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arXiv:1411.5443 · New Journal of Physics

An adjustable-length cavity and Bose–Einstein condensate apparatus for multimode cavity QED

Alicia J. Kollár, Alexander T. Papageorge, Kristian Baumann, Michael A. Armen, Benjamin Lev

Published Apr 13, 2015• 66 citations
arXivHTMLPDF

Abstract

We present a novel cavity QED system in which a Bose–Einstein condensate (BEC) is trapped within a high-finesse optical cavity whose length may be adjusted to access both single-mode and multimode configurations. We demonstrate the coupling of an atomic ensemble to the cavity in both configurations and measure that the single-atom, -mode cooperativity exceeds unity. The atoms are confined either within an intracavity far-off-resonance optical dipole trap or a crossed optical dipole trap via transversely oriented lasers. Multimode cavity QED provides fully emergent and dynamical optical lattices for intracavity BECs, in that the process of atomic self-organization may be described as a continuous symmetry breaking phase transition resulting in the emergence of a compliant lattice with phonon-like excitations. Such systems will enable explorations of quantum soft matter, including superfluid smectics, superfluid glasses, and spin glasses as well as neuromorphic associative memory.

DOI
10.1088/1367-2630/17/4/043012

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We present a novel cavity QED system in which a Bose–Einstein condensate (BEC) is trapped within a high-finesse optical cavity whose length may be adjusted to access both single-mode and multimode configurations. We demonstrate the coupling of an atomic ensemble to the cavity in both configurations and measure that the single-atom, -mode cooperativity exceeds unity. The atoms are confined either within an intracavity far-off-resonance optical dipole trap or a crossed optical dipole trap via transversely oriented lasers. Multimode cavity QED provides fully emergent and dynamical optical lattices for intracavity BECs, in that the process of atomic self-organization may be described as a continuous symmetry breaking phase transition resulting in the emergence of a compliant lattice with phonon-like excitations. Such systems will enable explorations of quantum soft matter, including superfluid smectics, superfluid glasses, and spin glasses as well as neuromorphic associative memory.
Cavity quantum electrodynamics (QED) with cooperativity far greater than unity enables high-fidelity quantum sensing and information processing.The high-cooperativity regime is often reached through the use of short single-mode resonators.More complicated multimode resonators, such as the near-confocal optical Fabry-Pérot cavity, can provide intracavity atomic imaging in addition to high cooperativity.This capability has recently proved important for exploring quantum many-body physics in the driven-dissipative setting.In this work, we show that a confocal-cavity-QED microscope can realize cooperativity in excess of 110.This cooperativity is on par with the very best single-mode cavities (which are far shorter) and 21 times greater than single-mode resonators of similar length and mirror radii.The 1.7-µm imaging resolution is naturally identical to the photon-mediated interaction range.We measure these quantities by determining the threshold of cavity superradiance when small optically tweezed Bose-Einstein condensates are pumped at various intracavity locations.Transmission measurements of an ex situ cavity corroborate these results.We provide a theoretical description that shows how cooperativity enhancement arises from the dispersive coupling to the atoms of many near-degenerate modes.
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 have used a fiber Fabry-Perot cavity on an atom chip to obtain strong, extremely stable atom-cavity coupling for single atoms and Bose-Einstein condensates trapped inside the cavity. The coherent atom-cavity coupling parameter, g0/2pi ~ 209 MHz, is larger than both cavity decay, kappa/2pi ~ 53 MHz and spontaneous emission gamma/2pi ~ 3 MHz. Due to the small mode volume, these values, well inside the strong coupling regime of cavity QED, are realized with a cavity finesse F ~ 36000, which is a moderate value compared to usual strong-coupling cavity QED experiments. The cavity also achieves a very high cooperativity parameter, C=g02/2kappagamma ~ 130.The use of trapped Bose-Einstein condensates (BECs) is a fundamentally new situation for cavity QED, which should enable a new class of experiments, where atoms that share a well-defined internal and external quantum state collectively interact with a quantized mode of the cavity. Besides, as the spatial extension of the BEC assumes the fundamental limit that can be attained for an atom cloud - much smaller than an optical wavelength in our case - an extremely strong, stable and uniform coupling to the cavity mode is achieved. This makes the system interesting for applications such as quantum memories. For single atoms, our combination of high resonator cooperativity with extreme positioning precision enables qubit detection with near-unit efficiency. This realizes a long-awaited milestone for quantum information processing on atom chips.
We present and characterize an experimental system in which we achieve the integration of an ultrahigh finesse optical cavity with a Bose-Einstein condensate (BEC). The conceptually novel design of the apparatus for the production of BECs features nested vacuum chambers and an in vacuo magnetic transport configuration. It grants large scale spatial access to the BEC for samples and probes via a modular and exchangeable “science platform.” We are able to produce Rb87 condensates of 5×106 atoms and to output couple continuous atom lasers. The cavity is mounted on the science platform on top of a vibration isolation system. The optical cavity works in the strong coupling regime of cavity quantum electrodynamics and serves as a quantum optical detector for single atoms. This system enables us to study atom optics on a single particle level and to further develop the field of quantum atom optics. We describe the technological modules and the operation of the combined BEC cavity apparatus. Its performance is characterized by single atom detection measurements for thermal and quantum degenerate atomic beams. The atom laser provides a fast and controllable supply of atoms coupling with the cavity mode and allows for an efficient study of atom field interactions in the strong coupling regime. Moreover, the high detection efficiency for quantum degenerate atoms distinguishes the cavity as a sensitive and weakly invasive probe for cold atomic clouds.
Ultracold atoms trapped in laser-generated optical lattices serve as a versatile platform for quantum simulations. However, as these lattices are infinitely stiff, they do not allow to emulate phonon degrees of freedom. This restriction can be lifted in emerged optical lattices inside multimode cavities. Motivated by recent experimental progress in multimode cavity QED, we propose a scheme to implement and study supersolid and droplet states with phononlike lattice excitations by coupling a Bose gas to many longitudinal modes of a ring cavity. The interplay between contact collisional and tunable-range cavity-mediated interactions leads to a rich phase diagram, which includes elastic supersolid as well as insulating droplet phases exhibiting roton-type mode softening for a continuous range of momenta across the superradiant phase transition. The nontrivial dynamic response of the system to a local density perturbation further proves the existence of phononlike modes.