Quantum optomechanics: radiation pressure at the single photon level

Project description

Optomechanics investigates the interaction of quantised light (photons) with microscopic vibrating objects such as mirrors, dielectric membranes or levitated nanoparticles [1]. Such interaction takes place via radiation pressure, a phenomenon initially predicted by Johannes Kepler in 1619 in the context of astronomy, and nowadays observed even at the single-photon level. Among other applications, optomechanics embodies a promising experimental platform to probe quantum effects in massive objects, and hence investigate the classical/quantum boundary.

The student will initially review a widely used effective Hamiltonian for cavity optomechanics (the "linear model") [2], which is analytically solvable and predicts the generation of nonclassical states of light as well as light-matter entanglement. Subsequently, he/she will delve into the more rigorous canonical quantization of an optomechanical system [3], and assess the crucial limitations of the more basic model. Unfortunately, the more rigorous "mircoscopic" Hamiltonian is currently intractable both analytically and numerically, so that novel approximation techniques will need to be developed to improve the basic model while retaining computability. An example of a preliminary study in this direction can be found in Ref. [4].

The broad objective of the project will be to develop new optomechanical models that strike an optimal balance between reliability and tractability. These will then be used to verify and refine a number of theoretical predictions that have been made in the literature, tipically based on the linear model alone. Such predictions pertain a variety of applications of optomechanical systems, ranging from quantum information science to gravitational wave detection and Planck-scale physics [5]. At the same time, an improved theoretical description will give us an opportunity to explore new physical effects and applications of these systems.

A futher ambitious goal of the project will be to develop a rigorous open quantum system model for optomechanics, improving the phenomenological approaches that are currently used in the literature.

Depending on the inclinations of the student, more emphasis can be put on either analytical or numerical work (e.g. via Matlab, Python or Mathematica).