Synchronization of micromasers

Abstract

We investigate synchronization effects in quantum self-sustained oscillators theoretically using the micromaser as a model system. We use the probability distribution for the relative phase as a tool for quantifying the emergence of preferred phases when two micromasers are coupled together. Using perturbation theory, we show that the behavior of the phase distribution is strongly dependent on exactly how the oscillators are coupled. In the quantum regime where photon occupation numbers are low we find that although synchronization effects are rather weak, they are nevertheless significantly stronger than expected from a semiclassical description of the phase dynamics. We also compare the behavior of the phase distribution with the mutual information of the two oscillators and show that they can behave in rather different ways.

Quantum synchronisation enabled by dynamical symmetries and dissipation

“…In figure 7 we demonstrate the synchronicity which results from the eigenmodes in equation (20). We initialise the system in a product state and, after quenching under the master equation in equation (19) observe how the x-magnetisation on each site synchronises perfectly, oscillating at the anticipated frequency.…”

“…where the coefficients D i are set by the initial state of the system. Due to the inter-site coupling and local dephasing the imaginary modes in equation (20) are completely translationally symmetric (see [25] for the explicit form of the steady state) and thus this observable is depent only on the cardinality M of the set B, not the specific sites within the set.…”

“…Remarkably, this harmonised response is occuring even in the presence of both magnetic and chemical disorder-emphasising the robustness of a symmetry-based approach to observing quantum synchronisation. The imaginary eigenmodes in equation (20) are translationally-invariant and hence λ (1) evaluates to 0 (see section 2.3). As with the previous example, this robust, synchronised behaviour is a result of a second-order response to the detuning.…”

“…The formation of a Bose-Einstein condensate (BEC), for example, could be considered perfect synchronisation [17] due to the collective condensation of the atoms in the bosonic gas. In closer analogy to classical systems, models of self-sustained quantum oscillators, such as quantum Van der Pol oscillators [13,18,19] or pairs of micromasers [20], have been shown to lock phases and reach coupled limit cycles. Quantum effects play a decisive role in either enhancing [21,22] or hindering [23] this synchronicity.…”

Synchronizing quantum harmonic oscillators through two-level systems

“…It is worth commenting, at this point, that the study of synchronization is often based on numerical treatments (see for example Refs. [16,23,24,26]), even though more analytical studies are also present [20,33]. Moreover, qualitative predictions based on the study of the normal modes and the individualization of leaking and protected ones are present in the literature(see for example Ref.…”