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The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition

Abstract

Spontaneous symmetry breaking plays a key role in our understanding of nature. In relativistic quantum field theory, a broken continuous symmetry leads to the emergence of two types of fundamental excitation: massless Nambu–Goldstone modes and a massive ‘Higgs’ amplitude mode. An excitation of Higgs type is of crucial importance in the standard model of elementary particle physics1, and also appears as a fundamental collective mode in quantum many-body systems2. Whether such a mode exists in low-dimensional systems as a resonance-like feature, or whether it becomes overdamped through coupling to Nambu–Goldstone modes, has been a subject of debate2,3,4,5,6,7,8,9. Here we experimentally find and study a Higgs mode in a two-dimensional neutral superfluid close to a quantum phase transition to a Mott insulating phase. We unambiguously identify the mode by observing the expected reduction in frequency of the onset of spectral response when approaching the transition point. In this regime, our system is described by an effective relativistic field theory with a two-component quantum field2,7, which constitutes a minimal model for spontaneous breaking of a continuous symmetry. Additionally, all microscopic parameters of our system are known from first principles and the resolution of our measurement allows us to detect excited states of the many-body system at the level of individual quasiparticles. This allows for an in-depth study of Higgs excitations that also addresses the consequences of the reduced dimensionality and confinement of the system. Our work constitutes a step towards exploring emergent relativistic models with ultracold atomic gases.

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Figure 1: Illustration of the Higgs mode and experimental sequence.
Figure 2: Softening of the Higgs mode.
Figure 3: Theory of in-trap response.
Figure 4: Scaling of the low-frequency response.
Figure 5: Response between the strongly interacting limit and the weakly interacting limit.

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Acknowledgements

We thank C. Weitenberg and J. F. Sherson for their contribution to the design and construction of the apparatus. We thank D. Podolsky, W. Zwerger, S. Sachdev, R. Sensarma, W. Hofstetter, U. Bissbort, L. Pollet and N. Prokof′ev for discussions. We acknowledge funding by the MPG, DFG, EU (NAMEQUAM, AQUTE, Marie Curie Fellowship to M.C.), JSPS (Postdoctoral Fellowship for Research Abroad to T.F.) and California Institute of Technology (IQIM and Lee A. DuBridge fellowship to D.P.). The computations in this paper were done on the Odyssey cluster supported by the FAS Science Division Research Computing Group at Harvard University.

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Correspondence to Manuel Endres.

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Endres, M., Fukuhara, T., Pekker, D. et al. The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition. Nature 487, 454–458 (2012). https://doi.org/10.1038/nature11255

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