Nanomechanical resonators (1)

Abstract

The first lesson introduced the notion of quantum machines, a class of systems to which cooled mechanical resonators belong in the regime where their energy appears clearly quantized. Quantum machines are characterized first and foremost by the sensitivity of their state to the process of observing that state. In a classical machine such as a crane, the crane operator can observe the movement of the charge he is handling without worrying about the feedback from the detection of photons illuminating the charge on its position. In contrast, when controlling a quantum machine, the processing of the signal used to observe the state of the machine must take into account the disturbance caused by the measurement of the state itself.

Artificial mechanical oscillators, as physical systems, are described by two main characteristics : their mass and their frequency. At one end of the classicity/quanticity spectrum are gravitational antennae, whose masses are expressed in kilograms and frequencies in hertz. At the other end of the spectrum are the fundamental modes of vibration of mechanical resonators manufactured by nano- and micro-lithography, whose effective masses are expressed in picograms and frequencies in gigahertz. In recent years, these resonators have been cooled to an excitation level close to their fundamental state. The difficulty of imposing quantum behavior on a macroscopic object containing a very large number of atoms can be understood by first considering a single molecule, such as the carbon monoxide molecule CO, which has an electric dipole moment. The relative movement of carbon and oxygen atoms, held at a distance by their chemical bond which acts like a spring, is therefore easy to observe. Its oscillation frequency is around 60 THz, with an effective mass of ^10-23 kg. It's easy to calculate the amplitude of the oscillation's zero-point quantum motion, which is 4 pm, or 1/25 the size of an atom. This characteristic magnitude corresponds to the typical amplitude of motion associated with an excitation quantum of the oscillator, called a phonon by reference to the vibration quantum of a crystal.
When atoms (masses) and chemical bonds (springs) are assembled to form a solid, the frequency decreases and the oscillating motion becomes easier to control, but at the same time, zero-point vibrations have an ever-smaller amplitude, reaching the femtometer, i.e. the size of the nucleus, for nanoresonators. How can such a small displacement be measured ? The fundamental principle applied by experiments in this field is based on the following idea : one of the mirrors of a Fabry-Perot resonator is attached to the oscillator's mass, and the oscillator's state of vibration is determined by very precisely probing the optical frequency of this resonator, which shifts with the position of the mass. The question arises as to how this positional resolution, more than eight orders of magnitude lower than that of the wavelength of light, can be achieved : the answer, which was one of the main objectives of the lecture, lies both in the very high quality factor of the optical resonator, and in the very large number of photons that can be excited in it. This type of argument, valid for optomechanical resonators in which an optical and a mechanical mode are coupled, can be extended to electro-mechanical resonators, in which the role of the optical mode is played by a radio frequency mode in the microwave range.