Project description
Photons do not directly interact with each other, but effective interactions between them can be obtained by exploiting the mediation of matter. Perhaps the most common systems in which these effective interactions are achieved are nonlinear crystals. The sophistication of modern experiments, however, allows us to consider the mediation of quantum systems such as single atoms and optomechanical devices, where light is coupled to the vibrational degrees of freedom of a mesoscopic mirror via radiation pressure.
For example, in typical experimental conditions, the interaction between light and a moving mirror (both of them being harmonic oscillators) is approximated well by "bilinear" Hamiltonians, such that when a photon is absorbed (emitted) an elementary excitation (phonon) of the oscillating mirror is created (annihilated) [1]. Truly nonlinear contributions that describe e.g. the conversion between two photons and one phonon are typically negligible. Such non-linear interactions (i.e. non-bilinear Hamiltonians) are, however, of great importance for many applications of photonics. To give a paradigmatic example, it has been shown that purely quadratic Hamiltonians are not sufficient to achieve universal quantum computation: a form of ‘nonlinearity’ is always required [2].
By exposing a quantum system to a periodic control field one can change its properties substantially. For example, if a vibrating mirror or atom is manipulated appropriately, then its interactions with other systems may be modified and controlled to a significant extent. In turn, this may permit us to effectively enhance the non-linear photonic processes mediated by these systems. The goal of the project is indeed to identify optimally designed control sequences that realise robust non-linear interactions between photons.
You would start the project by studying an interaction between two modes of resonator (cavity) mediated by an atom that is modeled by a ground state and two excited states (known as V-system). Each of the atomic transitions is close to resonance with a cavity mode. The goal of this sub-project would be to identify time-dependent control fields for the atom that results in nonlinear effective Hamiltonians for the light fields. While the project will involve some numerical work, this will be complemented and guided by various analytical techniques for the approximate description of time-dependent Hamiltonians.
In the rest of your PhD project you will investigate a variety of quantum systems, and assess their capability of mediating photonic interactions. Optomechanical systems will likely be your object of study, and it is probable that other promising research directions will have arisen during the first few months. Since oscillating mirrors are mesoscopic objects, they typically feature substantial dissipation that can not be neglected. You would thus need to study the quantum control of dissipative systems, which requires a more general theoretical framework as compared to the purely Hamiltonian dynamics discussed earlier [3, 4]. Depending on your preliminary results and inclinations, you may identify a variety of long-term goals for this project. These may include the creation, verification and exploitation of light-matter entanglement, or the use of the achieved non-linear interactions for fundamental tests of quantum mechanics (e.g. the study of macroscopic superpositions and their implications in gravitational collapse models) [3, 4].
This project will involve close collaboration with Dr. Florian Mintert of the Controlled Quantum Dynamics theory group, Imperial College London.