Characterization of a Two-Photon Quantum Battery: Initial Conditions, Stability and Work Extraction

Abstract

We consider a quantum battery that is based on a two-level system coupled with a cavity radiation by means of a two-photon interaction. Various figures of merit, such as stored energy, average charging power, energy fluctuations, and extractable work are investigated, considering, as possible initial conditions for the cavity, a Fock state, a coherent state, and a squeezed state. We show that the first state leads to better performances for the battery. However, a coherent state with the same average number of photons, even if it is affected by stronger fluctuations in the stored energy, results in quite interesting performance, in particular since it allows for almost completely extracting the stored energy as usable work at short enough times.

Keywords: quantum battery; two-photon Jaynes-Cummings model.

Figure 1

Schematic representation of a QB where a TLS with level spacing ${\omega }_a$ between its ground ($|g\rangle$) and excited ($|e\rangle$) state interacts with a single cavity mode of frequency ${\omega }_c$ via a two-photon coupling in the resonant regime ${\omega }_a=2{\omega }_c$.

Figure 2

(Color on-line) Behaviour of the stored energy $E\left(t\right)$ as a function of time for a Fock state (blue full curve), a coherent state (green dashed curve), and a squeezed state (red dash-dotted curve) with an average number of photons $N=8$.

Figure 3

(Color on-line) Time evolution of the quantum state of the TLS, up to the first maximum of the energy in Equation (26), in the Bloch sphere for a Fock state (a), a coherent state (b), and a squeezed state (c) with an average number of photons $N=8$. The other parameters are: ${\omega }_a/\lambda =200$.

Figure 4

(Color on-line) Behaviour of the average charging power $P\left(t\right)$ as a function of time for a Fock state (blue full curve), a coherent state (green dashed curve), and a squeezed state (red dotted-dashed curve) with an average number of photons $N=8$.

Figure 5

(Color on-line) Behaviour of the stored energy fluctuations $\Xi \left(t\right)$ as a function of time for a Fock state (blue full curve), a coherent state (green dashed curve), and a squeezed state (red dotted-dashed curve) with an average number of photons $N=8$.

Figure 6

(Color on-line) Behaviour of the ergotropy $\mathcal{E}\left(t\right)$ as a function of time for a Fock state (blue full curve), a coherent state (green dashed curve), and a squeezed state (red dash-dotted curve) with average number of photons $N=8$.

Figure 7

(Color on-line) Behaviour of the ratio $\eta \left(t\right)$ as a function of time for a Fock state (blue full curve), a coherent state (green dashed curve), and a squeezed state (red dash-dotted curve) with average number of photons $N=8$.