Observing strongly-coupled Mie polaritons using water droplets

Mie theory, the analytical solution for electromagnetic wave scattering off a spherical particle, provides a powerful approach for understanding scattering spectra in terms of different multipole resonances. While the assumption of spherical symmetry is often merely an approximation, Mie theory can nevertheless give useful insights in more realistic settings such as resonances of cylindrical high refractive index nanopillars.

One setting where spherical scatterers arise quite naturally is in liquids with high surface tension, which promotes the formation of spherical droplets. Remarkably, for the case of water droplets with radii of a few microns, the Mie resonances coincide with the infrared stretching and bending vibrational resonances of the H2O molecule! This leads to strong coupling between electromagnetic and vibrational degrees of freedom leading to the formation of polaritons, as reported in recent work published in Physical Review Letters: Self-Hybridized Vibrational-Mie Polaritons in Water Droplets.

Observing the key signature of strong coupling - Rabi splitting between upper and lower polariton resonances (corresponding to electromagnetic and vibrational oscillations being in or out of phase) - using water droplets is complicated by the non-uniform droplet sizes. Thus, the measured scattering spectrum involved not just a few resonances at specific frequencies, but a distribution of different resonance frequencies dependent on the particles' sizes.

To overcome this, the authors of the study also measured the scattering spectra of droplets of heavy water, where the vibrational modes become red-shifted due to the increased mass of the deuterium atoms. The authors observed that the absorption peaks associated with the strong coupling between vibrational and electromagnetic resonances are also red-shifted.

In addition to applications to the spectra of water droplets in the atmosphere, it will be interesting to explore similar strong coupling phenomena in other high surface tension liquids and applications to polariton chemistry, whereby strong coupling between electromagnetic and molecular degrees of freedom shows promise as a means of controlling rates of chemical reactions.

From NISQ to small logical quantum circuits

After six years of huge interest in NISQ (noisy intermediate-scale quantum) circuits there are still no practical applications where a noisy quantum device can outperform the best classical methods. Noise is too detrimental, and classical methods are too powerful. Experts continue to argue that now is not the time for commercial applications: quantum error correction, hundreds of logical qubits, and millions of error-corrected gates are needed.

Then what's next? Circuits of a moderate size with some limited error correction capabilities. LISQ (logical intermediate-scale quantum) or something else, for short.

What can we expect from these up and coming small scale logical circuits?

First, a lot of the tools developed for the NISQ era will become obsolete. For example, variational quantum circuits involving continuously-parameterised quantum gates cannot be easily implemented in a fault-tolerant manner. Instead, post-variational hybrid quantum-classical algorithms for this era will need to offload the continuously-parameterised part of the algorithm to a classical computer, with the quantum circuit used to measure a set of (hopefully classically-intractable) observables that are used as inputs to the classical tunable model.

Second, the hardware, algorithms, and the error correcting code cannot be considered in isolation. Choosing the right error correcting code will be essential to get the most out of the current hardware. Examples of this can be seen in QuEra's logical circuit demonstration from late last year, where the use of a 3D quantum error correction code allowed them to perform random IQP circuit sampling with error detection, and Quantinuum's recent demonstration of repeated error correction. Similar to the NISQ era, different hardware platforms will have different strengths and limitations in what kinds of circuits they will be able to run.

Finally, the most valuable software tools in the NISQ era were for quantum control and state tomography, essential to get the most out of the noisy hardware. These tools will remain important, since fidelities at the physical qubit level directly affect the amount of quantum error correction overhead required. As we move to logical circuits, the new valuable quantum software will be in the form of compilers that will take all the hassle out of hardware and error code selection out of the end-user and translate a given logical circuit into simple, understandable hardware requirements.