Ga(Al)As semiconductor microcavities provide a versatile platform to study strong light-matter interactions and their coupling to confined GHz-frequency acoustic phonons. In these systems, exciton-polaritons—hybrid quasiparticles resulting from the strong coupling between excitons and cavity photons—combine pronounced nonlinearities with efficient coupling to bulk acoustic waves (BAWs) confined within the microcavity. Under non-resonant continuous-wave excitation, polaritons can undergo Bose-Einstein condensation above a threshold pump power, forming spin-polarized condensates with a well-defined pseudospin arising from the interplay between light polarization and exciton spin. We recently demonstrated that, in the presence of a trapping potential, the condensate pseudospin can spontaneously enter a regime of self-sustained precession, breaking continuous time-translation symmetry—thus forming a continuous time crystal (CTC) [1]. This self-induced dynamic can resonantly drive the mechanical modes of the system, generating coherent vibrations that feed back into the condensate and lead to frequency locking of the CTC [1, 2, 3].

Here we show that introducing a resonant optical drive enables coherent control over the polariton modes and their pseudospin precession via frequency pulling and injection locking. This allows for precise tuning of the condensate’s energy and phase, and even full suppression of the precessional dynamic. Furthermore, when the resonant laser is red- or blue-detuned from the polariton modes by an amount equal to the phonon frequency, mechanical vibrations can be externally driven and controlled. This interaction leads to the emergence of complex nonlinear trajectories in polarization space (on the Poincaré sphere), including period doubling with respect to the phonon frequency, as also captured by our theoretical model. These mechanisms open new avenues for manipulating time-crystalline phases, tailoring inter-site coupling in polariton lattices, and implementing novel schemes for non-reciprocal or topological transport.

[1] I. Carraro-Haddad, D. L. Chafatinos, A. S. Kuznetsov, et al. Solid-state continuous time crystal in a polariton condensate with a built-in mechanical clock. Science 384, 995-1000 (2024).
[2] D.L. Chafatinos, A.S. Kuznetsov, A.A. Reynoso, et al. Asynchronous locking in metamaterials of fluids of light and sound. Nat Commun 14, 3485 (2023).
[3] I. A. Ramos-Pérez, I. Carraro-Haddad, F. Fainstein, et al. Theory of optomechanical locking in driven-dissipative coupled polariton condensates. Phys. Rev. B 109, 165305 (2024)