Energy-level attraction and heating-resistant cooling of mechanical resonators with exceptional points

Abstract

We study the energy-level evolution and ground-state cooling of mechanical resonators under a synthetic phononic gauge field. The tunable gauge phase is mediated by the phase difference between the PT -and anti-PT -symmetric mechanical couplings in a multimode optomechanical system. The transmission spectrum then exhibits an asymmetric Fano line shape or a double optomechanically induced transparency by modulating the gauge phase. Moreover, the eigenvalues will collapse and become degenerate, although the mechanical coupling is continuously increased. Such counterintuitive energy-level attraction, instead of anticrossing, is attributed to destructive interferences between PT -and anti-PT -symmetric couplings. We find that the energy-level attraction, as well as the accompanying exceptional points (EPs), can be clearly observed in the cavity output power spectrum where the mechanical eigenvalues correspond to distinct peaks. For mechanical cooling, the average phonon occupation number is minimized at the EPs. Especially, phonon transport becomes nonreciprocal and even ideally unidirectional at the EPs. Finally, we propose a heating-resistant ground-state cooling based on the nonreciprocal phonon transport, which is mediated by the gauge field. Towards the quantum regime of macroscopic mechanical resonators, most optomechanical systems are ultimately limited by their intrinsic cavity or mechanical heating. Our work shows that the thermal energy transfer can be blocked by tuning the gauge phase, which suggests a promising route to bypass the heating limitations.

Chaos control and exceptional point engineering via dissipative optomechanical coupling

“…This condition on σ can be fulfilled in our proposal by tuning the driving field instead of η, which is not easily tunable like the driving field. The parameters for our numerical simulations are from the realistic optomechanical setup implemented in [31], and the parameter η lies within the range 0  η  10 −5 which is in agreement with the experimental values derived above. Figure 2 shows the agreement between the numerical stability and the analytical investigation by the EP.…”

“…Moreover, under the condition κ ? (G, γ j ), which is satisfied in our analysis, the cavity field can be eliminated adiabatically, and this leads us to the effective dynamical system for the two mechanical resonators [31]:…”

Static synthetic gauge field control of double optomechanically induced transparency in a closed-contour interaction scheme

“…Note added. Recently, we became aware of the work of Jiang et al based on a similar optomechanical setting reporting the ground-state cooling of mechanical resonators mediated by a phononic gauge field [93].…”

Optical coupling control of isolated mechanical resonators

“…Additionally, optomechanical devices in various configurations provide an excellent platform to study optically mediated interactions between mechanical resonators 12 – 14 . This lead to several phenomenon such as P and PT symmetry in mechanical resonators 15 – 17 , and dark mode control 9 . Optomechanical systems are a promising platform 18 – 23 to build sensors 19 , 24 and quantum information transducers 25 , 26 relying on the effect of electromagnetic radiation pressure on the vibrational modes of mechanical objects 27 , 28 ; for example, suspended micromirrors, membranes, microtoroids, microsphere resonators, micromembranes in superconducting circuits, 2D photonic crystals, photonic crystal nanobeams, and cold atoms in optical cavities 4 .…”