  Recently there has been a great deal of interest on the possibility to
exploit quantum-mechanical effects to increase the performance of energy
storage systems. Here we introduce and solve a model of a quantum
supercapacitor. This consists of two chains, one containing electrons and the
other one holes, hosted by arrays of double quantum dots, the latter being a
building block of experimental architectures for realizing charge and spin
qubits. The two chains are in close proximity and embedded in the same photonic
cavity, which is responsible for long-range coupling between all the qubits, in
the same spirit of the Dicke model. By employing a variational approach, we
find the phase diagram of the model, which displays ferromagnetic and
antiferromagnetic phases for suitable pseudospin degrees of freedom, together
with phases characterized by collective superradiant behavior. Importantly, we
show that when transitioning from the ferro/antiferromagnetic to the
superradiant phase, the quantum capacitance of the model is greatly enhanced.
Our work offers opportunities for the experimental realization of a novel class
of quantum supercapacitors with an enhanced storing power stemming from
exquisite quantum mechanical effects.
