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Control of mechanical quantum resonators reaches new levels of precision

20 May 2022
Artistic impression of a crystal
Sound solution: both experiments made us of quantized sound in crystalline materials. (Courtesy: Shutterstock/Dmitriy-Rybin)

New levels of precision control over the quantized energy levels of mechanical resonators have been achieved by teams in the US and Switzerland, who independently measured the number of phonons in a cavity without disturbing it. In addition, the US group produced an entangling gate comprising two nanomechanical oscillators. The work could potentially have implications for quantum networking and quantum error correction.

Just as electromagnetic energy is quantized into propagating photons, acoustic energy propagates in quanta called phonons. The science of photon behaviour – called quantum electrodynamics – is an important branch of modern physics because it provides a relativistic description of the interaction of light with matter. Scientists have used the theory in a variety of applications such as atomic clocks and quantum computation.  In recent years, scientists have begun applying some of the same concepts to phonons in a field called quantum acoustodynamics. Last year, for example, two groups independently used laser-based measurements to entangle the oscillations of membranes in cavities.

Quantum acoustodynamics is attractive for quantum networking and quantum information processing for several reasons. First, whereas it is extremely difficult to isolate photons from unwanted thermal and electrical noise in a superconducting qubit, sound only propagates within a medium. Therefore, isolated mechanical resonators can have a much longer lifetime, which could make them useful in quantum memory applications and quantum error correction. Despite this isolation, such resonators can also be interfaced with a wide variety of different quantum technologies – and this could prove invaluable for connecting superconducting, trapped ion or atomic quantum computers. “Everything that we have in our physical world talks to mechanical vibrations,” explains Uwe von Lüpke of ETH Zurich.

Changing energy

Reading out the energy level of a mechanical resonator, however, poses a challenge. The simplest way is to tune another system such as an electronic circuit or laser onto a resonance – much as one could ascertain the frequency of a laser by pumping it at multiple frequencies and finding out which one worked. This creates a problem, however: “If you have this resonant energy exchange, you’re actually changing the energy of the resonator,” explains von Lüpke.

In the new research, two groups – one at ETH Zurich led by Yiwen Chu and one at Stanford University in California headed by Amir Safavi-Naeini – have independently made “quantum non-demolition” measurements of the states of mechanical resonators. They interfaced mechanical resonators with superconducting qubits through piezo-electric materials, which expand when subjected to electric currents.

They did not, however, tune the frequency of the current oscillations into resonance with the mechanical oscillation. Instead, they utilized the fact that the number of phonons in the cavity alters its resonant frequency. Therefore, by measuring the relative phases of the oscillations between the cavity and the qubit (effectively measuring how far apart their frequencies were), they could determine the number of phonons in the cavity.

Long stability

“This effect is typically used to read out superconducting qubits,” explains von Lüpke, who is first author on the paper describing the ETH Zurich work. This type of measurement is only possible in the so-called strong dispersive regime, in which the coupled phononic-electronic states are stable long enough to allow sufficiently precise measurements of the frequency of the mechanical resonator. The two groups are the first to reach this regime.

The groups’ approaches, however, were different. The ETH Zurich team used bulk density waves in a sapphire wafer. The Stanford group fabricated two nanoscale, periodic “phononic crystals” on a lithium niobate chip. These are analogous to photonic crystals in that they preferentially support specific phonon frequencies. Like the ETH Zurich group, the Stanford team interfaced their phononic crystal resonators with a qubit and performed quantum non-demolition measurements of the number of phonons in each one.

The Stanford group then used the fact that both acoustic resonators were connected to the same electronic qubit to perform an entangling gate operation, which is a measurement of the qubit that left the two resonators in an entangled state. This could potentially be useful in quantum error correction, allowing the states of superconducting qubits to be stored in longer-lived mechanical qubits and removing the need for large amounts of redundancy to protect the integrity of quantum algorithms.

Towards hybrid technologies

“I think that’s what’s really motivated both of our groups to develop these sorts of heterogeneously integrated devices,” says Amir Safavi-Naeini. “That’s the direction where a lot of the field is going – towards these hybrid technologies.”

Warwick Bowen of the University of Queensland in Australia believes that both teams have achieved significant progress in creating their systems. “I think they’re very different, and they’ll have different applications,” he says. He points out that the bulk acoustic waves utilized by the ETH Zurich group can generate very long lifetimes, which could be useful in quantum memories – especially as a superconducting circuit could be mounted directly on the mechanical resonator. However, the Stanford group has already demonstrated entanglement generation (albeit with less than 60% fidelity, compared with over 99% fidelity required in viable quantum gates).

Bowen also says that the miniaturization of the phononic crystal approach has inherent benefits. “Nanoscale is good in terms of being able to pack more devices into the same area…and because they’re so much smaller it turns out they have a much stronger interaction with light. So, if you wanted to build a quantum interface between microwaves and light, this system is much better suited to that.”

The Stanford research is described in Nature. The ETH Zurich work is unveiled in Nature Physics.

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