Abstract

The quantum version of Jarzynski equality was theoretically investigated for the work operator in the interaction picture. Since the Hamiltonian is time-dependent, it does not commute with itself at different times, then we have solved analytically its dynamics with lie-algebraic techniques. The physical object is a superconducting optical cavity. It was shown that the quantum dynamics of a cavity does not obey Jarzynski’s equality in the small temperature regime \((\beta \omega _0 \hbar \gg 1)\), if we consider a quantum work operator defined in a protocol interaction picture. The case of higher temperatures \((\beta \omega _0 \hbar \ll 1)\) we are in Jarzynski regime and Jarzynski equality can be used to obtain statistical information about work done on the cavity. Since, for all used parameters, the state is a thermal state and its dynamics is of the harmonic oscillator, then this quantum regime is related to the protocol action. The protocol can be implemented by injecting a field in the cavity, thus it creates quantum resources.

Graphic Abstract

中文翻译：

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超导光学腔的量子Jarzynski不等式

摘要

从理论上研究了相互作用图中工作算符的Jarzynski等式的量子形式。由于哈密顿量是与时间有关的，因此它不会在不同的时间与自己通勤，因此我们已经使用谎言代数技术解析地解决了它的动力学问题。物理对象是超导光学腔。结果表明，如果我们考虑在协议交互图中定义的量子功算子，则在小温度范围\（（\ beta \ omega _0 \ hbar \ gg 1）\）中，腔的量子动力学不服从Jarzynski的等式。。温度较高的情况\（（\ beta \ omega _0 \ hbar \ ll 1）\）我们处于Jarzynski政权下，可以使用Jarzynski相等性来获得有关在型腔上完成的工作的统计信息。因为对于所有使用的参数，状态是热状态，其动力学是谐波振荡器的状态，所以这种量子状态与协议行为有关。该协议可以通过在腔中注入一个场来实现，从而创建量子资源。

图形摘要