Sampaio Rui, Suomela Samu, Ala-Nissila Tapio
COMP Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland.
Department of Physics, P.O. Box 1843, Brown University, Providence, Rhode Island 02912-1843, USA.
Phys Rev E. 2016 Dec;94(6-1):062122. doi: 10.1103/PhysRevE.94.062122. Epub 2016 Dec 15.
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.
最近有人提出量热测量作为一种很有前景的技术，用于测量耗散超导量子比特中的热力学量。这些测量依赖于这样一个事实，即每当系统与环境交换能量时，系统就会投影到能量本征态。这一要求对可以用这种方式测量的系统类别施加了限制。在这里，我们将量热协议扩展到驱动量子谐振子中功的测量。我们采用基于双能级近似的方案，该方案利用了一个实验上可获取的量，并展示了它与通过标准双测量协议获得的功之间的关系。我们发现，对于短驱动时间，在欠阻尼 regime 中平均功得到了很好的近似，而在过阻尼 regime 中，对于任何驱动时间都是如此。然而，对于有限温度下功的方差和更高阶矩，这种近似失效。此外，我们展示了如何将通过该方案获得的功统计与双测量协议给出的功统计联系起来。
