Optimal charging of a quantum battery consisting of electron spin qubits

When the size of a system is reduced to the scale of single particles, classical thermodynamics fails to predict the system’s behaviour as quantum fluctuations come into play. Recently it has been proven by Binder et all. [1] that theoretically a quantum battery, consisting of qubits, can be charged faster (i.e. with higher power per qubit) when the qubits become entangled during the charging process. In this thesis such optimal charging is investigated for one specific type of quantum battery: an array of two identical electron spin qubits rotated by microwave radiation, coupled by nearest-neighbouring exchange interaction and considered in an environment without dissipation. As the wave function notation does not support environmental impact, the density matrix notation is used to describe the quantum dynamics of the driven electron spins. Solving the Von Neumann equation results in the solution describing the time evolution of such a quantum battery. This solution is used to calculate the extractable work; the result is an expression for extractable work which is not dependent on the exchange interaction. The reason for this independence is that exchange interaction couples two states which have the same energy level. Therefore, coupling qubits does not lead to faster charging of quantum battery. This conclusion is true for a quantum battery as defined before. For other assumptions entanglement could lead to optimal charging.

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