标题： 增强反馈的参数谐振器中波动的压缩或冷却 显示英文标题

标题： Feedback-enhanced squeezing or cooling of fluctuations in a parametric resonator

摘要： 在这里，我们分析了超越单自由度参量谐振器的$-6$~dB 极限的深亚阈值参量压缩波动的方法。 实现这一目标的一种方法是通过锁相放大器反馈回路。 首先，我们计算了加入交流信号后的相位依赖性参量放大与反馈。 在一种方法中，我们使用平均法来获得放大增益，而在第二种方法中，我们使用谐波平衡法来获得带有反馈的参量放大器的交流响应。 在后一种方法中，反馈与一个积分项成正比，该积分项模拟了锁相放大器的余弦分量输出，并乘以与锁相放大器相同频率的正弦波。 我们发现，当积分项的积分时间跨度为频率周期的整数倍时，这两种方法得到的增益是相同的。 当这种情况不成立时，我们可以获得显著的衰减。 最后，我们分析了由这种积分微分模型描述的带有反馈的参量谐振器对附加白噪声在频域中的响应。 利用这个模型，我们除了计算压缩外，还计算了带有反馈的谐振器中的噪声谱密度。 可以获得非常强的压缩或冷却。 显示英文摘要

摘要： Here we analyse ways to achieve deep subthreshold parametric squeezing of fluctuations beyond the $-6$~dB limit of single degree-of-freedom parametric resonators. One way of accomplishing this is via a lock-in amplifier feedback loop. Initially, we calculate the phase-dependent parametric amplification with feedback of an added ac signal. In one approach, we use the averaging method to obtain the amplification gain, while in the second approach, we obtain the ac response of the parametric amplifier with feedback using the harmonic balance method. In this latter approach, the feedback is proportional to an integral term that emulates the cosine quadrature output of a lock-in amplifier multiplied by a sine at the same tone of the lock-in. We find that the gain obtained via these two methods are the same whenever the integration time span of the integral is a multiple of the tone period. When this is not the case, we can obtain considerable deamplification. Finally, we analyse the response of the parametric resonator with feedback, described by this integro-differential model, to an added white noise in the frequency domain. Using this model we were able to calculate, in addition to squeezing, the noise spectral density in this resonator with feedback. Very strong squeezing or cooling can be obtained.