Exciton-polariton ring Josephson junction. N. Voronova, A. Grudinina, R. Panico, D. Trypogeorgos, M. De Giorgi, K. Baldwin, L. Pfeiffer, D. Sanvitto and D. Ballarini in Nature Comm. 16:466 (2025).  What the paper says!?

In this mainly-experimental work (but first author theorist), the Authors implement a Josephson junction in a polariton ring condensate intersected by a weak link (potential barrier) controlled optically. They study the net circulation around the ring as a function of the barrier, distinguishing between a superfluid-hydrodynamic and a Josephson regime.

They define the weak link as « areas of a system (superconducting or superfluid) with the size of the order of the healing length, where the system’s order parameter is substantially suppressed». There's a full review on this very topic.

They define the hydrodynamics regime as when «the order parameter is not fully suppressed in the barrier region». The wavefunction remains fully connected by the phase, over the weak link. There is a linear dependence of the velocity on the circulation.

They define the Josephson regime as when the order parameter cancels exactly inside the link, leading to undetermined phase inside the link and phase jumps across its two sides, resulting in a breaking of the linear relationship.

At critical circulations, a true Josephson junction is formed with zero density across the barrier and phase

discontinuity at its extremes

They measure the superfluid velocity from the phase difference on both sides of the barrier ($d$ is its width):

and the average circulation as follows:

From various cases, they recover this statistical relationship:

which is what they call the current-phase relationship.

I am puzzled by several statements and am not always sure what exactly the Authors want to say.

First I'm unclear as to what they want to say here:

It has been argued, however, that coherent oscillations in double- well-confined BECs may be regarded as the a.c. Josephson effect and such a setting can be reasonably called a Josephson junction only in the case when there is no confinement by the two sides of the barrier, i.e. in the limit of an infinite system [20], or when the barrier is high enough to

suppress the order parameter to zero [17].

So apparently they make a distinction between the ac Josephson effect and a Josephson junction. The way this is addressed in Ref.  does not seem to corroborate this interpretation. Maybe this is more clear in Ref. 

Regarding the previous Josephson-effect claims, they write «the observation of oscillations (akin to a.c. Josephson effect)». Is the "akin" to mean no Josephson effect was previously observed? Apparently yes since they later write this «can more simply be interpreted as nonlinear Rabi oscillations in a coherent two-level system», which is also unclear because both have shown the Rabi regime of Josephson oscillations and Abbarchi demonstrated the strongly-interacting case on purpose to evidence self-trapping.

Their claim:

Here, we demonstrate the first all-optical realisation of a ring

Josephson junction with [...] polaritons

It's unclear if the "first all-optical" is to mean the barrier as well, or first polaritonic Josephson junction.

They also say that «no characteristic current-phase relation has been reported», which is puzzling as they both reported population-imbalances and phases. Do they mean this wasn't explicitly plotted one as a function of the other? (on this I would agree but mainly in the sense of plotting on the Bloch sphere).

Finally, the also state that the «Josephson regime [is] characterized by a sinusoidal tunneling current», which they evidence in their Fig. 4(a) [where it is very difficult to separate full-circles from empty-ones due to the overlapping]. They apparently mean the ac Josephson effect, where the "voltage" is the "applied circulation" which follows from the natural polariton flow that is disrupted by the barrier:

These are key conditions for establishing of the Josephson regime. Here, a sinusoidal behaviour of the tunneling current versus applied circulation is demonstrated while the hydrodynamic flow is

suppressed.

Shouldn't they show the dc effect then, a given current for no applied circulation.

More extracts with peculiar statements:

At critical circulations, a true Josephson junction is formed with zero density across the barrier and phase

discontinuity at its extremes

Separation of the two regimes:

Our experiments provide direct evidence of the switching between hydrodynamic and Josephson

regimes in an exciton-polaritons quantum fluid.

They say that their results are «leveraging the nonlinear behavior of exciton-polaritons», but it is unclear it does, besides, the superconducting Josephson doesn't require nonlinearities.

When I showed to Nina our results with Amir in Ref.  which called to strongly re-interpret her earlier results in Ref. , I remember she told me «if it's true it's textbook material», to which I replied that it probably was textbook material indeed but what had no room for doubt in any case is whether it was true. It was more than true, it was obvious. I don't know if I convinced her since she does not even cite us. To be fair, she doesn't cite her own papers either. Apparently she know understand something very different for Josephson-effects.