Spontaneous emergence of van der Waals interaction in piezo-resonators - a road to phase coherence at mK temperatures

We present the experimental results on the spontaneous emergence of the phase coherence in the system of oscillating electric dipoles in quartz piezo-resonators caused by the van der Waals interaction. Spontaneous emergence of the phase coherence in these systems is manifested via temperature-dependent, extremely accurate tune-up of their resonance frequencies in 9th order with relative spectral line-width $\delta f_0/f_0$ less than 3.10$^{-8}$ (this number is comparable with that in lasers) along with the very high frequency stability characterized by the low values of the Allan deviations. We also show that the application of an incoherent (noise) excitation signal leads to a spontaneous formation of the phase coherent state, and that the dissipation processes do not affect this phase coherent state (i.e. the resonance frequency of the system). All above-mentioned signatures are typical characteristics for a Bose-Einstein condensate of excitations. Smallness of the relative spectral lime-width in quartz piezo-resonators opens their potential application as alternative time etalons.