Fig. 1. (a) Schematic of a Brillouin interaction in the parity-time symmetric system. The modes a2, a3, and b in the lossy cavity represent the anti-Stokes mode, Stokes mode, and mechanical mode, respectively, and the gain microsphere supports the cavity mode a1. The waveguide can couple the light into the cavity and collect the cavity emission power for sensing. (b) The cavity modes and mechanical mode are illustrated in the frequency domain.

Fig. 2. Mechanical responses and the supermodes spectrum as a function of γ3. Frequency shifts are plotted in A1 and B1; A2 and B2 denote the optical damping rate Γopt. Here the real and imaginary parts of complex numbers ω± are denoted by the red and blue dashed lines, respectively. A1–A3 indicate the mechanical responses and supermode spectrum with blue-detuned driving. B1–B3 plot the mechanical responses and supermode spectrum in the red sideband driving regime. The parameters used are κ=1  MHz, Pin=17.5  μW, γ2=2.6  MHz, g0=4  Hz, Ωm=50  MHz, Γm=1  kHz, J=κ, δ3=−1.95  kHz, and δ1=0.99δ3.

Fig. 3. Absolute value of the mechanical frequency shift ΔΩm(ν) and effective linewidth Γ(ν) with the perturbation ν. The red lines show the absolute value of the mechanical frequency shift and the blue dashed lines plot Γ(ν) in (a) and (b) with δ1=δ3=5  kHz. The difference between Abs(ΔΩm(ν)) and Γν are plotted in (c) and (d) with the detuning δ3 and the perturbation ν. The coupling rates J are 0.97κ and 1.01κ in (c) and (d), respectively. Other parameters used here are γ3=1  MHz, κ=0.975γ3, and Γ=5  Hz.

Fig. 4. Cavity emission spectrum with the effect of laser frequency noise in (a) and (b). The perturbation ν equals 300 Hz and the mechanical linewidth is 1 Hz. The insets show the mechanical frequency shift induced by laser frequency noise σ. The coupling rate J=0.8κ in (a) and J=κ in (b). (c) We plot η as a function of σ with different coupling rates J. The red line indicates the system is robust to laser frequency noise near the exceptional point. The parameters used here are γ3=1.00  MHz, Δ1=Ωm, Δ3=Ωm, κ=0.985γ3, and Γ=1  Hz.

Fig. 5. (a) Normalized output spectra with different optical frequency shifts ν. The black solid line represents the cavity emission spectrum without external perturbation when the mechanical linewidth is 1 Hz. And the output spectrum is normalized to 1 separately. (b) The resolution of ν as a function of the coupling rate J. The red, green, and blue solid lines indicate the minimum detectable optical cavity resonance shift with Γ=2, 1, and 0.5 Hz, respectively. The parameters used here are γ3=1.00  MHz, Δ1=Ωm, Δ3=Ωm, and κ=0.985γ3. And the coupling rate J=κ in (a).