Emergent and broken symmetries of atomic self-organization arising from Gouy phase shifts in multimode cavity QED

Yudan Guo, Varun D. Vaidya, Ronen M. Kroeze, Rhiannon A. Lunney, Benjamin L. Lev, Jonathan Keeling

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Optical cavities can induce photon-mediated interactions among intracavity-trapped atoms. Multimode cavities provide the ability to tune the form of these interactions, e.g., by inducing a nonlocal sign-changing term to the interaction. By accounting for the Gouy phase shifts of the modes in a nearly degenerate, confocal, Fabry-Pérot cavity, we provide a theoretical description of this interaction, along with additional experimental confirmation to complement that presented in the companion paper [Y. Guo et al., Phys. Rev. Lett. 122, 193601 (2019)]. Furthermore, we show that this interaction should be written in terms of a complex order parameter, allowing for a U(1) symmetry to emerge. This symmetry corresponds to the phase of the atomic density wave arising from self-organization when the cavity is transversely pumped above a critical threshold power. We show theoretically and experimentally how this phase depends on the position of the Bose-Einstein condensate within the cavity and discuss mechanisms that break the U(1) symmetry and lock this phase. We then consider alternative Fabry-Pérot multimode cavity geometries (i.e., beyond the confocal) and schemes with more than one pump laser and show that these provide additional capabilities for tuning the cavity-meditated interaction among atoms, including the ability to restore the U(1) symmetry despite the presence of symmetry-breaking effects. These photon-mediated interactions may be exploited for realizing quantum liquid crystalline states and spin glasses using multimode optical cavities.
Original languageEnglish
Article number053818
Number of pages15
JournalPhysical Review. A, Atomic, molecular, and optical physics
Issue number5
Early online date14 May 2019
Publication statusPublished - May 2019


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