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Bulletin of the American Physical Society

Photons as phonons: Flexible crystals of atoms and light in multimode cavities

Sarang Gopalakrishnan, D. Zeb Rocklin, Benjamin Lev, Paul M. Goldbart

Published Mar 19, 2010• 0 citations
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The self-organization of a Bose-Einstein condensate (BEC) in a transversely pumped optical cavity is a process akin to crystallization: when pumped by a laser of sufficient intensity, the coupled matter and light fields evolve, spontaneously, into a spatially modulated pattern, or crystal, whose lattice structure is dictated by the geometry of the cavity. In cavities having multiple degenerate modes, the quasicontinuum of possible lattice arrangements, and the continuous symmetry breaking associated with the adoption of a particular lattice arrangement, give rise to phenomena such as phonons, defects, and frustration, which have hitherto been unexplored in ultracold atomic settings involving neutral atoms. The present work develops a nonequilibrium field-theoretic approach to explore the self-organization of a BEC in a pumped, lossy optical cavity. We find that the transition is well described, in the regime of primary interest, by an effective equilibrium theory. At nonzero temperatures, the self-organization occurs via a fluctuation-driven first-order phase transition of the Brazovskii class; this transition persists to zero temperature and crosses over into a quantum phase transition. We make further use of our field-theoretic description to investigate the role of nonequilibrium fluctuations in the self-organization transition, as well as to explore the nucleation of ordered-phase droplets, the nature and energetics of topological defects, supersolidity in the ordered phase, and the possibility of frustration controlled by the cavity geometry. In addition, we discuss the range of experimental parameters for which we expect the phenomena described here to be observable, along with possible schemes for detecting ordering and fluctuations via either atomic correlations or the correlations of the light emitted from the cavity.
We design and implement an atomic frequency comb quantum memory for 793-nm wavelength photons using a monolithic cavity based on a thulium- (Tm-) doped Y3Al5O12{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}Y3​Al5​O12​ crystal. Approximate impedance matching results in the absorption of 90% of input photons and a memory efficiency of $(27.5\ifmmode\pm\else\textpm\fi{}2.7)%$ over a 500-MHz bandwidth. The cavity enhancement leads to a significant improvement over the previous efficiency in Tm-doped crystals using a quantum memory protocol. In turn, this allows us to store and recall quantum states of light in such a memory. Our results demonstrate progress toward efficient and faithful storage of single-photon qubits with a large time-bandwidth product and multimode capacity for quantum networking.