超越Born和Markov近似的纳机电系统中的动量和位置检测
Momentum and position detection in nanoelectromechanical systems beyond Born and Markov approximations
摘要：
我们提出并分析了不同的方案来探测纳米机电系统（NEMS）的量子性质的隧道结探测器。使用Keldysh技术，我们能够调查的动态组合系统的任意比例的$eV/\hbar Ω$，其中V是所施加的隧道结的偏压和$Ω$的振荡器的本征频率。在这个意义上说，我们超越了马尔可夫近似以前的作品，这些参数被限制到政权$eV/\hbar Ω\gg 1$。此外，我们还超越了玻恩近似，因为我们计算了隧道结的有限频率电流噪声高达四阶的隧道振幅。有趣的是，我们发现了不同的方法来探测NEMS的位置和动量属性。一方面，对于非稳态振荡器，我们发现隧道结的噪声是有限频率的。通过分别分析这种噪声的实部和虚部，我们得出结论，一个简单的隧道结探测器可以探测基于位置和动量的非平稳振荡器的可观测量。另一方面，对于固定振荡器，需要基于Aharonov-Bohm环隧道结检测器的更复杂的设置。它仍然允许我们提取振子的位置和动量信息。对于这种类型的探测器，我们分析了第一次会发生什么，如果能量尺度$eV$，$\hbar Ω$，和$k_B T$采取任意值相对于彼此，其中T是一个外部热浴的温度。在这种情况下，我们证明了通过有限频率的噪声测量来唯一识别振子的量子态是可能的。
英文摘要：
We propose and analyze different schemes to probe the quantum nature of nanoelectromechanical systems (NEMS) by a tunnel junction detector. Using the Keldysh technique, we are able to investigate the dynamics of the combined system for an arbitrary ratio of $eV/\hbar Ω$, where V is the applied bias of the tunnel junction and $Ω$ the eigenfrequency of the oscillator. In this sense, we go beyond the Markov approximation of previous works where these parameters were restricted to the regime $eV/\hbar Ω\gg 1$. Furthermore, we also go beyond the Born approximation because we calculate the finite frequency current noise of the tunnel junction up to fourth order in the tunneling amplitudes. Interestingly, we discover different ways to probe both position and momentum properties of NEMS. On the one hand, for a non-stationary oscillator, we find a complex finite frequency noise of the tunnel junction. By analyzing the real and the imaginary part of this noise separately, we conclude that a simple tunnel junction detector can probe both position- and momentum-based observables of the non-stationary oscillator. On the other hand, for a stationary oscillator, a more complicated setup based on an Aharonov-Bohm-loop tunnel junction detector is needed. It still allows us to extract position and momentum information of the oscillator. For this type of detector, we analyze for the first time what happens if the energy scales $eV$, $\hbar Ω$, and $k_B T$ take arbitrary values with respect to each other where T is the temperature of an external heat bath. Under these circumstances, we show that it is possible to uniquely identify the quantum state of the oscillator by a finite frequency noise measurement.
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