Selective Control and Imaging of Higgs and Goldstone Modes with a Quantum Simulator

We realize the mesoscopic Bose-Hubbard model at unit-filling on a two-dimensional array of transmon qubits and selectively excite collective modes associated with amplitude or phase fluctuations of the superfluid order parameter. We identify these modes respectively as the Higgs and Goldstone modes using complementary local observables, extracted from measuring the number of particles on each site. Modulation of the coupling between sites excites the Higgs mode, which we detect via the density of doubly occupied sites. In contrast, modulation of the local chemical potential with an appropriately chosen spatial profile excites the lowest-frequency Goldstone mode, which we detect via changes in the local density. The two modes have different symmetries and do not couple to one another. By varying the system geometry, we characterize the impact of finite system size on the evolution of both modes. In the thermodynamic limit, decay into a continuum of lower-energy excitations can obscure the Higgs response. In our mesoscopic system, however, the finite system size leads to spectral gaps and allows us to detect the Higgs mode as a coherent, long-lived excitation. Our work demonstrates how finite quantum simulators can isolate and probe physical phenomena that become difficult to resolve in the thermodynamic, large-scale limit.