Frequency locking and controllable chaos through exceptional points in optomechanics

Abstract

We engineer mechanical gain (loss) in system formed by two optomechanical cavities (OMCs), that are mechanically coupled. The gain (loss) is controlled by driving the resonator with laser that is blue (red) detuned. We predict analytically the existence of multiple exceptional points (EPs), a form of degeneracy where the eigenvalues of the system coalesce. At each EP, phase transition occurs, and the system switches from weak to strong coupling regimes and vice versa. In the weak coupling regime, the system locks on an intermediate frequency, resulting from coalescence at the EP. In strong coupling regime, however, two or several mechanical modes are excited depending on system parameters. The mechanical resonators exhibit Rabi-oscillations when two mechanical modes are involved, otherwise the interaction triggers chaos in strong coupling regime. This chaos is bounded by EPs, making it easily controllable by tuning these degeneracies. Moreover, this chaotic attractor shows up for low driving power, compared to what happens when the coupled OMCs are both drived in blue sidebands. This works opens up promising avenues to use EPs as a new tool to study collective phenomena (synchronization, locking effects) in nonlinear systems, and to control chaos.

Exceptional Point Enhances Sensitivity of Optomechanical Mass Sensors

“…(3). This can be straightforwardly done by approaching the mechanical oscillations with the ansatz, β j (t) =β j + A j exp(−iω lock t) (see more details in [20]). β j is a constant shift in the origin of the movement, A j is the slowly time dependent amplitude, and ω lock is the mechanical degenerated frequency when the resonators experience frequency locking phenomenon.…”

“…and [20]. The eigenfrequencies and the dampings of the system are defined as the real [ω ± = Re(λ ± )] and imaginary [γ ± = Im(λ ± )] parts of λ ± , respectively.…”

“…This benchmark system has an advantage that it enables to get an effective coupled mechanical system, where mechanical gain (loss) can be easily engineered by driving the cavity with a blue (red) detuned laser. At the balance between gain and loss, the system features EP in its mechanical spectrum [20], which is the key point of our optomechanical mass sensorbased EP. The proposed sensor differs from those known [16][17][18][19] on at least three points: (i) it operates at an EP generated on its mechanical spectrum (instead of the optical spectrum), (ii) the gain and loss are selfengineered while the cavities are driven, and (iii) it does not needs the PT -symmetric requirement.…”

Self-organized synchronization of mechanically coupled resonators based on optomechanics gain-loss balance

“…1(c)]. After this amplification phase, the system settles into a self-sustained mechanical oscillations regime, above which complex nonlinear behaviors such as period doubling and chaos could emerge for strong enough driving strength [26]. As we are looking for collective dynamics such as synchronization and frequency locking phenomena, we limit ourselves in this work to the self-sustained oscillations regime.…”

Nonlinear dynamics of weakly dissipative optomechanical systems

“…Classical nonlinear optomechanics is relevant in the case of highly populated optical and mechanical modes. Though it attracted slightly less attention during the initial evolution of modern cavity optomechanics, a number of significant theoretical studies have been devoted to understanding the structure of the phase space, including limit cycles and multistability [22][23][24][25][26], and chaotic dynamics [27,28]. Experimental studies have been relatively rare, but important phenomena have already been observed, including limit cycles [29,30], period doubling and chaos [31][32][33][34][35][36], the predicted multistable attractor diagram [37,38] which is characteristic for optomechanical systems, as well as further aspects [39,40].…”