Prediction of Ultra-Narrow Higgs Resonance in Magnon Bose-Condensates

Abstract

Higgs resonance modes in condensed matter systems are generally broad; meaning large decay widths or short relaxation times. This common feature has obscured and limited their observation to a select few systems. Contrary to this, the present work predicts that Higgs resonances in magnetic field induced, three-dimensional magnon Bose-condensates have vanishingly small decay widths. Specifically for parameters relating to TlCuCl3, we find an energy (∆H ) to width (ΓH ) ratio ∆H /ΓH ∼ 500, making this the narrowest predicted Higgs mode in a condensed matter system, some two orders of magnitude 'narrower' than the sharpest condensed matter Higgs observed so far.PACS numbers: 64.70. Tg, 75.40.Gb, 75.10.Jm, 74.20.De The Higgs mechanism, and associated Higgs modes, play a central role in modern physics. The mechanism is responsible for the mass generation of all observed particles in nature, and is the only known, universal mechanism to do so. Higgs modes are a generic property of systems with a spontaneously broken continuous symmetry. This includes prominent condensed matter phenomena; superconductivity, Bose condensation (BEC) and superfluidity, quantum magnetism, etc., as well as the Electroweak vacuum. Due to the ubiquity and importance of Higgs modes across many branches of physics, their detection has been an exciting, yet difficult, challenge. Notably, the discovery of the Electroweak Higgs boson [1, 2] meets both of these descriptions. Also attracting a great deal of attention, and proving to host their own difficulties, are the Higgs modes of condensed matter systems. They have been observed in the following settings; the charge density wave superconductor NbSe 2 (1981) [3,4], three dimensional quantum antiferromagnet (AFM) TlCuCl 3 (2008) [5], superfluid 87 Rb atoms in an optical lattice (2012) [6], superconducting NbN (2013) [7,8], and two dimensional quantum AFM Ca 2 RuO 4 (2017) [9]. Each setting offers unique insights into the dynamics of Higgs modes and, in particular, the role played by symmetry, dimensionality, as well as the coupling to different degrees of freedom. Such factors are seen to have a dramatic influence on the dynamical properties and, ultimately, the observability of the Higgs modes.