Multi-Modes Systems in Quantum Optics

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• Ben Yuen (Metamaterials Group, University of Birmingham)
• Thursday 19 March 2020, 13:15-14:45
• Theory Library.

If you have a question about this talk, please contact Dr Hannah Price.

A dipole oscillating in an electromagnetic field is ubiquitous in modern physics. Physically and theoretically this system is beautifully simple. Despite this simplicity, it is striking that we are yet to discover an exact analytic solution to Rabi’s model which describes it. Only its approximated form – the Jaynes—Cummings model – has been solved exactly. Furthermore, we must ask what happens beyond the very simplest of situations to understand the real world. The world is full of colour. What happens when the light with which atoms interact is polychromatic?

I will present promising new methods for tackling the polychromatic Rabi and Jaynes-Cummings models — where a dipole is driven by a field with multiple frequency modes [1-3]. These simple systems have a surprisingly rich range of dynamics, exhibiting collapse, revivals and signatures of chaos. I will show how these methods can be applied when the field is considered quantum or classical to produce accurate analytic descriptions of the time evolution of the system. I will indicate how considering the single frequency Rabi model within a multi-frequency formalism allows progress to be made on finding an exact analytic solution to this 80 year old problem. Furthermore, these methods can be connected through the Lie algebra of the system Hamiltonian. The Lie algebra, which is not closed, gives insight into the difficulty of finding exact solutions. This motivates a search for similar models where the Lie algebra is closed, which can in principle be solved, such as the Tavis-Cummings model and a network of coupled cavities. I show that even in this case the dynamics can resemble those of an open quantum system.

[1] Yuen, B. (2018). Quantum Mechanics in Technicolor; Analytic Expressions for a Spin-Half Particle Driven by Polychromatic Light. arXiv preprint arXiv:1805.05922.

[2] Yuen, B., & Foot, C. J. (2019). Multi-Frequency Atom-Photon Interactions. arXiv preprint arXiv:1907.01469.

[3] Luksch, K., Bentine, E., Barker, A. J., Sunami, S., Harte, T. L., Yuen, B., & Foot, C. J. (2018). Probing multiple-frequency atom-photon interactions with ultracold atoms. arXiv preprint arXiv:1812.05545.

This talk is part of the Theoretical Physics Seminars series.

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