons, analyzing how their performance depends on the photon detection efficiency. We consider schemes based on measurement of one or two photons and compare them in ter
ms of the probability to obtain the detection event and of the conditional fidelity with which the desired entangled state is created. Based on an unravelling of the master equation, we quantify the parameter regimes in which one or the other scheme is more efficient, including the possible combination of the one-photon scheme with state purification. In general, protocols based on one-photon detection are more efficient in set-ups characterized by low photon detection efficiency, while at larger values two-photon protocols are preferable. We give numerical examples based on current experiments.
We show theoretically that two atomic dipoles in a resonator constitute a non-linear medium, whose properties can be controlled through the relative position of the atoms inside the cavity and the detuning and intensity of the driving laser. We ident
ify the parameter regime where the system operates as a parametric amplifier, based on the cascade emission of the collective dipole of the atoms, and determine the corresponding spectrum of squeezing of the field at the cavity output. This dynamics could be observed as a result of self-organization of laser-cooled atoms in resonators.
