Nanofabrication for On-Chip Optical Levitation, Atom-Trapping, and Superconducting Quantum Circuits

Researchers have spent decades refining and improving their methods for fabricating smaller, finer-tuned, higher-quality nanoscale optical elements with the goal of making more sensitive and accurate measurements of the world around them using optics. Quantum optics has been a well-established tool of choice in making these increasingly sensitive measurements which have repeatedly pushed the limits on the accuracy of measurement set forth by quantum mechanics. A recent development in quantum optics has been a creative integration of robust, high-quality, and well-established macroscopic experimental systems with highly-engineerable on-chip nanoscale oscillators fabricated in cleanrooms. However, merging large systems with nanoscale oscillators often require them to have extremely high aspect-ratios, which make them extremely delicate and difficult to fabricate with an "experimentally reasonable" repeatability, yield and high quality. In this work we give an overview of our research, which focused on microscopic oscillators which are coupled with macroscopic optical cavities towards the goal of cooling them to their motional ground state in room temperature environments. The quality factor of a mechanical resonator is an important figure of merit for various sensing applications and observing quantum behavior. We demonstrated a technique for pushing the quality factor of a micromechanical resonator beyond conventional material and fabrication limits by using an optical field to stiffen and trap a particular motional mode of a nanoscale oscillator. Optical forces increase the oscillation frequency by storing most of the mechanical energy in a nearly loss-less optical potential, thereby strongly diluting the effects of material dissipation. By placing a 130 nm thick SiO₂ pendulum in an optical standing wave, we achieve an increase in the pendulum center-of-mass frequency from 6.2 to 145 kHz. The corresponding quality factor increases 50-fold from its intrinsic value to a final value of Q_m = 5.8(1.1) x 10⁵, representing more than an order of magnitude improvement over the conventional limits of SiO₂ for a pendulum geometry. Our technique may enable new opportunities for mechanical sensing and facilitate observations of quantum behavior in this class of mechanical systems. We then give a detailed overview of the techniques used to produce high-aspect-ratio nanostructures with applications in a wide range of quantum optics experiments. The ability to fabricate such nanodevices with high precision opens the door to a vast array of experiments which integrate macroscopic optical setups with lithographically engineered nanodevices. Coupled with atom-trapping experiments in the Kimble Lab, we use these techniques to realize a new waveguide chip designed to address ultra-cold atoms along lithographically patterned nanobeams which have large atom-photon coupling and near 4π Steradian optical access for cooling and trapping atoms. We describe a fully integrated and scalable design where cold atoms are spatially overlapped with the nanostring cavities in order to observe a resonant optical depth of d₀ ≈ 0.15. The nanodevice illuminates new possibilities for integrating atoms into photonic circuits and engineering quantum states of atoms and light on a microscopic scale. We then describe our work with superconducting microwave resonators coupled to a phononic cavity towards the goal of building an integrated device for quantum-limited microwave-to-optical wavelength conversion. We give an overview of our characterizations of several types of substrates for fabricating a low-loss high-frequency electromechanical system. We describe our electromechanical system fabricated on a Si₃N₄ membrane which consists of a 12 GHz superconducting LC resonator coupled capacitively to the high frequency localized modes of a phononic nanobeam. Using our suspended membrane geometry we isolate our system from substrates with significant loss tangents, drastically reducing the parasitic capacitance of our superconducting circuit to ≈ 2.5$ fF. This opens up a number of possibilities in making a new class of low-loss high-frequency electromechanics with relatively large electromechanical coupling. We present our substrate studies, fabrication methods, and device characterization.

Análise de guias de ondas pelos métodos vetorial magnético e dos elementos-finitos

Neste trabalho, é apresentada uma formulação apropriada à análise de guias de ondas eletromagnéticos, cobrindo do espectro de microondas até o da óptica. Nas regiões a partir do ultravioleta, os comprimentos de onda são equivalentes às dimensões atômicas e a formulação necessita de uma abordagem quântica, que não é considerada neste estudo. A formulação é fundamentada nos métodos vetorial magnético e dos elementos finitos (MEF), em meios não homogêneos, anisotrópicos e não dissipativos, embora a dissipação possa ser facilmente introduzida na análise. Deu-se preferência à formulação com o campo magnético em vez do elétrico, pelo fato do campo magnético ignorar descontinuidades elétricas. Ele é contínuo em regiões de permeabilidade homogênea, propriedade dos meios dielétricos em geral ( = 0), independente da permissividade dos respectivos meios, conquanto os campos elétricos sejam descontínuos entre regiões de permissividades diferentes.

Strong atom-light interactions along nanostructures: Transition from free-space to nanophotonic interfaces

An exciting frontier in quantum information science is the integration of otherwise "simple'' quantum elements into complex quantum networks. The laboratory realization of even small quantum networks enables the exploration of physical systems that have not heretofore existed in the natural world. Within this context, there is active research to achieve nanoscale quantum optical circuits, for which atoms are trapped near nano-scopic dielectric structures and "wired'' together by photons propagating through the circuit elements. Single atoms and atomic ensembles endow quantum functionality for otherwise linear optical circuits and thereby enable the capability of building quantum networks component by component. Toward these goals, we have experimentally investigated three different systems, from conventional to rather exotic systems : free-space atomic ensembles, optical nano fibers, and photonics crystal waveguides. First, we demonstrate measurement-induced quadripartite entanglement among four quantum memories. Next, following the landmark realization of a nanofiber trap, we demonstrate the implementation of a state-insensitive, compensated nanofiber trap. Finally, we reach more exotic systems based on photonics crystal devices. Beyond conventional topologies of resonators and waveguides, new opportunities emerge from the powerful capabilities of dispersion and modal engineering in photonic crystal waveguides. We have implemented an integrated optical circuit with a photonics crystal waveguide capable of both trapping and interfacing atoms with guided photons, and have observed the collective effect, superradiance, mediated by the guided photons. These advances provide an important capability for engineered light-matter interactions, enabling explorations of novel quantum transport and quantum many-body phenomena.

溶胶-凝胶光波导环形谐振腔的挥发性有机化合物传感特性

采用溶胶-凝胶法制作波导环形谐振腔, 讨论了环形谐振腔器件的传输特性。测量了在不同物质、不同体积分数的挥发性有机化合物(VOC)蒸气气氛下器件的传输光谱的敏感性。结果表明, 谐振波长随甲醇、乙醇、丙醇等醇类化合物, 以及丙酮、甲醛等蒸气体积分数的上升而向长波方向移动, 具有高的灵敏度, 且两者基本呈线性关系。其中, 对丙醇最敏感, 灵敏度达到1.403 pm/10-6。对甲烷和二甲苯也有微弱反应, 但是其灵敏度很低。也测量了水蒸气对传输谱特性的影响。观察到传输谱衬比度对不同挥发性有机化合物物质蒸气的不同敏

溶胶-凝胶条波导Sagnac环的乙醇蒸气传感特性

采用有机/无机混合溶胶-凝胶法制作条形光波导,并将条波导接入光纤Sagnac 环中,测量了输出光功率随环境气氛中乙醇蒸气体积分数变化的特性,表明在实验研究的范围内,输出信号与乙醇蒸气体积分数呈正弦变化。根据Sagnac环结构输出特性的基本关系,反映了溶胶-凝胶条波导在乙醇蒸气气氛下产生了双折射效应。观察到双折射相移与乙醇体积分数的亚线性关系。对实验数据拟合,计算了偏振相移的线性项和二次项系数,得到所制备的条波导的双折射对乙醇体积分数的响应为Δn≈4.4×10-2。测量了信号变化的时间演变特性,典型的上升和

长周期光纤光栅波导色散因子和有效折射率热光系数的测量

对串联的长周期光纤光栅(CLPFG)的透射谱特性进行了理论分析和实验研究。分析表明，长周期光纤光栅中纤芯模和包层模之间的马赫-曾德尔干涉效应导致在长周期光纤光栅谐振峰内的梳状滤波结构特性；其峰值位置和峰间距同串联区光纤的长度以及光纤的波导色散因子有关。测量了长周期光纤光栅的透射谱，并研究了其温度特性。根据测量数据，得到对应于1554nm波长处，所用单模光纤HE14模的波导色散因子γ为0．874；纤芯／包层有效折射率差的热光系数为4．8×10^-5℃^-1。并对这一测试方法和结果，以及长周期光纤光栅的应用进

Analysis of a second-order polarization-independent filter made of a single ring resonator and a Sagnac interferometer

A novel second-order polarization-independent filter made of a single ring resonator and a Sagnac interferometer (SRRSI) is proposed, and its filtering characteristics are investigated. By using birefringence in waveguide, a single ring resonator can be used to synthesize a filter with second-order response. Analytical formulas are derived for characteristics of the SRRSI varied with waveguide parameters.. such as the coupling coefficient; and the critical condition of a second-order Butterworth filter is given. The influence of loss in the ring resonator is also analyzed. (c) 2005 Elsevier B.V. All rights reserved.

有源波导环形谐振腔滤波特性分析

将掺铒有源波导材料引入环形谐振腔结构，从理论上分析了有源波导环形谐振腔的滤波特性。结果表明由于抽运光提供的增益补偿了腔内损耗，使得环形谐振腔满足临界耦合条件，实现对信号光的最佳陷波，同时发现通过改变抽运光功率，可以对精细度和带宽进行动态调谐。分析了铒离子掺杂浓度、信号光功率以及抽运光耦合系数对最佳陷波抽运功率的影响，为有源波导器件设计制作提供了理论依据。

平面弯曲波导耦合器的特性分析

根据耦合模理论和弯曲波导耦合器的结构特点,对平面弯曲波导耦合器的特性进行了分析,结果表明弯曲波导耦合器的弯曲半径和最小间距两个可调变量,增加了波导器件设计的灵活性;同时由于等效耦合长度的调制作用使得弯曲波导耦合器在波分复用/解复用中比平行直波导耦合器具有更大的复用带宽;分析了弯曲半径和最小间距对弯曲波导耦合器复用带宽的影响,为实际波导器件的设计制作提供了一定的理论依据.

低损耗有机无机混合溶胶凝胶波导的实验研究

利用有机无机混合的溶胶凝胶方法在硅基底上制备波导薄膜．采用正硅酸四乙酯和苯基三乙氧基硅烷作为反应先驱物，利用旋涂的方法成膜，对其折射率，传输损耗以及条形波导的光刻、刻蚀特性进行了研究．测量了波导薄膜折射率随成分变化的关系．实验表明，该方法工艺简单，可以获得具有较低损耗的波导薄膜．测试得到632．8nm波段的损耗系数为0．23dB／cm．采用ICP刻蚀工艺获得了较为平整的条形波导．

利用有机-无机溶胶-凝胶方法制备平面波导环形谐振腔

采用简单的有机一无机混合的溶胶一凝胶方法制备了折射率在一定范围内可调的波导材料，并利用其制备了平面波导环形谐振腔器件。波导结构呈现倒脊形，其制备工艺首先是利用感应耦合等离子体刻蚀技术（ICP）在二氧化硅衬底上刻蚀波导结构的凹槽，然后再沉积波导薄膜。利用光谱仪对器件的传输特性进行了测量，观测到具有10dB对比度，自由光谱范围0．182nm周期性谐振现象，结合环形谐振腔的传输特性，得到环形腔具有较低的传输损耗1．7dB／cm。同时对环形谐振腔的温度特性进行了测量，得出波导材料的热光系数为-1．54×10^-4

一种离子交换制备的玻璃光波导谐振腔滤波器

采用AgNO3、KNO3混和熔盐作为离子交换源，在K9玻璃上制备了跑道形谐振腔滤波器。测试得到该滤波器的自由光谱范围为0．178nm，两个输出端口的衬比度分别为1．47dB和6．5dB，分析得到耦合器的分束比和谐振腔的传输损耗分别为κ=0．16和α=8．1dB／cm。利用热光效应在16℃的温度变化范围内，滤波器实现了2π的相位调制，同时分析得到波导材料的热光系数约为1．28×10^-5／℃。

利用离子交换技术制备跑道形波导谐振腔滤波器的研究

采用AgNO3和KNO3混和熔盐作为离子交换源，在K9玻璃上制备了跑道形波导谐振腔滤波器。利用ASE宽带光源和光谱仪对器件特性进行了测试，得到的该滤波器自由光谱范围为0．176nm。对比对Cr=4dB和3dB带宽δλ=0.13nm来说，耦合系数和传输损耗分别为κ=0．9和α=3．2dB／cm。测试了环形腔的热光调相特性，在16℃的变化范围内实现了2π的相移。通过分析，波导材料的热光系数约为1．49×10^-5/C。该滤波器不仅可用于滤波、传感等领域，而且也可与其它波导结构相结合实现新的功能。

跑道形玻璃波导谐振腔滤波器的研制

采用Ag^＋-Na^＋离子工艺，在K9玻璃上制备了跑道形波导谐振腔滤波器．测试得到该滤波器自由光谱范围为FSR=0．177nm，对比对为Cr=7．5dB．同时分析得到耦合器的耦合系数为κ=0．916，耦合器和环形腔的损耗因子分别为δ=0．55，γ=0．48．耦合器的两波导几乎相连、条波导边缘不规则和一次离子交换波导表面缺陷是造成该波导滤波器具有较大损耗的主要原因。通过改进工艺技术降低波导损耗，该滤波器可以用于光通信、传感等领域，也可与其它波导结构相结合实现新的功能。

The resolution of the thermodynamic paradox and the theory of guided wave propagation in anisotropic media

The resolution of the so-called thermodynamic paradox is presented in this paper. It is shown, in direct contradiction to the results of several previously published papers, that the cutoff modes (evanescent modes having complex propagation constants) can carry power in a waveguide containing ferrite. The errors in all previous “proofs” which purport to show that the cutoff modes cannot carry power are uncovered. The boundary value problem underlying the paradox is studied in detail; it is shown that, although the solution is somewhat complicated, there is nothing paradoxical about it.

The general problem of electromagnetic wave propagation through rectangular guides filled inhomogeneously in cross-section with transversely magnetized ferrite is also studied. Application of the standard waveguide techniques reduces the TM part to the well-known self-adjoint Sturm Liouville eigenvalue equation. The TE part, however, leads in general to a non-self-adjoint eigenvalue equation. This equation and the associated expansion problem are studied in detail. Expansion coefficients and actual fields are determined for a particular problem.