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arXiv:1809.08774 · Physical Review A

Collective excitation profiles and the dynamics of photonic condensates

Benjamin T. Walker, Henry J. Hesten, Robert A. Nyman, Florian Mintert

Published Nov 13, 2019• 8 citations
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Abstract

Photonic condensates are complex systems exhibiting phase transitions due to the interaction with their molecular environment. Given the macroscopic number of molecules that form a reservoir of excitations, numerical simulations are expensive, even for systems with few cavity modes. We present a systematic construction of molecular excitation profiles with a clear hierarchical ordering, such that only modes in the lowest order in the hierarchy directly affect the cavity photon dynamics. In addition to a substantial gain in computational efficiency for simulations of photon dynamics, the explicit spatial shape of the mode profiles offers a clear physical insight into the competition among the cavity modes for access to molecular excitations.

DOI
10.1103/physreva.100.053828

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Photonic condensates are complex systems exhibiting phase transitions due to the interaction with their molecular environment. Given the macroscopic number of molecules that form a reservoir of excitations, numerical simulations are expensive, even for systems with few cavity modes. We present a systematic construction of molecular excitation profiles with a clear hierarchical ordering, such that only modes in the lowest order in the hierarchy directly affect the cavity photon dynamics. In addition to a substantial gain in computational efficiency for simulations of photon dynamics, the explicit spatial shape of the mode profiles offers a clear physical insight into the competition among the cavity modes for access to molecular excitations.
We investigate the response of a photonic gas interacting with a reservoir of pumped dye molecules to quenches in the pump power. In addition to the expected dramatic critical slowing down of the equilibration time around phase transitions, we find extremely slow equilibration even far away from phase transitions. This noncritical slowing down can be accounted for quantitatively by fierce competition among cavity modes for access to the molecular environment, and we provide a quantitative explanation for this noncritical slowing down.
The photonic Bose-Einstein condensate is a recently observed collective ground state of a coupled light-matter system. We describe this quantum state based on macroscopic quantum electrodynamics in dispersing and absorbing environments. To model the coupled photon-dye dynamics, we derive a master equation using a nested-open-quantum-systems approach yielding all parameters essential to describe the condensation process. This approach allows us to describe photon condensates of arbitrary shapes because all geometry-dependent decay constants can be expressed in terms of the Green's tensor. In particular, we obtain the cavity mode absorption and emission rates of the dye molecules.
Lloyd C. L. Hollenberg Centre for Quantum Computer Technology, School of Physics, University of Melbourne, VIC 3010, Australia Condensed matter physics studies complex systems of interacting particles to understand macroscopic and emergent phenomena of those systems. In general, sample perfection and homogeneity are critical to the observation of most many-body effects. Conversely, quantum optics has conventionally looked at interactions between some of the most perfect and isolated systems available, for example monochromatic optical fields and single atoms. The perfection and control of large ensembles of strongly interacting particles is extending to levels of uniformity never before reached, although often with only global control and readout, while quantum optical techniques are now increasingly allowing the treatment of systems of increasing complexity, but with the added advantage of local control and readout. Coupled cavity systems are ideally placed to straddle this gap of scales, i.e., local control of small systems vs global control of large systems, to give insight into both fields. Systems of interacting photons in coupled cavities have been predicted to show quantum phase transitions (QPTs), and may be important as quantum simulators of complex dynamics. But the nature of the interactions is subtly different from more conventional condensed matter models. Here we describe the emergence of Hubbard-like dynamics in coupled cavity systems spanning finite to infinite structures, the nature of the excitations involved, how these coupled cavity systems can be understood as the optical analog of a solid-state system, and prospects for structures that can be fabricated to demonstrate the required interactions.
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Coupling between quantum emitters and modes of light is foundational to studies of quantum systems. Coherent interactions between matter and light have greatly advanced the development of quantum technologies. When an ensemble of atoms interacts with light that is confined within a cavity---a resonator for photons---light also mediates atom-atom interactions, leading to collective phenomena that cannot be extrapolated from microscopic behaviors. Understanding how interactions among quantum particles lead to macroscopic phenomena, such as phase transitions and breaking of symmetries, remains a challenge in modern physics. In this dissertation, I present results addressing this challenge in the context of mesoscopic arrays of optical-tweezer-trapped atoms interfaced with a high-finesse optical cavity. In particular, the physics we investigate arises from the collective scattering of light. Utilizing the ability to place atoms with nanometer-scale precision, we engineer superradiant and subradiant states, where control over interference of the emission from multiple atoms leads to collectively enhanced or suppressed amounts of scattered light. Building on this work, we investigate the emergence of optomechanical self-organization, mediated by superradiance in the cavity electromagnetic field. By coupling atoms to the same cavity mode, the atoms exert forces on one another through the exchange of photons, leading them to autonomously order themselves spatially. We characterize mesoscopic fluctuations and their effect on symmetry-breaking dynamics associated with self-organization. Finally, we extend this framework to theoretically investigate how the phase of the atom-cavity coupling can be altered to generate higher symmetries. Our analysis reveals first-order phase transitions and instabilities induced by non-reciprocal forces. Altogether, this work establishes a path towards realizing mesoscopic systems of complex phases of matter in cavity quantum electrodynamics with unprecedented programmability.