Dicke Quantum Battery The Dicke quantum battery uses the
Dicke model to store energy. This battery was first proposed due to its relation with
superradiant emission and its practical feasibility. The Dicke model describes the collective interaction of an ensemble of N two-level atoms (TLSs) with a single mode of the cavity field. Cavities are typically composed of two or more mirrors that reflect light back and forth, creating a
standing wave of
electromagnetic radiation, with frequencies determined by the cavity's geometry. H_{\text{Dicke}} = \omega_c \hat{a}^\dagger \hat{a} + \omega_0 \sum_{i=1}^{N} \hat{\sigma}i^z + g \sum_{i=1}^{N} \hat{\sigma}_i^x \left( \hat{a}^\dagger + \hat{a} \right) The first term describes the energy of the photons. The second term describes the energy of the qubits. The third term describes the interaction between photons and qubits. g is the coupling parameter. This model initially seemed to show that the mean charging power scaled in a super-extensive manner: \langle P \rangle _t \propto N^{3/2}. However, this Hamiltonian is not well-defined in the
thermodynamic limit (N \to \infty, V \to \infty while keeping N/V constant). To fix this, it is necessary to substitute: g \to g_{\text{TD}} = \frac{g}{\sqrt{N}} By doing so, scientists found that this battery does not provide any quantum advantage.
SYK Quantum Battery The SYK quantum battery uses the
Sachdev–Ye–Kitaev model to store energy. This battery uses the direct charging protocol:H_B(t) = H_B^{(0)} + \lambda(t) \left( H_B^{(1)} - H_B^{(0)} \right) where • H_B^{(0)} = \sum_{i=0}^N \omega_0\hat{\sigma}_i^y is the battery hamiltonian • H_B^{(1)} = \sum_{i,j,k,l=1}^{N} J_{i,j,k,l} \hat{c}_i^\dagger \hat{c}_j^\dagger \hat{c}_k \hat{c}_l is the interaction hamiltonian. This is the first many-body model that shows a super extensive charging power. \langle P \rangle _t \propto N^{3/2} == References ==