Nanomechanical resonators (5)

Abstract

Now equipped with all the classical notions needed to understand cooling, in the fifth lesson we addressed the question of the temperature limit attainable in the quantum regime where the electrical resonator is, in the absence of a pump, close to its fundamental state. The electromechanical system from the previous lesson is now assumed to be in the resolved sideband regime, which means that the frequency of the mechanical oscillator is very large compared to the linewidth of the electrical oscillator, which of course has a resonance frequency much higher than that of the mechanical oscillator. Finally, the very low damping of the electrical oscillator ensures that its linewidth is very small compared to that of the mechanical oscillator.

This device bears a strong resemblance to the one where several nuclear spins are coupled to one electron spin. The electron spin relaxes very quickly, whereas the nuclear spin is extremely slow. Nuclear spins can be cooled well below their thermodynamic equilibrium temperature by irradiating the system at a frequency equal to the difference between the Larmor frequency of the electron spin and that of the nuclear spin. In this process, known as " dynamic polarization " of nuclear spins, the electron spin becomes excited under the combined influence of radiation, from which it subtracts a photon, and a quantum of nuclear excitation. The electron excitation is rapidly dissipated in the reservoir in contact with the electron, and the cycle can begin again, each time pumping energy out of the nuclear spin system, which gradually cools down. The temperature limit of this spin system results from a balance between the rate of quantum transfer from the nuclear spins to the electron spins, itself determined by the strength of the coupling and the amplitude of irradiation, and the rate of relaxation of the nuclear spins.