Emergent self-organization and crystallization phenomena are ubiquitous mechanisms in nature, and understanding their foundations could disrupt several research domains. Ultracold atom systems are routinely used as simulators for the study of phase transitions, and spontaneous symmetry breaking in different configurations; the most widely adopted couples a Bose-condensed atomic sample to a single electromagnetic mode of a stationary wave cavity, and it allowed to observe the Dicke phase transition [Bau2010] and to cool atoms below the recoil limit [Wol2012] among other. In such configuration, the boundary conditions imposed by the retroreflection at the cavity mirrors set stringent constraints on the system, e.g. imposing specific discrete phases for the emerging atomic and light structures, in the end limiting the potential reach of the findings.
In the last years a new class of experiments has been implemented, to observe ordering phenomena in the presence of less constraints imposed by the system; to this aim, ultracold atoms have been coupled to traveling wave cavities [Kli2006,Nai2018] –where no boundary conditions exist at the mirrors–, to degenerate cavities [Vai2018] –where the atom can choose with which mode to interact with–, or held in optical lattices [Vie2019] –where the light frequency and phase is externally controlled–. The result is the possibility to study order emergence in a broader context, where the atoms interact not with only a single e.m. mode of a cavity, but with a discrete number of them.
In this context, trapping atoms in the quasi 1D configuration represented by the hollow core of a photonic fiber would open the possibility to let the atom interact with a continuum of e.m. modes, a new regime studied only theoretically in the group of Prof. H. Ritsch in Innsbruck, and where the transition from homogeneous to periodic order consists in a crystallization of both light and ultracold atoms breaking a continuous translational symmetry. The scheme would allow the observation of supersolid-like components, and possibly of quasi-crystals.
CRYST³ (crystal of light, crystal of matter both in a photonic crystal fiber) is a project that seeks to build on state-of-the-art research at the frontier of quantum many-body physics of atoms and photons, fiber photonics and ultracold atoms. The objective is to cool (at temperatures of the order of the microkelvin) and load Rubidium 87 atoms into a hollow core photonic crystal fiber (HCPCF), using a protocol relying on dark-states and gray molasses in the presence of a large differential light shift [Nai2020], then observe and characterize the emergence of spontaneous crystallization of the atoms and the photons, caused by scattering of light by long-range interactions between the atoms mediated by the light field and at the same time by the scattering of light in a collective way that results in a superradiant emission, breaking the translation symmetry. The absence of boundaries in the direction of the fiber enables us to use the continuum of electromagnetic modes of the light in free space, unlike a cavity that sets a specific mode. This promises the rise of new technologies and numerous research lines.
[Bau2010]K. Baumann et al., Nature 464, 1301 (2010)
[Wol2012]M. Wolke et al., Science 337, 75 (2012)
[Vai2018]V. Vaidya et al., Phys. Rev. X 8, 011002 (2018)
[Vie2019]K. Viebahn et al., Phys. Rev. Lett. 122, 110404 (2019)
[Nai2020]D.S. Naiket al., Phys. Rev. Res. 2, 013212 (2020)
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