Cavity optomechanics
Cavity optomechanics is a branch of physics which focuses on the interaction between light and mechanical objects on low-energy scales.
[2] The name of the field relates to the main effect of interest: the enhancement of radiation pressure interaction between light (photons) and matter using optical resonators (cavities).
Macroscopic objects consisting of billions of atoms share collective degrees of freedom which may behave quantum mechanically (e.g. a sphere of micrometer diameter being in a spatial superposition between two different places).
Optomechanical structures provide new methods to test the predictions of quantum mechanics and decoherence models and thereby might allow to answer some of the most fundamental questions in modern physics.
[3][4][5] There is a broad range of experimental optomechanical systems which are almost equivalent in their description, but completely different in size, mass, and frequency.
[6] The most elementary light-matter interaction is a light beam scattering off an arbitrary object (atom, molecule, nanobeam etc.).
However, it is always possible to have Brillouin scattering independent of the internal electronic details of atoms or molecules due to the object's mechanical vibrations:
The vibrations gain or lose energy, respectively, for these Stokes/anti-Stokes processes, while optical sidebands are created around the incoming light frequency:
Since the momentum of photons is extremely small and not enough to change the position of a suspended mirror significantly, the interaction needs to be enhanced.
The number of times a photon can transfer its momentum is directly related to the finesse of the cavity, which can be improved with highly reflective mirror surfaces.
Therefore, the detuning—which determines the light amplitude inside the cavity—between the changed cavity and the unchanged laser driving frequency is modified.
[1][8] Some first effects of the light on the mechanical resonator can be captured by converting the radiation pressure force into a potential,
[10] However, the model is incomplete as it neglects retardation effects due to the finite cavity photon decay rate
The consequence of this delayed radiation force during one cycle of oscillation is that work is performed, in this particular case it is negative,
[12] It is important for reaching the quantum regime of the mechanical oscillator where thermal noise effects on the device become negligible.
In this case the extra, light-induced damping is negative and leads to amplification of the mechanical motion (heating).
The standard optomechanical setup is a Fabry–Pérot cavity, where one mirror is movable and thus provides an additional mechanical degree of freedom.
The coupling originates from the radiation pressure of the light field that eventually moves the mirror, which changes the cavity length and resonance frequency.
It determines the amount of cavity resonance frequency shift if the mechanical oscillator is displaced by the zero point uncertainty
With a strong enough drive, the dynamics of the system can be considered as quantum fluctuations around a classical steady state, i.e.
can be omitted as it leads to a constant radiation pressure force which simply shifts the resonator's equilibrium position.
The clearest distinction can be made between the following three cases:[1][18] From the linearized Hamiltonian, the so-called linearized quantum Langevin equations, which govern the dynamics of the optomechanical system, can be derived when dissipation and noise terms to the Heisenberg equations of motion are added.
For the mechanical oscillator thermal noise has to be taken into account and is the reason why many experiments are placed in additional cooling environments to lower the ambient temperature.
These first order differential equations can be solved easily when they are rewritten in frequency space (i.e. a Fourier transform is applied).
The equation above is termed the optical-spring effect and may lead to significant frequency shifts in the case of low-frequency oscillators, such as pendulum mirrors.
For a harmonic oscillator, the relation between a frequency shift and a change in the spring constant originates from Hooke's law.
[19] Examples of real optomechanical implementations are: A purpose of studying different designs of the same system is the different parameter regimes that are accessible by different setups and their different potential to be converted into tools of commercial use.
[35] Years before cavity optomechanics gained the status of an independent field of research, many of its techniques were already used in gravitational wave detectors where it is necessary to measure displacements of mirrors on the order of the Planck scale.
Even if these detectors do not address the measurement of quantum effects, they encounter related issues (photon shot noise) and use similar tricks (squeezed coherent states) to enhance the precision.
These systems share very similar Hamiltonians, but have fewer particles (about 10 for ion traps and 105–108 for Bose–Einstein condensates) interacting with the field of light.
