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Atom–atom interactions around the band edge of a photonic crystal waveguide

Research paper by Jonathan D. Hood, Akihisa Goban, Ana Asenjo-Garcia, Mingwu Lu, Su-Peng Yu, Darrick E. Chang, H. J. Kimble

Indexed on: 01 Sep '16Published on: 31 Aug '16Published in: PNAS



Abstract

Tailoring the interactions between quantum emitters and single photons constitutes one of the cornerstones of quantum optics. Coupling a quantum emitter to the band edge of a photonic crystal waveguide (PCW) provides a unique platform for tuning these interactions. In particular, the cross-over from propagating fields <mml:math><mml:mrow><mml:mi mathvariant="italic">E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="italic">x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>∝</mml:mo><mml:msup><mml:mi mathvariant="italic">e</mml:mi><mml:mrow><mml:mo>±</mml:mo><mml:mi mathvariant="italic">i</mml:mi><mml:msub><mml:mi mathvariant="italic">k</mml:mi><mml:mi mathvariant="italic">x</mml:mi></mml:msub><mml:mi mathvariant="italic">x</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>E(x)∝e±ikxx outside the bandgap to localized fields <mml:math><mml:mrow><mml:mi mathvariant="italic">E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="italic">x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>∝</mml:mo><mml:msup><mml:mi mathvariant="italic">e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi mathvariant="normal">κ</mml:mi><mml:mi mathvariant="italic">x</mml:mi></mml:msub><mml:mrow><mml:mo>|</mml:mo><mml:mi mathvariant="italic">x</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:math>E(x)∝e−κx|x| within the bandgap should be accompanied by a transition from largely dissipative atom–atom interactions to a regime where dispersive atom–atom interactions are dominant. Here, we experimentally observe this transition by shifting the band edge frequency of the PCW relative to the <mml:math><mml:mrow><mml:msub><mml:mi mathvariant="normal">D</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math>D1 line of atomic cesium for <mml:math><mml:mrow><mml:mrow><mml:mover accent="true"><mml:mi mathvariant="italic">N</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mn>3.0</mml:mn><mml:mo>±</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:math>N¯=3.0±0.5 atoms trapped along the PCW. Our results are the initial demonstration of this paradigm for coherent atom–atom interactions with low dissipation into the guided mode.