光力系统利用光子碰撞镜子等方法，以辐射压的方式实现了光场与机械振子之间的动力学耦合。通常情况下这种耦合是非常微弱的，这也是为什么我们在生活中难以察觉光的辐射压力的原因。谐振腔的引入大大增强了耦合的强度，但是要在实验中要探测单个光子辐射压仍然是非常困难的。一方面是由于这种耦合实在是太过于微弱，引起的辐射压效应在数值上很小。而在另一方面，量子理论中的存在的量子涨落现象，也对辐射压的探测精度施加了限制。按照一般的实验条件估算，在单个光子撞击镜子并反射的情形下，引起的镜子振动的最大振幅值在{{10}^{-8}x_{zpf}-10}^{-6}x_{zpf}之间，其中x_{zpf}为基态下镜子振幅的量子涨落。而在引入谐振腔的情形下，最大振幅值也不会超过x_{zpf}的范围。
鉴于上述原因，本文提出了一种单光子的光力放大理论模型，实现了单光子辐射压的放大。我们假设利用激光冷却的方法，使机械振子的初始时处于基态，然后利用单光子与机械振子的碰撞产生动力学耦合。所不同的是我们采用了形如(\left|1\ket_A\right|0\ket_B+\left|0\ket_A\right|1\ket_B)/\sqrt2的单光子态，也就是将机械振子放置在了一个马赫-曾德尔干涉仪中。由于光子的非局域性质，从经典力学的视角看来，镜子处于一种类似于受迫运动的状态中。而从量子力学的视角看来，经过时间演化之后的机械振子会从基态演变成叠加态。如果我们对光子的Fock态空间，引入后选择(\left|1\ket_A\right|0\ket_B-e^{i\theta}\left|0\ket_A\right|1\ket_B)/\sqrt2。那么在特定时间测量机械振子的振幅，我们可以得到超出基态量子涨落x_{zpf}的振幅值。
在强耦合的情况下，获得这种超出量子涨落的振幅值是很自然的一件事。但是在弱耦合的情况下，出现这种结果是很不寻常的。我们在理论上证明，这种有趣的现象出现的原因，与阿哈罗诺夫（Aharonov）等人提出的弱测量（Weak-Measurement）理论有关。人为引入的后选择，放大了相互作用哈密顿量中的参数。因此可以等价地认为，耦合强度被放大了。因此在弱耦合的条件下，我们实现了单光子辐射压的放大。

 

The opto-mechanical system realizes the dynamic coupling between the optical field and the mechanical oscillator in the form of radiation pressure by means of photons colliding with mirrors. Usually, the coupling strength is very weak, which is why it is difficult for us to detect the radiation pressure of light in our life. The introduction of the resonant cavity greatly enhances the coupling strength, but it is still very difficult to detect single-photon radiation pressure in the current experiments. On the one hand, because the coupling strength is too weak, the radiation pressure effect is small in value. On the other hand, the existence of quantum fluctuations in quantum theory also imposes limitations on the detection accuracy of radiation pressure. According to the general experimental conditions, when a single photon hits the mirror and is reflected, the maximum amplitude of the mirror is about {{10}^{-8}x_{zpf}-10}^{-6}x_{zpf} , where x_{zpf} is the quantum fluctuation of the amplitude of the ground state of the mirror. In the case of containing a resonant cavity, the maximum amplitude value does not exceed the range of x_{zpf} either.
In view of the above reasons, a theoretical model of single-photon opto-mechanical amplification is proposed in this paper, which realizes the amplification of single-photon radiation pressure effect. We assume that the mechanical oscillator is initially at the ground state by means of laser cooling, and then the dynamic coupling is generated by the collision of a single photon with the mechanical oscillator. The difference is that we use a single photon whose quantum state is (\left|1\ket_A\right|0\ket_B+\left|0\ket_A\right|1\ket_B)/\sqrt2,which means placing the mechanical oscillator in a Mach-Zehnder interferometer. Due to the non-local nature of photons, the mirror is in a state similar to forced motion from the perspective of classical mechanics. From the perspective of quantum mechanics, the mechanical oscillator will evolve from the ground state to the superposition state after time evolution. If in the Fock state space of the photon, we have the post-selection (\left|1\ket_A\right|0\ket_B-e^{i\theta}\left|0\ket_A\right|1\ket_B)/\sqrt2. Then we can get the amplitude value beyond the ground state quantum fluctuation x_{zpf} at a specific time.
In the case of strong coupling, it is natural to obtain such amplitude values beyond quantum fluctuations. But in the case of weak coupling, this result is quite unusual. We theoretically prove that the reason for this interesting phenomenon is related to the Weak-Measurement theory proposed by Aharonov et al. The artificially introduced post-selection amplifies the parameters in the interacting Hamiltonian. It can therefore be considered equivalently that the coupling strength is amplified. Therefore, under the condition of weak coupling, we realize the amplification of single-photon radiation pressure effect.