High-order exceptional points in optomechanics

Abstract

We study mechanical cooling in systems of coupled passive (lossy) and active (with gain) optical resonators. We find that for a driving laser which is red-detuned with respect to the cavity frequency, the supermode structure of the system is radically changed, featuring the emergence of genuine high-order exceptional points. This in turn leads to giant enhancement of both the mechanical damping and the spring stiffness, facilitating low-power mechanical cooling in the vicinity of gain-loss balance. This opens up new avenues of steering micromechanical devices with exceptional points beyond the lowest-order two.

Figure 1

(a) Schematic illustration of a COM system with an active resonator coupled to a passive resonator containing a mechanical mode. (b) The off-resonance case has an EP which is of order 2, due to the coalescing optical modes. This features a pair of amplifying and decaying optical supermodes, $a_{\pm }=(a_1\pm a_2)/\sqrt{2}$, with frequencies ω _± (for details on ω _0,±, see the Method). (c) When the optical red detuning equals ω _m, an EP of order 3 emerges, leading to low-power phonon cooling in the vicinity of gain-loss balance (see the text).

Figure 2

The supermode spectrum for the COM system in active-passive-coupled resonators (J/γ = 1). Here the input power is fixed as P _in = 1 mW.

Figure 3

The effective mechanical frequency and damping rate for (a,b) the single passive resonator, (c,d) the passive-passive resonators, or (e,f) the active-passive resonators, with the fixed value J/γ = 1.

Figure 4

(a–c) The cooling enhancement factor β = n/n ₀, as a function of Δ/ω _m for various values of κ/γ, when (a,b) P _in = 0.1 mW, and (c) P _in = 1 mW. (d) Achievable minimum phonon number n at the gain-loss balance for P _in = 0.12 mW, when the initial temperature T is 300 K, 20 K, or 650 mK (i.e., cryogenic temperature), respectively.

Figure 5

(a) The phonon number n ₀ for the conventional COM composed of a single passive resonator at different powers when the system is initially at room temperature. The parameter values used in this simulation is the same as those given in the main text. (b) The phonon number for the COM system composed of active-passive-coupled resonators, with respect to the temperature and the input pump power.