Cavity-Heisenberg spin- <i>j</i> chain quantum battery and reinforcement learning optimization

Abstract In the realm of quantum batteries (QBs), model construction and performance optimization are central tasks which can be addressed by exploiting machine learning algorithms. Here, we propose a cavity-Heisenberg spin chain QB model with spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>j</mml:mi> <mml:mtext> </mml:mtext> <mml:mo stretchy="false">(</mml:mo> <mml:mi>j</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> and investigate the charging performance under both closed and open quantum cases, considering spin–spin interactions, ambient temperature, and cavity dissipation. By employing a reinforcement learning (RL) algorithm to modulate the cavity-battery coupling, we further optimize the QB performance, enhancing the charging capability of the spin chain. It is shown that the charging energy and the power of the QB are significantly improved with the spin size. In particular, the use of a RL algorithm in case of large spin <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>j</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> in presence of cavity losses allows for more stability in the optimization of the cavity-spin coupling strength, which in perspective makes an experimental realization more feasible. We analyze the optimization mechanism and find an intrinsic relationship between cavity-spin entanglement and charging performance: while in the closed-system scenario the charging energy increases together with the cavity-spin entanglement, in the open-system scenario the increase of the charging energy can be accompanied by a decrease of entanglement. Our results provide a possible scheme for design and optimization of QBs.