摘要
概括地说,量子腔光力系统能够为量子操控机械振子提供普适的工具。随着制造工艺的提高,光力系统的振子装置已经可以覆盖很大地参数范围,例如机械频率从几个赫兹到109赫兹,质量从10-20克到千克量级。从基础研究角度来看,腔光力系统为确定以及操控真正宏观物体的量子态提供了有力的方案,并且有助于实现对量子力学产生深刻认识的实验；从实际应用的角度来看,量子腔光力学技术在光学和微波频域内都会提供接近量子力学极限的运动和力的精细测量。因此腔光力学的量子操控要求机械振子处于或者接近于其量子基态。此外光力系统的压缩效应不仅是宏观物体的一种量子基本特征,同时还是实现超过标准量子极限的位置和力测量的关键,例如构建下一代的引力波观测仪器。近年来研究光力系统中机械振子的制冷以及压缩效应成为研究的热点。
鉴于光力系统中机械振子冷却以及压缩的重要性,本文的主要研究动机就是如何寻找到更好的方法来提高和改善机械振子的冷却结果以及获得振子运动更好的压缩结果。我们首先提出了一个快速的光力系统基态冷却机制,它与广泛研究并在实验上实现的边带冷却方案不同,边带冷却机制中的冷却过程会受到腔场的低耗散速率以及与失谐量相比弱的驱动强度的制约。我们的理论模型由双模光学腔以及并在腔内放置1/4玻片构成。两个腔模的偏振方向相互垂直,其中一个腔模的光子能快速的耗散到腔外而另一个腔模的光子以很慢的速率耗散到腔外,并且两个腔模通过1/4玻片产生线性混合相互作用。在弱耦合条件下我们将腔场绝热消除得到振子的运动主方程。结果,我们发现振子的制冷过程主要由通过快速耗散通道的散射作用决定,与resolved-sideband光力冷却机制相比较,制冷速率明显地提高。同时,利用两个腔模通过1/4玻片产生的线性混合作用,加热过程能发生相消量子干涉现象,加热速率能明显地被抑制。
最近理论上提出了一类新的腔光力系统：耗散型光力系统即振子的运动会同时改变腔场的共振频率以及腔模的线宽,并且在微波频域的实验中得到了研究。在光学频域内一类等效的耗散型光力系统也在理论研究上被提了出来并发现利用量子噪声的相消干涉效应能够得到机械振子的基态。我们采用这类耗散型光力系统来研究机械振子的压缩效应。通过对光腔场中注入压缩真空库以及相干驱动激光场,来产生振子运动的压缩态。我们首先依据库理论,推导出腔—振子系统的主方程。当振子与腔场之间的耦合较弱时,我们发现如果将腔场绝热消除掉,利用量子噪声的干涉效应,腔场能等效地表示为振子运动的压缩真空库。因此,在耗散光力系统中,压缩能有效地从光场转移到振子运动。此外,当振子与腔场的耦合达到中等强度时,通过解腔-振子系统的主方程,我们发现光子的激发能抑制量子干涉效应,导致振子的运动偏离了理想的压缩态。
同样是在耗散型光力系统中我们采用了另外一种不同的方法来制备振动振子的运动压缩态。通过利用一束强的相干驱动激光场以及两束周期性调制的光场来驱动光学谐振腔,首先将噪声库绝热消除得到腔-振子系统的主方程,然后我们同样采用对系统的动力学过程进行线性化处理的方法,即假设系统中的每一个算符可以表示为其平均值以及一个涨落分量的和,来分析振子运动的量子压缩特性。采用密度矩阵的方法我们分析了相空间中腔场和振子变量的半经典运动方程,然后通过将主方程线性化,求解腔场—振子系统主方程。我们数值计算了振子运动量子涨落的方差,发现振子能够在基态附近实现压缩态。另外,我们通过将腔场绝热消除,得到振子运动的主方程,同样计算了振子运动的涨落的方程,发现近似解析结果与数值计算的结果吻合。因此在调制激光场驱动的耗散型光力系统中,利用量子噪声的干涉效应,制冷效果不受resolved-sideband机制的限制,得到的压缩态比较稳定,对热噪声也更具有抗干扰性。
前面几章介绍的腔光力系统中需要利用强激光场相干增强腔场与振子之间光力耦合强度以及线性化处理,腔光力相互作用为线性的。但是,内秉光力相互作用本身是非线性的,并且随着实验和技术的发展,人们正在趋近于这类内秉非线性相互作用。本章中我们研究了在单光子强耦合腔光力系统中利用三色激光场驱动腔场,镜子的运动态可以演化至暗态同时腔场处于真空模式。镜子运动态与腔场模式之间以及腔场模式与外驱动激光场之间完全退耦合。在单光子平移表象中,通过调节驱动激光场的三个频率成分使其分别与携载、红边带和蓝边带跃迁共振,镜子运动暗态会呈现出非经典性质,例如当系统处在Lamb-Dicke区内,振子运动态为压缩相干态，在Lamb-Dicke区外,振子运动态变为压缩的非高斯态。
最后,我们给出了我们研究内容的总结并且对相关的研究问题提出了一些展望。
Broadly speaking, quantum optomechanics provides a universal tool to achieve the quan-tum control of mechanical motion. With the advancement of fabrication technology, it does that in devices spanning a vast range of parameters, with mechanical frequencies from a few Hertz to GHz, and with masses from10-20g to several kilos. At a fundamental level, it offers a route to determine and control the quantum state of truly macroscopic objects and paves the way to experiments that may lead to a more profound understanding of quantum mechanics; and from the point of view of applications, quantum optomechanical techniques in both the optical and microwave regimes will provide motion and force detection near the fundament limit imposed by quantum mechanics. Optomechanical quantum control requires the mechanical oscillator to be in or near its quantum ground state. Moreover, optomechanical squeezing is not only a fun-damental feature of quantum character of macroscopic objects but also critical for surpassing standard quantum limits on position and force sensing, and for constructing the next generation of gravitational-wave observatories. Therefore, nowadays the investigations of optomechanical cooling and squeezing of mechanical oscillators become a research focus.
Our research motivations are mainly based on how to find the methods to improve the mechanical cooling performance and achieve better squeezing of mechanical motion. We first propose a fast ground-state optomechanical cooling scheme compared with the widely imple-mented resolved-sideband regime, where the cooling process is limited by small damping rate of the cavity field and small driving strength with respect to the detuning. Our model is con-sisted of a two-mode optical cavity with a quarter-wave plate inside. Two cavity modes are orthogonally polarized, and one cavity mode dissipates to the external environment at a fast rate while the other dissipates at a slow rate. The quarter-wave plate provides linear mixing interaction between these two cavity modes. We adiabatically eliminate the cavity variables in the weak coupling limit and find that the cooling process for the oscillator is dominated by scattering process via the fast-decay channel, which is significantly enhanced as compared with that obtained in the resolved-sideband optomechanical cooling scheme. Meanwhile, the heating process is significantly suppressed by exploiting the destructive quantum interference between the two cavity modes with the help of the quarter-wave plate.
Recently a new type of optomechanics:dissipative optomechanics in which the oscillating mirror modulates both the resonance frequency and the linewidth of the cavity mode, is theoret-ically proposed and experimentally investigated in microwave domain. An effective dissipation optomechanics in optical domain has already theoretically investigated to achieve the ground s- tate cooling of oscillator via utilizing the completely destructive interference of quantum noise. We investigate the generation of squeezed states in a movable mirror in dissipation optome-chanics. Via feeding broadband squeezed-vacuum light accompanying a coherent driving laser field into the cavity, the master equation for the cavity-mirror system is derived by following the general reservoir theory. When the mirror is weakly coupled to the cavity mode, we find that the driven cavity field can effectively perform as a squeezed-vacuum reservoir for the movable mirror via utilizing the completely destructive interference of quantum noise. Efficient trans-fer of squeezing from the light to the movable mirror occurs, irrespective of the ratio between the cavity damping rate and the mechanical frequency. Moreover, when themirror is moder-ately coupled to the cavity mode, photonic excitation can preclude the completely destructive interference of quantum noise. As a consequence, the mirror deviates from the ideal squeezed state.
Alternatively we investigate another method to generate the squeezed state of the mirror motion in a dissipative optomechanical system via driving the optical resonator with a strong laser field accompanied with two periodically-modulated lights. We also proceed the lineariza-tion method on the quantum dynamics to analyze the squeezing of oscillator motion, i.e., as-suming that each operator in the system can be written as the sum of its mean value and a small fluctuation. Using the density operator approach we calculate the variances of quantum fluctu-ations around the classical orbits, and then analyze the quantum behavior of the system around the classical value. Both the numerical and analytical results predict that the squeezed state of the mirror motion around its ground state is achievable. Moreover, the obtained squeezed state is robust against the thermal noise because of the strong cooling effect outside the resolved-sideband regime, which arises from the destructive interference of quantum noise.
At last we summerize our research contents and present some outlooks on the research topic.
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