(Nanowerk News) In a paper published in Nature Communications (“Asynchronous locking in fluid light and sound metamaterial”), researchers from the Paul Drude Institute in Berlin, Germany, and the Instituto Balseiro, Bariloche, Argentina, demonstrated that light emitters with different resonant frequencies can asynchronously self-lock their relative energies by exchanging mechanical energy. This finding paves the way for improved light source control and GHz to THz interconversion relevant to quantum technologies.
Oscillators with slightly different resonant frequencies tend to lock their frequencies to the same value when they start interacting with each other. This phenomenon was originally observed in a system of two pendulas sharing a common support by Christiaan Huygens, the inventor of the clock, in the 17th century. Huygens first realized that it was difficult to manufacture two pendulas with the same oscillation frequency—a necessary condition for making a precise clock. However, if he hung them on the same pedestal, the clocks would slowly synchronize their movement and, after a time, oscillate at the same frequency.
The synchronization process described above is a general property of oscillating systems known as mode locking or entrainment. It appears in a variety of oscillators from the extremely precise time synchronization required for GPS to the synchronization of the human biological clock that regulates its daily rhythm. The mechanism behind sync is far from trivial.
To understand it, we must first consider that the amount of energy stored in a pendulum depends on the frequency and amplitude of its motion. In addition, a pendulum can oscillate with a frequency within a narrow band, the width of which depends on the rate at which the pendulum loses energy (that is, how quickly the pendulum stops). The frequency locking between the two Huygen pendula depends on the exchange of energy through the rods that support the pendula.
This process requires that the narrow frequency bands of the two pendulas overlap, and that the rate of energy transfer is much faster than the decay time of their oscillations. If these conditions are met, energy is transferred back and forth between the pendulas until their vibrations lock on a single frequency. In the locked regime, the clean exchange of energy between them disappears.
In Huygens’ experiment, the pendula has nearly the same frequency. A new study from the Institut Paul Drude and Instituto Balseiro set out to show how one can synchronize the motions of pendulas with very different resonant frequencies – that is, with the difference Δω between their resonant frequencies much greater than the individual pendulum’s frequency band. This scenario occurs if the pendula has different lengths and different resonant frequencies, as illustrated at the top of Figure 1.
This process – asynchronous frequency locking – is relevant for several applications including precise frequency locking using phase-lock-loop (PLL) in electronic circuits as well as the generation of radio waves or light beams with well-defined frequency differences.
In their publication, Chafatinos et al. demonstrated an integrated array of asynchronously locked laser-like emitters irradiating different frequencies at multiples of a well-defined amount/quantity ωM. (cf. Figure 1, bottom panel). Laser-like light is generated by a μm sized emitter array fed into a hybrid semiconductor opto-mechanical resonator with a mechanical resonant frequency ωM around 20 GHz. The transmitter is stimulated by an external continuous wave laser beam.
Chafatinos et al. demonstrated that emitters can self-adjust their respective energies under laser excitation until they satisfy the conditions for asynchronous latching. At this point, the relative energy separation between emitters automatically locks in a multiple of ωM through the exchange of quanta of mechanical energy. The entire array then starts self-oscillating at the mechanical frequency ωM.
Asynchronous locking in a coupled pendula can be achieved by coupling it to a mechanical resonator with a frequency ωM close to a multiple of Δω. Such a mechanical resonator is illustrated by the spring bar system in the top panel of Figure 1.
Energy exchange via a mechanical oscillator provides the frequency offset required for latching. In fact, it can be shown that the requirements for asynchronous latching are the same as those for conventional latching when these frequency offsets are taken into account.
An analogous process occurs for the light emitting array in the bottom panel of the figure. Here, the optomechanical interaction excites the vibrations and, simultaneously, induces the energy offset required for asynchronous latching. Interestingly, a very similar asynchronous latching behavior was reported recently in a completely different context: Pitangus sulphuratus, a bird from America, managed to lock on the difference in frequency between its two vocal cords.
The work of Chafatinos et al. demonstrated a new concept for optomechanical materials based on µm-sized central arrays that interact strongly with finite GHz vibrations. These results pave the way for ultrafast mechanical control of coherent light sources and relevant interstate transitions for quantum technologies.