Normal mode splitting induced synchronization blockade in coupled quantum van der Pol oscillators

Abstract

We report a normal-mode induced synchronization blockade in coupled quantum van der Pol oscillators under the influence of external drive. In this mechanism, the coupling hybridizes the oscillator modes into spectrally split normal modes. The destructive interference between the transitions to these modes blocks synchronization. We find that this blockade can be controlled simply by tuning the coupling strength and detuning allowing dynamic manipulation of quantum synchronization through collective mode dynamics. We analyze the phase-locking behaviour using perturbation analysis. Further, by deriving steady-state probability amplitudes we show how the energy redistribution and spectral splitting forms the basis of the blockade. Our results might provide new insights into how synchronization can be controlled in quantum systems.

Figures (5)

• Figure 1: Schematic energy level diagram of the coupled quantum van der Pol oscillator under the influence of external drive.
• Figure 2: Relative phase distribution $P(\varphi)$ in Eq. (\ref{['phase_relative']}), as a function of coupling strength $V/\gamma_1$ for (a) $E/\gamma_1=0.1$ and (b) $E/\gamma_1=0.5$ and $\Delta_1=\Delta_2=0$. Phase distribution of individual oscillators $P(\phi_1)$ and $P(\phi_2)$, see Eq. (\ref{['single_phase']}), are plotted in (c) and (d) respectively, for $V/\gamma_1=1.0$ (solid curve) and $V/\gamma_1=3.0$ (dashed curve) with $E/\gamma_1=0.5$. In all these cases we have considered $\gamma_2/\gamma_1=10$.
• Figure 3: Absolute value of synchronization measure $S_1$ (panels (a) and (d)), $S_2$ (panels (b) and (e)) and $S_3$ (panels (c) and (f)), defined in Eq. (\ref{['synch_meas']}), plotted as a function of $\Delta_1$ (first column) and $\Delta_2$ (second column) for different coupling strengths (values shown in the inset of panel (d)) with $E/\gamma_1=0.5$ and $\gamma_2/\gamma_1=10$.
• Figure 4: Synchronization measures $|S_i|$, $i=1,2,3$ (Eq. (\ref{['synch_meas']})), as a function of $\Delta_1$ and $\Delta_2$. Panels (a)-(c) are plotted for coupling strength $V/\gamma_1=0.6$ and panels (d)-(f) are plotted for coupling strength $V/\gamma_1=4.0$ with $E/\gamma_1=0.5$ and $\gamma_2/\gamma_1=10$.
• Figure 5: In the first row panels (a)-(c) synchronization measures $|S_i|$, $i=1,2,3$, are plotted as a function of $\Delta_1$ and $\gamma_2/\gamma_1$ with $\Delta_2=0$. In the second row panels (d)-(f) synchronization measures $|S_i|$ ($i=1,2,3$), defined in Eq. (\ref{['synch_meas']}), are plotted as a function of $\Delta_2$ and $\gamma_2/\gamma_1$ with $\Delta_1=0$. In all these figures we consider $V/\gamma_1=5.0$ and $E/\gamma_1=0.5$.