Resonating with the generalised uncertainty principle

—by Will Campbell

EQUS researchers have improved constraints on the minimum length scale as postulated by some quantum gravity models, using a cryogenic quartz resonator.

Various theories that attempt to provide a description of gravity at the quantum level propose the introduction of a fundamental minimum length scale, at which space is broken up into discrete segments.  This has immediate implications for the momentum of a harmonic oscillator, as per a perturbation to the Heisenberg uncertainty relations.  Such phenomenology is known as the generalised uncertainty principle.

In our recent work (https://arxiv.org/abs/2304.00688), my supervisor Mike Tobar, colleagues Serge Galliou and Maxim Goryachev, and I utilised a cryogenic quartz mechanical resonator to investigate the momentum perturbation that would be caused by the existence of such a minimum length scale.  By constraining nonlinear perturbations to the resonant frequency of the mechanical modes of the crystal, the minimum length scale may be constrained.

Owing to the precision metrological nature of quartz bulk-acoustic-wave resonators, the low-noise cryogenic environment, and the macroscopic effective mass of the crystal modes, the constraints on minimum length attained improve on previous bounds made by mechanical resonators by three orders in magnitude.

Understanding the theoretical implications of the generalised uncertainty principle in the context of the quartz resonator required some calculation.  We determined that the same degree of frequency perturbations apply to the anti-resonant modes of the device, as well as the resonant modes.

For an experimentalist like me, such calculations and arguments provided an interesting but welcome challenge.  Our work represents a substantial contribution to growing investigations into minimum length, and the implications of quantum mechanics for low-energy macroscopic systems.

Several different crystal materials, such as lithium niobate and teryllium oxide are being investigated to see whether they could provide more stringent results.  We are looking for crystals with low inherent nonlinearities due to higher-order elastic effects.  In addition, we wish to develop a single-phonon mechanical system to explore the quantum ground state and the more theoretically motivated application of the generalised uncertainty principle to single-(quasi)particle quantum systems.

William Campbell is a PhD Student at The University of Western Australia, working under the supervision of Chief Investigator Prof. Michael Tobar on mechanical resonators for fundamental physics.