Hybridization of the amplitude mode in a confined fermionic superfluid

Abstract

In phase transitions, spontaneous symmetry breaking results in a non-zero order parameter and two collective excitations: the Goldstone and the amplitude mode. These modes, which define key properties of superconductors and fermionic superfluids, are well-understood in homogeneous systems. However, their behavior under strong confinement remains largely unexplored, particularly when their excitation energy becomes comparable to the imposed discrete level spacing. In this scenario, hybridization between different collective modes is expected to take place. Here, we show how the amplitude mode hybridizes with a spatial mode in a confined fermionic superfluid. Using lattice modulation spectroscopy, we observe the evolution of the mode throughout the entire crossover from the Bardeen-Cooper-Schrieffer (BCS) state to Bose-Einstein condensation (BEC) of molecules. In the BCS regime, the excitation energy is located at twice the pairing gap, then gradually becomes an in-gap excitation in the strongly correlated regime. Further to the BEC limit, the excitation energy approaches twice the level spacing. The spectral weight of this mode vanishes when approaching the superfluid critical temperature. Our experimental results are in excellent agreement with an effective field theory, providing strong evidence that amplitude oscillations hybridize with and eventually transform into breathing oscillations of the order parameter. The strong modification of the excitation spectrum reveals how confinement and finite-size effects impact fundamental modes of symmetry-broken states.