Micromasers as quantum batteries

Abstract

We show that a micromaser is an excellent model of quantum battery. A highly excited, pure, and effectively steady state of the cavity mode, charged by coherent qubits, can be achieved, also in the ultrastrong coupling regime of field-matter interaction. Stability of these appealing features against loss of coherence of the qubits and the effect of counter-rotating terms in the interaction Hamiltonian are also discussed.

Lossy Micromaser Battery: Almost Pure States in the Jaynes–Cummings Regime

“…The incoherent protocol corresponds to , where the qubits are in a fully mixed state and without any degree of coherence. The other limiting case, (The effect of a complex phase in the coherence parameter, i.e., , has been considered at length, both in the Jaynes–Cummings as well as in presence of counter-rotating terms, in [ 25 ]. For the Jaynes–Cummings dynamics, the presence of a phase factor is completely irrelevant and can be neglected), corresponds to the fully coherent protocol, where the battery is charged by a stream of qubits prepared in a pure state, with the superposition of the states and .…”

“…For completeness and ease of comparison with the incoherent case, let us now consider the case in which the qubits are coherent, i.e., in Equation ( 7 ), which was the subject of Ref. [ 25 ]. We will focus on the case , which means that the incoming qubits are in a superposition state: …”

“…On the other hand, the robustness of such steady states for perturbations of the value has been discussed only recently in Ref. [ 25 ]. In view of the discussion conducted in the previous section, this is the most interesting case to consider, since the steady state itself is fragile for perturbations of the parameters in the incoherent case .…”

“…Recently, collision models have been used to describe the charging process of quantum batteries [ 13 , 14 , 15 , 16 , 24 , 25 ], that is, of quantum mechanical systems suitable to store energy in some excited states [ 15 , 16 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 ], to be later released on demand. The charging of the battery, modeled by a quantum harmonic oscillator or a large spin, via sequential interactions (collisions) with a stream of qubits, has exhibited enhanced performances with respect to classical counterpart, when the qubits are prepared in some coherent state, with respect to the classical, incoherent charging [ 15 , 16 ].…”

“…Moreover, it has been possible to show that by this charging protocol, and when the incoming qubits have a certain degree of coherence, the cavity reaches an effectively steady state which is both highly excited and essentially pure . Interestingly, these features extend beyond the weak coupling regime, and are present both in the strong and ultrastrong coupling regimes of field–matter interaction [ 25 ]. Achieving a pure state is appealing in terms of ergotropy [ 55 , 56 , 57 ], that is, of the amount of energy that can be extracted from a battery via unitary operations, and while for a mixed state part of the excitation energy (measured from the ground state energy of the quantum battery) cannot be used, for a pure state it is always possible to reach the ground state by a suitable unitary operation.…”