Joel Corney

Controlled chaos in ultra cold matter systems

Utracold atoms in optical lattices provide an elegant, reconfigurable arena for exploring many-body quantum physics in a precisely controlled way. In particular they can be used to probe how the features of dynamical chaos (a classical phenomenon of nonlinear systems) survive in the quantum regime. This project will map out the phase-space of novel lattice systems (with enough degrees of freedom to show chaos in the classical limit, yet small enough such that a quantum description is tractable) and map chaotic features onto the Wigner distribution of the corresponding quantum state. A key goal will be to understand the role of apparent chaotic behaviour in the thermalisation of isolated quantum systems. The project will involve a combination of analytic and computational work. Prior computational experience (in any language) would be an advantage.

Quantum Squeezing via Self-Induced Transparency

Optical fibres offer a versatile medium for squeezing the quantum state of light for application in quantum information and communication, and precision metrology. However, the amount and quality of squeezing is limited by interactions with vibrational modes in the silica. A promising alternative is microstructured fibre with a gas-filled hollow core [1]. Here a strong nonlinear response can be provided via self-induced trans- parency, wherein an intense pulse of light is coherently absorbed and then emitted without loss, resulting in the kind of intensity-dependent phase shift required for squeezing.

In this project, you will develop and implement a realistic computational model of resonant atom-light interaction in this system, including coupling to relevant reservoirs, to make accurate predictions of the amount of squeezing possible. A key aspect of the work is to adapt the quantum noise techniques previously used to successfully predict squeezing in dispersive media [2] to resonant interactions. The results will play a vital role in guiding current and future experiments in quantum squeezing with microstruc- tured fibre.

[1] Ulrich Vogl, Florian Sedlmeir, Nicolas Y Joly, Christoph Marquardt, and Gerd Leuchs. Generation of non-classical light via self-induced transparency in mercury- filled hollow core photonic crystal fibers. In Frontiers in Optics 2016, 2016.

[2] Joel F Corney, Joel Heersink, Ruifang Dong, Vincent Josse, Peter D Drummond, Gerd Leuchs, and Ulrik L Andersen. Simulations and experiments on polarization squeezing in optical fiber. Phys. Rev. A, 78(2):23831, 2008.

Photons in the Fermi sea

Novel “epsilon-near-zero” materials, where the electric permittivity vanishes at certain wavelengths, have recently been demonstrated to have very high nonlinear optical response [1], i.e. these materials enable photons effectively to interact with each other. These interactions could be be used to manipulate the intrinsic quantum fluctuations in the light - an effect known as quantum squeezing. Quantum squeezing has applications in precision measurement, quantum information and quantum communication.

This project will analyse the interaction between photons and degenerate electrons at the quantum level (existing theory so far has just focussed on the classical response), to produce quantitative predictions of the quantum squeezing available in such materials.

The project will involve a combination of analytic and computational work. Prior computational experience (in any language) would be an advantage. During the project you will have the opportunity to learn the basics of stochastic calculus and how to implement stochastic processes numerically.

[1] Alam, M. Zahirul, Sebastian A. Schulz, Jeremy Upham, Israel De Leon, and Robert W. Boyd. “Large Optical Nonlinearity of Nanoantennas Coupled to an Epsilon-near-Zero Material” Nature Photonics 12, no. 2 (2018): 79–83. https://doi.org/10.1038/s41566-017-0089-9

Squeezing in whispering-gallery-mode resonators

Nonlinear effects in an optical material can be enhanced through a long interaction length (like an optical fibre) or by use of an optical cavity/resonator (whereby each photon is reflected back through the medium many times before emerging through the mirror).

Optical resonators formed from microspheres or microdisks support high-quality whispering gallery modes, in which the incoupled light circulates many times in a highly confined space. This project will investigate the use of whispering-gallery-modes for quantum squeezing, calculating the squeezing spectrum that different configurations can generate.

The project will involve a combination of analytic and computational work. Prior computational experience (in any language) would be an advantage. During the project you will have the opportunity to learn the basics of stochastic calculus and how to implement stochastic processes numerically.