Tunable anti–parity-time-symmetric chaos in optomechanics

The chaotic light source is one of the most crucial foundations in optical physics studies and photonic devices. The microcavity provides the predominant solution of compact chaotic light sources in integrated photonics. Still, its prefixed feature has severely ruled out access to tuning for meeting the ever-increasing demands of the general-purpose chaotic light source in engineering. Here we report a demonstration of a chaotic light source with a switchable bandpass–band-stop chaotic emission and tunable bandwidth in a spinning microcavity anti-parity-time (anti-$\mathcal{PT}$). system. In addition, the arrangement of anti-$\mathcal{PT}$ microcavity presents several phenomena such as loss-induced chaotic emission and two different chaotic emissions from one microcavity light source. Such advantages offer another possible way to advance multiplex photonic devices and on-chip chaotic light source fabrication. These results provide a promising approach for the tunable chaotic source and serve as tools for applications in secure communications, electromechanical switching, and exploring non-Hermitian physics.

Figure 1

(a) Realization of a spinning microcavity anti-$\mathcal{PT}$ OMS. The microcavity is driven by two lasers with the same angular frequency from ports A and B, generating the clockwise mode $a_1$, counterclockwise mode $a_2$, and mechanical mode $b$. The rotational speed of microcavity $\mathrm{\Omega }$ adjusts the anti-$\mathcal{PT}$ symmetry [38], which induces two opposite angular frequency shifts on two optical modes. (b) Solutions of the real and imaginary parts of the eigenvalues ${\lambda }_{+}$ (top) and ${\lambda }_{-}$ (bottom) in the absence of mechanical motion.

Figure 2

Evolutions of $I_1$ (upper) and $x$ (lower) for (a) ${\gamma }_c\approx 1.88\kappa$, (b) ${\gamma }_c\approx 2.1\kappa$, and (c) ${\gamma }_c\approx 2.35\kappa$. (d) Lyapunov exponent of $I_1$ versus ${\gamma }_c/\kappa$. (e) Pseudocolormap describes the evolutions of the PSD of $I_1$ versus $\omega /{\omega }_m$ and ${\gamma }_c/\kappa$. The parameters are ${\omega }_c=1216$ THz corresponding to 1550 nm, $\kappa =8$ kHz, $g=100$ Hz, ${\omega }_m/2\pi =10$ kHz, ${\omega }_m/2\pi =1$ kHz, ${\omega }_c={\omega }_d$, $P=55$ pW, and ${\mathrm{\Delta }}_{\text{Sag}}=1$ kHz.

Figure 3

Bifurcation diagrams of $I_1$ and $I_2$ versus $({\omega }_c-{\omega }_d)/{\omega }_m$ for (a) and (b) ${\mathrm{\Delta }}_{\text{Sag}}=5.8$ kHz, (c) and (d) ${\mathrm{\Delta }}_{\text{Sag}}=6.5$ kHz, (e) and (f) ${\mathrm{\Delta }}_{\text{Sag}}=7$ kHz, (g) and (h) ${\mathrm{\Delta }}_{\text{Sag}}=8$ kHz, and (i) and (j) ${\mathrm{\Delta }}_{\text{Sag}}=9$ kHz. The insets in (a) show two trajectories of the mechanical motion at ${\mathrm{\Delta }}_{\text{Sag}}=5.8$ kHz in phase space with the opposite detuning ${\omega }_c-{\omega }_d=\mp 0.4{\omega }_m$ and ${\gamma }_c\approx 1.57\gamma$.

Figure 4

Evolutions of $I_1$ (thicker line) and $I_2$ (thinner line) with the incident direction of input from (a) and (d) port A, (b) and (e) port B, and (c) and (f) both ports, for ${\mathrm{\Delta }}_{\text{Sag}}=8$ kHz and detunings of (a)–(c) ${\omega }_d={\omega }_c-0.5{\omega }_m$ and (d)–(f) ${\omega }_d={\omega }_c+0.3{\omega }_m$. The insets in (a), (b), (d), and (e) show the corresponding trajectories of the mechanical motion in phase space.

Figure 5

Bifurcation diagrams of $I_1$ and $I_2$ versus power $P$ when light is incident from (a) and (b) port A, (c) and (d) port B, and (e) and (f) both ports, for a detuning of ${\omega }_d={\omega }_c-0.5{\omega }_m$.