Asynchronous locking of frequencies in optomechanical systems

In a recent publication in Nature Communications, scientists from the Paul Drude Institute in Berlin, Germany, and the Instituto Balseiro in Bariloche, Argentina, have made a significant breakthrough in the field of light emitters and their resonance frequencies. They have demonstrated that these emitters, which have different resonance frequencies, can effectively synchronize their energies by exchanging mechanical energy. This discovery holds great promise for enhancing control over light sources and enabling GHz-to-THz interconversion, which is highly relevant to the advancement of quantum technology.

The phenomenon of synchronization, also known as mode locking or entrainment, occurs when oscillators with slightly different resonance frequencies adjust their frequencies to a common value as they interact with each other. This concept was initially observed by Christiaan Huygens in the 17th century when he noticed the synchronization of two pendula that shared the same support. Huygens realized that it was challenging to create two pendula with precisely matching oscillation frequencies, which is crucial for accurate timekeeping. However, when he hung them on a common support, the pendula gradually synchronized their motions and eventually oscillated at the same frequency.

Understanding the mechanism behind synchronization requires considering the energy stored in a pendulum, which depends on its frequency and amplitude of motion. A pendulum can oscillate within a narrow frequency band, the width of which is determined by how quickly the pendulum loses energy and comes to rest.

In the case of Huygens’ pendula, the frequency locking occurs through the exchange of energy via the bar supporting the pendula. For successful energy transfer, the narrow frequency bands of the two pendula must overlap, and the energy transfer rate should be much faster than the decay time of their oscillations. When these conditions are met, energy is transferred back and forth between the pendula until their vibrations synchronize to a single frequency. In the synchronized state, there is no net energy exchange between them.

The recent study by the Paul Drude Institute and the Instituto Balseiro aimed to demonstrate how the motion of pendula with significantly different resonance frequencies could be synchronized. For instance, if the pendula have different lengths, their resonance frequencies would also differ. The researchers illustrated this scenario in Figure 1. Achieving asynchronous frequency locking like this has implications for various applications, including precise frequency locking in electronic circuitry using phase-lock loops (PLL) and generating radio waves or light beams with well-defined frequency differences.

In their published work, Chafatinos and colleagues presented an integrated array of laser-like emitters that were asynchronously locked and emitted light at frequencies differing by multiples of a specific amount, denoted as ωₘ. The laser-like light was generated by an array of micrometer-sized emitters placed within a hybrid semiconductor opto-mechanical resonator. This resonator had a mechanical resonance frequency of approximately 20 GHz, denoted as ωₘ. The emitters were excited by an external continuous wave laser beam.

The researchers demonstrated that the emitters could autonomously adjust their individual energies under laser excitation until they satisfied the conditions for asynchronous locking. At this point, the relative energy separations between the emitters automatically synchronized to multiples of ωₘ through the exchange of quanta of mechanical energy. Consequently, the entire array started self-oscillating at the mechanical frequency ωₘ.

To achieve asynchronous locking in coupled pendula, the researchers coupled them to a mechanical resonator with a frequency ωₘ close to a multiple of the difference in resonance frequencies (Δω), denoted as Δω = nωₘ (where n is an integer). This mechanical resonator is depicted as a spring-bar system in the upper panel of Figure 1. The exchange of energy via the mechanical oscillator provides the necessary frequency offset for locking. Remarkably, a similar asynchronous locking behavior has been observed in a completely different context, involving the vocal cords of the Pitangus sulphuratus bird, native to the Americas. This bird manages to synchronize the frequency difference between its two vocal cords.

The groundbreaking work by Chafatinos and his colleagues introduces a novel concept for optomechanical materials, utilizing arrays of micrometer-sized centers that strongly interact with confined GHz vibrations. This research opens up exciting possibilities for achieving ultrafast GHz coherent mechanical control of light sources and interstate transitions, which are crucial for advancements in quantum technologies.

In conclusion, the recent study published in Nature Communications by researchers from the Paul Drude Institute and the Instituto Balseiro highlights the remarkable phenomenon of asynchronous locking in light emitters with different resonance frequencies. By exchanging mechanical energy, these emitters can synchronize their energies, leading to enhanced control over light sources and enabling advancements in quantum technologies. This research has significant implications for a wide range of fields and sets the stage for further exploration and development in the realm of optomechanical materials and GHz coherent mechanical control.

Source: Paul-Drude-Institut für Festkörperelektronik

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