Thermal noise computation in gravitational wave interferometers from first principles

We propose a universal method of computation of thermal noise in mirrors of gravitational wave interferometers based on first principles. We imagine a situation where a mirror is part of a Fabry–Perot cavity. The movement of the mirror's surface produces variation of the eigen frequency of the cavity, which is computed by evaluating the variation of the energy stored in cavity. We consider two particular examples: first, the thermal noise from a dielectric slab inside the Fabry–Perot cavity, and second, the polarization-dependent thermal noise in the folded cavity.     

Experimental study of the thermal noise of mirrors with an inhomogeneous loss used in gravitational wave detectors

Our recent theoretical research [Phys. Lett. A 305 (2002) 18] showed that the actual thermal noise of mirrors with an inhomogeneous loss in interferometric gravitational wave detectors is largely different from the traditional evaluation by modal expansion. We have tested this prediction experimentally using an oscillator similar to a mirror. The experimental result was consistent with our previous Letter.     

Diamagnetic levitation of a milligram-scale silica using permanent magnets for the use in a macroscopic quantum measurement

Verification of macroscopic quantum mechanics requires that the position measurement accuracy of mirrors of various mass scales reach the Standard Quantum Limit (SQL) derived from Heisenberg's uncertainty principle. At mg-scale, thermal noise of the suspension wire of the mirror is an issue to reach the SQL. We propose to use a magnetic levitation system consisting of permanent magnets and yokes, noting the fact that a silica mirror is diamagnetic, and have succeeded in the experimental verification to levitate a 0.1-1 mg silica mass. This is the first demonstration of the levitation system with this mass scale and this magnetic susceptibility scale using permanent magnets as far as we know. We also estimated major noise sources for a 0.1 mg silica mirror and found the noise level to be lower than the SQL at 400 Hz-18 kHz. In conclusion, the levitation system of a mg-scale mirror for the use in a macroscopic quantum measurement was realized.     

Cryogenics and Einstein Telescope

The dominant noises which limit the present sensitivity of the gravitational wave detectors are the thermal noise of the suspended mirrors and the shot noise. For the third generation of gravitational wave detectors as the Einstein Telescope (ET), the reduction of the shot noise implies to increase the power stored in the detector at 1 MW level and, at the same time, to compensate the huge optic distortion due to induced thermal lensing. At low temperature it is possible to reduce both these effects. However, lowering the temperature of the test masses without injecting vibration noise from the cooling system is a technological challenge. We review here the thermal noise impact on the ultimate ET sensitivity limit and we discuss possible cryogenic configurations to cool the mirror.     

Optimizing X‐ray mirror thermal performance using matched profile cooling

To cover a large photon energy range, the length of an X‐ray mirror is often longer than the beam footprint length for much of the applicable energy range. To limit thermal deformation of such a water‐cooled X‐ray mirror, a technique using side cooling with a cooled length shorter than the beam footprint length is proposed. This cooling length can be optimized by using finite‐element analysis. For the Kirkpatrick–Baez (KB) mirrors at LCLS‐II, the thermal deformation can be reduced by a factor of up to 30, compared with full‐length cooling. Furthermore, a second, alternative technique, based on a similar principle is presented: using a long, single‐length cooling block on each side of the mirror and adding electric heaters between the cooling blocks and the mirror substrate. The electric heaters consist of a number of cells, located along the mirror length. The total effective length of the electric heater can then be adjusted by choosing which cells to energize, using electric power supplies. The residual height error can be minimized to 0.02 nm RMS by using optimal heater parameters (length and power density). Compared with a case without heaters, this residual height error is reduced by a factor of up to 45. The residual height error in the LCLS‐II KB mirrors, due to free‐electron laser beam heat load, can be reduced by a factor of ～11 below the requirement. The proposed techniques are also effective in reducing thermal slope errors and are, therefore, applicable to white beam mirrors in synchrotron radiation beamlines.     

Enhanced excess noise in laser cavities with tilted mirrors

Enhancement of the transverse excess-noise factor is theoretically predicted in optical laser cavities with tilted end mirrors and nonuniform transverse loss. In particular, it is shown that in a loss-guided laser close to the plane-plane geometric instability boundary the excess-noise factor that is induced by mirror tilting may largely exceed that predicted for the aligned cavity. This excess noise is related to beam walk-off induced by mirror tilting, which makes possible transient amplification of noise in the transverse plane.     

激光器腔镜夹持方式对热变形的影响

 分析了当前大功率激光器腔镜采用的几种夹持方式特点，采用有限元软件计算了腔镜不同夹持方式下的镜面热变形和镜体最大应力，并对两种夹持方式下的应力破坏进行了分析。发现夹持方式对大功率激光器腔镜镜面变形影响很大，镜体边界沿径向固定的压圈法效果优于沿轴向固定的弹性压板法。     

Interferometers for displacement-noise-free gravitational-wave detection

We propose a class of displacement- and laser-noise-free gravitational-wave-interferometer configurations, which does not sense nongeodesic mirror motion and laser noise, but provides a nonvanishing gravitational-wave signal. Our interferometers consist of four mirrors and two beam splitters, which form four Mach-Zehnder interferometers. By contrast to previous works, no composite mirrors with multiple reflective surfaces are required. Each mirror in our configuration is sensed redundantly, by at least two pairs of incident and reflected beams. Displacement- and laser-noise-free detection is achieved when output signals from these four interferometers are combined appropriately. Our 3-dimensional interferometer configuration has a low-frequency response proportional to f2, which is better than the f3 achievable by previous 2-dimensional configurations.     

Influence of polarization and material on Brownian thermal noise of binary grating reflectors

Grating reflectors are a potential low-noise replacement for amorphous multilayer mirrors. We investigate the influence of polarization and refractive index on Brownian thermal noise of binary grating reflectors using Maxwell's stress tensor. Our results demonstrate that the refractive index of the grating material is a critical parameter for thermal noise in these structures. In contrast to multilayer mirrors, a low coating thickness does not necessarily lead to a low thermal noise amplitude for structures with low refractive index. We find that an improved noise performance of grating reflectors requires materials of refractive index ?2.5. We present a factorized expression for the thermal noise of grating reflectors made of arbitrary materials by simply scaling the noise amplitude with the related material parameters.     

Large intensity noise from symmetric low-Q cavity semiconductor lasers driven with pump-noise-suppressed current injection in the high-pump regime

We have measured the intensity noise from symmetric low-Q cavity laser diodes (LD's) operated far above threshold in a constant-current mode. The single-sided output noise exhibits significant dependence on the mirror reflectivities of the laser cavity, in good agreement with the theoretical predictions based on a quantum-mechanical traveling-wave analysis. In an antireflection-coated LD with a residual mirror reflectivity of 5%, intensity noise as large as 9 dB above the shot-noise level was observed at a pumping rate of 10 times the threshold. This is caused by amplification of the vacuum-field fluctuations coupled by the low-reflectivity mirrors into the laser cavity.     

Reducing thermal noise in future gravitational wave detectors by employing Khalili etalons

Reduction of thermal noise in dielectric mirror coatings is a key issue for the sensitivity improvement in the second and third generation interferometric gravitational wave detectors. Replacing an end mirror of the interferometer by an anti-resonant cavity (a so-called Khalili cavity) has been proposed to realize the reduction of the overall thermal noise level. In this article we show that the use of a Khalili etalon, which requires less hardware than a Khalili cavity, yields still a significant reduction of thermal noise. We identify the optimum distribution of coating layers on the front and rear surfaces of the etalon and compare the total noise budget with a conventional mirror. In addition we briefly discuss advantages and disadvantages of the Khalili etalon compared with the Khalili cavity in terms of technical aspects, such as interferometric length control and thermal lensing.     

300mm平面标准镜装卡结构的关键参数

为了实现大口径平面标准镜的高精结构装卡,对其在重力作用下的面形变化进行了研究。首先,对结构胶的有限元建模进行了理论分析,建立了大口径平面标准镜胶结装卡结构有限元模型。然后,分析了不同胶点数量及分布、不同胶接面积以及不同镜框支撑方式等关键结构参数对参考面面形的影响。最后,设计了大口径平面标准镜胶结及支撑的结构。结果表明,采用胶点直径为5 mm,12×3胶点分布形式胶结时,参考面面形的PV值为24.06 nm,RMS值为6.78 nm,满足了大口径平面标准镜面形精度的要求。     

Reduction of thermal fluctuations in a cryogenic laser interferometric gravitational wave detector

The thermal fluctuation of mirror surfaces is the fundamental limitation for interferometric gravitational wave (GW) detectors. Here, we experimentally demonstrate for the first time a reduction in a mirror's thermal fluctuation in a GW detector with sapphire mirrors from the Cryogenic Laser Interferometer Observatory at 17 and 18 K. The detector sensitivity, which was limited by the mirror's thermal fluctuation at room temperature, was improved in the frequency range of 90 to 240 Hz by cooling the mirrors. The improved sensitivity reached a maximum of 2.2×10(-19) m/√Hz at 165 Hz.     

Competitive relaxation of the lumped-distributed feedback intensity in dye lasers

Relaxation oscillations of intensity in lumped-distributed feedback dye lasers are observed. These are caused by a competition between distributed feedback (DFB) and a feedback caused by an external mirror cavity. The effect is interpreted in terms of rate equations which include the time delay of radiation reflected from external mirrors relative to radiation due to periodic structure.     

Quantum entanglement in an oscillating macroscopic mirror

In this paper, we revisit the problem of quantum entanglement in an oscillating macroscopic mirror previously studied by Marshall et al. consisting of a modified Michelson interferometer where one of the mirrors is free to oscillate about its center of mass. A photon incident upon the oscillating mirror becomes entangled with the mirror, driving the mirror into a superposition of quantum states. Once the photon and mirror decouple, the mirror returns to its initial state. The purpose of our investigations was to optimize the parameter regime, taking into consideration the current state of technology and the demands imposed by the need to maintain a stable environment in the presence of thermal noise. Optimization should not demand ultra-low temperatures and this is reflected in our results. Our results also show that if the separation between states is maintained at 10^-14 m, the mirror size is reduced, making it easier to induce superposition in the mirror. The critical nature of mirror reflectivity and its connection to cavity decay rate was also revealed by our investigations. The results obtained through our investigations could be useful in quantum error correction, where decoherence negatively affects the results of computations performed by quantum computers. Finally, we note that we are only concerned with an isolated system, where no losses to the external environment occur and any decoherence that occurs within the system remains internal to the system; that is, any mention of decoherence refers specifically to recoverable decoherence.     

Lorentz lattice gases,abnormal diffusion,and polymer statistics

Diffusive behavior in various Lorentz lattice gases, especially wind-tree-like models, is discussed. Comparisons between lattice and continuum models as well as deterministic and probabilistic models are made. In one deterministic model, where the scatterers behave like double-sided mirrors, a new kind of abnormal diffusion is found, viz., the mean square displacement is proportional to the time, but the probability density distribution function is non-Gaussian. The connections of this mirror model with the percolation problem and the statistics of polymer chains on a lattice are also discussed.     

高功率激光反射镜的几个关键技术

 分析了制作高功率连续激光反射镜材料的热性能、缺陷及其加工工艺, 提出了制作高功率激光反射镜应考虑的几个关键问题: 反射镜材料的综合热性能比值S, 材料的微观结构、缺陷的大小和晶向的选择, 以及加工工艺的设计。并介绍了实验结果。     

Entanglement generation and protection for two atoms in the presence of two parallel mirrors

We study, in the framework of open quantum systems, the entanglement generation of two atoms in between two parallel mirrors in a thermal bath of quantum scalar fields. We find that the presence of mirrors plays an important role in entanglement generation and protection. The entanglement dynamics is crucially dependent on the geometric configurations of the two-atom system with respect to the mirrors, and the ranges of temperature and interatomic separation within which entanglement can be generated are significantly changed compared with those in a free space. In particular, when the atomic transition wavelength is larger than twice the distance between the two mirrors, the atoms behave as if they were isolated from the environment and the entanglement can persist in the steady state if the atoms are initially entangled and no entanglement can be created if they are initially separable, no matter how the atoms are placed with respect to the mirrors and to each other. This is in sharp contrast to the fact that in a free space, steady-state entanglement is possible only when the two atoms are placed extremely close to each other, while in the presence of one mirror, it is possible when the two atoms placed extremely close to the mirror.     

强激光热管冷却镜的数值研究

 为消除强激光微沟道水冷镜冷却水压力和扰动对激光输出稳定性的影响和冷却水道对冷却水流量的限制,提出并设计了热管冷却镜。采用ANSYS有限元软件,模拟计算了相同结构下镜面热吸收为12 W/cm²,实心镜、微沟道水冷镜与热管冷却镜连续工作60 s下镜体温升和镜面变形量。计算结果表明：热管冷却镜镜面轴向位移最大峰谷值为0.109 4 μm,微沟道水冷镜最大峰谷值为0.845 μm,实心镜镜面最大峰谷值为1.33 μm,热管冷却镜对镜面变形改善显著。     

Heating by Optical Absorption and Cooling of High Power Laser Mirrors

In high power laser system, laser mirror is the core and the most sensitive optical component, which influences the increase of laser power and the quality of laser. Absorption of light at mirrors causes wavefront distortions through the thermal deformations of substrates. The analytical solutions of the two-dimensional transient thermal theory of high power laser mirrors are developed, copious graphical results in our case are presented, and the predicted results are compared with those of the experiment.