Scientists in Switzerland have shown how a superconducting circuit can be used to investigate the physics of topological lattices such as strained graphene. They say their work—an implementation of what is known as cavity optomechanics—could potentially be used to create highly entangled mechanical states, a valuable resource for quantum computing and communication based on mechanical oscillators (Nature, doi: 10.1038/s41586-022-05367-9).
Optically probing mechanical systems
Optomechanical systems use electromagnetic fields to control the vibrations of mechanical objects, taking advantage of the fact that light carries momentum and can therefore exert pressure. At visible wavelengths, such systems involve a laser propagating in an optical cavity whose end mirror is free to vibrate. Microwave devices instead couple longer-wavelength radiation to an LC circuit featuring a vibrating capacitor.
In recent years, physicists have also started to use optomechanics to probe the quantum behavior of macroscopic mechanical systems. This has involved manipulating such systems in a number of ways, such as cooling them to their quantum ground states or entangling mechanical oscillators located some distance from one another.
Such systems, however, tend to comprise only one or two optomechanical modes. Researchers would like to develop 2D lattices of optomechanical oscillators, as these could shed light on more complex phenomena such as the topology of light and sound or the quantum many-body dynamics of macroscopic systems.
Precise control via improved fabrication
Building optomechanical lattices where each building block consists of mechanical and optical modes requires very precise control of the properties of individual lattice sites. Tobias Kippenberg, Amir Youssefi and colleagues at the Swiss Federal Institute of Technology Lausanne (EPFL) have now shown how this is possible by constructing an optomechanical system from a superconducting circuit.
Key to the work is a parallel-plate vacuum capacitor, which features a suspended top plate that can vibrate. The conventional method for fabricating such capacitors makes it hard to control the size of the gap between the device’s two plates, and with that the resonant mechanical and microwave frequencies as well as the coupling strength between those.
Kippenberg and colleagues got round this problem by devising a new fabrication process. First, they etched a trench in a silicon substrate; then, they placed a thin slice of aluminum on the bottom of the trench to serve as the capacitor’s lower plate, before covering that with a layer of silicon dioxide. After that, they leveled off the surface of the silicon dioxide using chemical mechanical polishing and rested a second aluminum plate on top of the leveled surface. By finally removing the silicon dioxide layer, they were able to suspend the upper aluminum plate precisely above the lower one.
The fact that the superconducting circuit had to be cooled to cryogenic temperatures induced a tensile stress in the upper plate. This kept the plate flat and the gap size dependent on the depth of the trench, thereby restricting fluctuations in the resonant frequencies of the microwaves and mechanical oscillations to 0.5% and 1%, respectively.
The researchers fabricated multiple instances of these capacitors, each one linked to a spiral-shaped inductor to produce a distinct LC resonator. Each resonator was in turn magnetically coupled to its neighbors, with the coupling magnitude determined by the physical distance between resonators.
Edge states and a honeycomb lattice
The EPFL team implemented two types of circuit. In one, the researchers lined up ten resonators in a chain to mimic what are known as topologically protected edge states. In the other they arranged 24 resonators in the shape of a honeycomb lattice, with the couplings along one of the three lattice axes set so that alternate couplings had high and low values. This allowed them to reproduce the physics of one-carbon-atom-thick sheets of graphene under strain—as can occur, for example, if the material is adsorbed onto substrates like silicon dioxide.
By studying the optomechanical interactions between the resonators, the researchers were able to directly measure the resonators’ collective behavior and work out the full Hamiltonian, a function expressing the system’s combined kinetic and potential energy. They say that previously it had only been possible to measure the behavior of such superconducting circuits indirectly, using (for example) near-field scanning probes or laser scanning microscopy.
The researchers reckon that such optomechanical lattices could in future shed light on “the rich physics in multimode optomechanics.” Using degenerate mechanical oscillators, the explain, should make it possible to “create collective long-range interactions and observe strong cooperative effects on mechanical motion.” Also, the system might enable highly entangled mechanical states to be created, according to the researchers—something that could benefit future quantum information technology based on mechanical oscillators.