I read the press release a few times and it's very confusing. The research paper is paywalled.
My guess is:
The "battery" is an atom that can be in the ground state or exited.
The two chargers are laser, let's call them A and B
A classic "battery" can go:
* Empty (total = 0) -> absorb a photon from A (total = A) -> absorb a photon from B (total = A+B)
or
* Empty (total = 0) -> absorb a photon from B (total = B) -> absorb a photon from A (total = A+B
But a quantum "battery" can go:
* Empty (total = 0) -> 50% absorb a photon from A and 50% absorb a photon from B and (total = (A+B)/2) -> absorb the other photon (total = A+B)
where 50%+50% is actually 1/sqrt(2)±1/sqrt(2) for technical reasons. (They are not absorbing the 50% of the photon.)
I don't understand the part of the weaker charger. If the laser A and B have the same frequency/color, then it does not make sense. If they are different, it is almost obvious because fine tuning the energy of the photons in the laser to the energy of the transitions of the levels of an atom is a good idea to promote absorption.
As I said, I'm guessing too much, so I'd be happy if anyone can post a better explanation.