Thermomechanical Two-Mode Squeezing in an Ultrahigh-QMembrane Resonator

Abstract

We realize a nondegenerate parametric amplifier in an ultrahigh Q mechanical membrane resonator and demonstrate two-mode thermomechanical noise squeezing. Our measurements are accurately described by a two-mode model that attributes this nonlinear mechanical interaction to a substrate-mediated process which is dramatically enhanced by the quality factors of the individual modes. This realization of strong multimode nonlinearities in a mechanical platform compatible with quantum-limited optical detection and cooling makes this a powerful system for nonlinear approaches to quantum metrology, transduction between optical and phononic fields and the quantum manipulation of phononic degrees of freedom.

Phonon Cooling by an Optomechanical Heat Pump

“…In that limit they can also be easily mechanically coupled to any other mode of oscillation of the mechanics by forcing an external modulation of the substrate of the mechanical resonator, as was experimentally realized in Ref. [4]. The advantage of this approach is that specific requirements for the optomechanical coupling and frequencies apply only to the two modes (optical and mechanical) comprising the polaritons, with no restrictions on the additional mechanical modes to be cooled.…”

“…The recent demonstration of parametric coupling of mechanical modes deep in the quantum regime offers the opportunity to explore a number of aspects of multimode phononics, such as the generation of nonclassical states of mechanical motion and the development of phonon interferometry [4,5]. While optomechanical sideband cooling [6,7] is typically applied to a single mechanical mode, in such multimode applications, and more generally in the emerging area of nonlinear phononics [8][9][10][11][12][13] there is much interest in simultaneously cooling two or more modes of relatively arbitrary frequencies [14].…”

“…The coupling between the phonon mode 'b' at frequency ω b and a second vibration mode 'c' at frequency ω c can be realized by actuating the substrate at a frequency ω s close to their frequency difference, ω s ≈ ω c − ω b [4]. The resulting coupling is described in a rotating frame at the modulation frequency ω s and in the rotating wave approximation by a "state transfer" Hamiltonian…”

Quantum Backaction Evading Measurement of Collective Mechanical Modes

“…Here, n θ ¼ n X þ cos 2 θ þ n P þ sin 2 θ, assuming the correlations between X þ and P þ are negligible. Note that other tomographic techniques for two-mode mechanical systems have recently been demonstrated [40][41][42].…”

Parametric amplification of light in a cavity with a moving dielectric membrane: Landau-Zener problem for the Maxwell field

“…13 where we find perfect agreement with the general result given in Eq. (69). It is instructive to plot the radiation pressure itself during passage through an avoided crossing, and this is done in Figs.…”