Direct observation of the quantum fluctuation driven amplitude mode in a microcavity polariton condensate

Abstract

The Higgs amplitude mode is a collective excitation studied and observed in a broad class of matter, including superconductors, charge density waves, antiferromagnets, 3 He p-wave superfluid, and ultracold atomic condensates. In all the observations reported thus far, the amplitude mode was excited by perturbing the condensate out of equilibrium. Studying an exciton-polariton condensate, here we report the first observation of this mode purely driven by intrinsic quantum fluctuations without such perturbations. By using an ultrahigh quality microcavity and a Raman spectrometer to maximally reject photoluminescence from the condensate, we observe weak but distinct photoluminescence at energies below the condensate emission. We identify this as the so-called ghost branches of the amplitude mode arising from quantum depletion of the condensate into this mode.These energies, as well as the overall structure of the photoluminescence spectra, are in good agreement with our theoretical analysis. I. INTRODUCTIONSpontaneous breaking of a continuous symmetry occurs in various branches of modern physics, such as cosmology [1,2], particle physics [3-5], and a variety of condensed matter systems [6][7][8]. In this broken phase, in addition to the phase (Goldstone) mode [9,10], a collective amplitude (Higgs) excitation [11,12] emerges ubiquitously in various condensates. Such a Higgs amplitude mode has been observed in many condensed matter systems: superconductors [13,14], charge density waves [15], antiferromagnets [16], p-wave superfluids of 3 He [17], ultracold Fermi superfluid in the Bardeen-Cooper-Schrieffer-Bose Einstein Condensate (BCS-BEC) crossover region [18], bosons loaded in an optical lattice [19], and a supersolid realized in two crossed optical cavities [20]. In all the above observations, it was essential to drive the condensate out of equilibrium to excite and detect this mode.However, these collective modes are intrinsically driven by quantum fluctuations without such external perturbations, even in the ground state where no thermal fluctuations exist. Being in a state of definite phase, interactions in the condensate enable processes that do not conserve the number of condensed particles. As a result, quantum fluctuations coherently expel the particles out of the condensate. This phenomenon, known as quantum depletion, was formulated by Bogoliubov [21] and was recently confirmed in an atomic BEC [22] and an exciton-polariton BEC experiment [23].The expelled particles occupy the collective modes of the condensate. The spectral signature of this fascinating property is a set of "ghost branches" (GB), the time-reversed partners of the normal collective modes (normal branch or NB) which appear at energies below the ground state. Since the quantum mechanical Bose statistics are crucial in occupying the GB, the observation of these branches provides an unambiguous signature of quantum depletion. Although

Bogoliubov excitations of a polariton condensate in dynamical equilibrium with an incoherent reservoir

“…However, these predictions have yet to be confirmed experimentally, and indeed it has recently been shown that any such modifications occur at momenta that are too low to be directly resolved in high-quality microcavities [34]. Furthermore, while the observed shape of the Bogoliubov spectrum in experiments has so far appeared to be consistent with conventional Bogoliubov theory [34][35][36][37][38][39][40][41][42][43], there are notable unexplained observations such as the recently measured occupations of the excitation branches [41].…”

Leaky exciton condensates in transition metal dichalcogenide moiré bilayers

“…Condensate depletion by interactions has recently gained significant experimental attention [72][73][74][75][76]. Relatedly, BdG modes are used to renormalize phonon-assisted photoluminescence line shapes, e.g.…”