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Crystalline Whispering Gallery Mode Resonators (WGMRs) have been shown to facilitate versatile sources of quantum states that can efficiently interact with atomic systems. These features make WGMRs an efficient platform for quantum information processing. Here, we experimentally show that it is possible to generate polarization entanglement from WGMRs by using an interferometric scheme. Our scheme gives us the flexibility to control the phase of the generated entangled state by changing the relative phase of the interferometer. The S value of the Clauser-Horne-Shimony-Holt's inequality in the system is $2.45 \pm 0.07$, which violates the inequality by more than 6 standard deviations.

In this work, we analyze the first whispering gallery mode resonator (WGMR) made from monocrystalline yttrium lithium fluoride (YLF). The disc-shaped resonator is fabricated using single-point diamond turning and exhibits a high intrinsic quality factor ($Q$) on the order of $10^9$. Moreover, we employ a novel method based on microscopic imaging of Newton's rings through the back of a trapezoidal prism. This method can be used to evanescently couple light in to a WGMR and monitor the separation between the cavity and the coupling prism. Accurately calibrating the distance between a coupling prism and a WGMR is desirable as it can be used to improve experimental control and conditions, i.e., accurate coupler gap calibration can aid in tuning into desired coupling regimes and can be used to avoid potential damage caused by collisions between the coupling prism and the WGMR. Here, we use two different trapezoidal prisms together with the high-$Q$ YLF WGMR to demonstrate and discuss this method., Comment: Main text (5 pages, 3 figures) Supplemental document (2 pages, 2 figures)

The National Aeronautics and Space Administration's Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. In this publication, we summarize the principal experimental goals of the Deep Space Quantum Link mission. These include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality., Comment: 74 pages, 24 figures

Titanium doped sapphire (Ti:sapphire) is a laser gain material with broad gain bandwidth benefiting from the material stability of sapphire. These favorable characteristics of Ti:sapphire have given rise to femtosecond lasers and optical frequency combs. Shaping a single Ti:sapphire crystal into a millimeter sized high quality whispering gallery mode resonator ($Q\sim10^8$) reduces the lasing threshold to 14.2 mW and increases the laser slope efficiency to 34%. The observed lasing can be both multi-mode and single-mode. This is the first demonstration of a Ti:sapphire whispering-gallery laser. Furthermore, a novel method of evaluating the gain in Ti:sapphire in the near infrared region is demonstrated by introducing a probe laser with a central wavelength of 795 nm. This method results in decreasing linewidth of the modes excited with the probe laser, consequently increasing their $Q$. These findings open avenues for the usage of whispering gallery mode resonators as cavities for the implementation of compact Ti:sapphire lasers. Moreover, Ti:sapphire can also be utilized as an amplifier inside its gain bandwidth by implementing a pump-probe configuration., Comment: Main text (13 pages, 7 figures) Supplemental document (11 pages, 9 figures)

Photon pairs and heralded single photons, obtained from cavity-assisted parametric down-conversion (PDC), play an important role in quantum communications and technology. This motivated a thorough study of the spectral and temporal properties of parametric light, both above the Optical Parametric Oscillator (OPO) threshold, where the semiclassical approach is justified, and deeply below it, where the linear cavity approximation is applicable. The pursuit of a higher two-photon emission rate leads into an interesting intermediate regime where the OPO still operates considerably below the threshold but the nonlinear cavity phenomena cannot be neglected anymore. Here, we investigate this intermediate regime and show that the spectral and temporal properties of the photon pairs, as well as their emission rate, may significantly differ from the widely accepted linear model. The observed phenomena include frequency pulling and broadening in the temporal correlation for the down-converted optical fields. These factors need to be taken into account when devising practical applications of the high-rate cavity-assisted SPDC sources.

Squeezed vacuum states enable optical measurements below the quantum limit and hence are a valuable resource for applications in quantum metrology and also quantum communication. However, most available sources require high pump powers in the milliwatt range and large setups, which hinders real world applications. Furthermore, degenerate operation of such systems presents a challenge. Here, we use a compact crystalline whispering gallery mode resonator made of lithium niobate as a degenerate parametric oscillator. We demonstrate about 1.4 dB noise reduction below the shot noise level for only 300 $\mu\text{W}$ of pump power in degenerate single mode operation. Furthermore, we report a record pump threshold as low as 1.35 $\mu\text{W}$. Our results show that the whispering gallery based approach presents a promising platform for a compact and efficient source for nonclassical light., Comment: $\copyright$ 2019 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved

Cavity-assisted spontaneous parametric down-conversion (SPDC) and spontaneous four-wave mixing (SFWM) in nonlinear optical materials are practical and versatile methods to generate narrowband time-energy entangled photon pairs. Time-energy entangled photons with tailored spectro-temporal properties are particularly useful for efficient quantum optical interfaces. In this work we study the generation of photon pairs in cavity-assisted SPDC and SFWM for the general case of off-resonant conversion, namely, when the frequencies of the generated photons do not match the cavity resonances. Such a frequency mismatch in particular depends on temperature and requires an additional control in the experiment. First, we propose a generic model, for description of cavity-assisted SPDC and SFWM. We show that in both processes the mismatch reduces the generation rate of photons, distorts the spectrum and the auto-correlation function of the generated fields, as well as affects the photon generation dynamics. Second, we verify the results experimentally using parametric generation of photon pairs in a nonlinear whispering gallery mode resonator (WGMR) as an experimental platform with controlled frequency mismatch. Our work reveals the role of the frequency mismatch in the photon generation process and shows a way to control it. Obtained results constitute one more step in the direction of full control over the spectro-temporal properties of entangled photon pairs and the heralded generation of single-photon pulses with a tailored temporal mode.

Non-classical concerns light whose properties cannot be explained by classical electrodynamics and which requires invoking quantum principles to be understood. Its existence is a direct consequence of field quantization; its study is a source of our understanding of many quantum phenomena. Non-classical light also has properties that may be of technological significance. We start this chapter by discussing the definition of non-classical light and basic examples. Then some of the most prominent applications of non-classical light are reviewed. After that, as the principal part of our discourse, we review the most common sources of non-classical light. We will find them surprisingly diverse, including physical systems of various sizes and complexity, ranging from single atoms to optical crystals and to semiconductor lasers. Putting all these dissimilar optical devices in the common perspective we attempt to establish a trend in the field and to foresee the new cross-disciplinary approaches and techniques of generating non-classical light., Comment: Chapter to be published in the Springer book "Advances in Quantum Photonics: from the First Single-photon and Nonlinear Optical Experiments to Modern Quantum Photonics" (Robert W. Boyd, Svetlana G. Lukishova, Victor N. Zadkov, Editors). 57 pages, 306 references

Whispering gallery mode (WGM) resonators are an important building block for linear, nonlinear and quantum optical experiments. In such experiments, independent control of coupling rates to different modes can lead to improved conversion efficiencies and greater flexibility in generation of non-classical states based on parametric down conversion. In this work, we introduce a scheme which enables selective out-coupling of WGMs belonging to a specific polarization family, while the orthogonally polarized modes remain largely unperturbed. Our technique utilizes material birefringence in both the resonator and coupler such that a negative (positive) birefringence allows selective coupling to TE (TM) polarized WGMs. We formulate a new coupling condition suitable for describing the case where the refractive indices of the resonator and the coupler are almost the same, from which we derive the criterion for polarization-selective coupling. We experimentally demonstrate our proposed method using a lithium niobate disk resonator coupled to a lithium niobate prism, where we show a 22dB suppression of coupling to TM modes relative to TE modes.

Optical Whispering Gallery Modes (WGMs) derive their name from a famous acoustic phenomenon of guiding a wave by a curved boundary observed nearly a century ago. This phenomenon has a rather general nature, equally applicable to sound and all other waves. It enables resonators of unique properties attractive both in science and engineering. Very high quality factors of optical WGM resonators persisting in a wide wavelength range spanning from radio frequencies to ultraviolet light, their small mode volume, and tunable in- and out- coupling make them exceptionally efficient for nonlinear optical applications. Nonlinear optics facilitates interaction of photons with each other and with other physical systems, and is of prime importance in quantum optics. In this paper we review numerous applications of WGM resonators in nonlinear and quantum optics. We outline the current areas of interest, summarize progress, highlight difficulties, and discuss possible future development trends in these areas., Comment: This is a review paper with 615 references, submitted to J. Opt

Linking classical microwave electrical circuits to the optical telecommunication band is at the core of modern communication. Future quantum information networks will require coherent microwave-to-optical conversion to link electronic quantum processors and memories via low-loss optical telecommunication networks. Efficient conversion can be achieved with electro-optical modulators operating at the single microwave photon level. In the standard electro-optic modulation scheme this is impossible because both, up- and downconverted, sidebands are necessarily present. Here we demonstrate true single sideband up- or downconversion in a triply resonant whispering gallery mode resonator by explicitly addressing modes with asymmetric free spectral range. Compared to previous experiments, we show a three orders of magnitude improvement of the electro-optical conversion efficiency reaching 0.1% photon number conversion for a 10GHz microwave tone at 0.42mW of optical pump power. The presented scheme is fully compatible with existing superconducting 3D circuit quantum electrodynamics technology and can be used for non-classical state conversion and communication. Our conversion bandwidth is larger than 1MHz and not fundamentally limited., Comment: 8 pages, 5 figures; comments welcome!

Quantum repeaters rely on an interfacing of flying qubits with quantum memories. The most common implementations include a narrowband single photon matched in bandwidth and central frequency to an atomic system. Previously, we demonstrated the compatibility of our versatile source of heralded single photons, which is based on parametric down-conversion in a triply-resonant whispering-gallery mode resonator, with alkaline transitions [Schunk et al., Optica 2, 773 (2015)]. In this paper, we analyze our source in terms of phase matching, available wavelength-tuning mechanisms, and applications to narrow-band atomic systems. We resonantly address the D1 transitions of cesium and rubidium with this optical parametric oscillator pumped above its oscillation threshold. Below threshold, the efficient coupling of single photons to atomic transitions heralded by single telecom-band photons is demonstrated. Finally, we present an accurate analytical description of our observations. Providing the demonstrated flexibility in connecting various atomic transitions with telecom wavelengths, we show a promising approach to realize an essential building block for quantum repeaters., Comment: 18 pages, 14 figures

Quantum information technology strongly relies on coupling of optical photons with narrowband quantum systems, such as quantum dots, color centers, and atomic systems. This coupling requires matching the optical wavelength and bandwidth to the desired system, which presents a considerable problem for most available sources of quantum light. Here we demonstrate coupling of alkali dipole transitions with a tunable source of photon pairs. Our source is based on spontaneous parametric down-conversion in a triply-resonant whispering-gallery mode resonator. For this, we have developed novel wavelength tuning mechanisms, which allow for a coarse tuning to either cesium or rubidium wavelength with subsequent continuous fine-tuning to the desired transition. As a demonstration of the functionality of the source, we performed a heralded single photon measurement of the atomic decay. We present a major advance in controlling the spontaneous down-conversion process, which makes our bright source of single photons now compatible with a plethora of narrow-band resonant systems., Comment: 8 pages, 5 figures

Identifying the mode numbers in whispering-gallery mode resonators (WGMRs) is important for tailoring them to experimental needs. Here we report on a novel experimental mode analysis technique based on the combination of frequency analysis and far-field imaging for high mode numbers of large WGMRs. The radial mode numbers q and the angular mode numbers p=$\ell$-m are identified and labeled via far-field imaging. The polar mode numbers $\ell$ are determined unambiguously by fitting the frequency differences between individual whispering gallery modes (WGMs). This allows for the accurate determination of the geometry and the refractive index at different temperatures of the WGMR. For future applications in classical and quantum optics, this mode analysis enables one to control the narrow-band phase-matching conditions in nonlinear processes such as second-harmonic generation or parametric down-conversion., Comment: 12 pages, 6 figures

We analyze an intensity interferometry measurement carried out with two point-like detectors facing a distant source (e.g., a star) that may be partially occluded by an absorptive object (e.g., a planet). Such a measurement, based on the perturbation of the observed covariance function due to the object's presence, can provide information of the object complementary to a direct optical intensity measurement. In particular, one can infer the orientation of the object's transient trajectory. We identify the key parameters that impact this perturbation and show that its magnitude is equal to the magnitude of the intensity variation caused by the same object. In astronomy applications, this value may be very small, so a differential measurement may be necessary. Finally, we discuss the signal-to-noise ratio that may be expected in this type of measurement.

We demonstrate sum-frequency generation in a nonlinear whispering gallery mode resonator between a telecom wavelength and the Rb D2 line, achieved through natural phase matching. Due to the strong optical field confinement and ultra high Q of the cavity, we achieve a 1000-fold enhancement in the conversion efficiency compared to existing waveguide-based devices. The experimental data are in agreement with the nonlinear dynamics and phase matching theory in the spherical geometry employed. The experimental and theoretical results point to a new platform to manipulate the color and quantum states of light waves toward applications such as atomic memory based quantum networking and logic operations with optical signals.

Optical frequency conversion processes in nonlinear materials are limited in wavelength by the accessible phase matching and the required high pump powers. In this letter, we report a novel broadband phase matching (PM) technique in high quality factor (Q) whispering gallery mode (WGM) resonators made of birefringent crystalline materials. This technique relies on two interacting WGMs, one with constant and the other with spatially oscillating phase velocity. Thus, phase matching occurs cyclically. The technique can be implemented with a WGM resonator with its disk plane parallel to the optic axis of the crystal. With a single beta barium borate (BBO) resonator in that configuration, we experimentally demonstrated efficient second harmonic generation (SHG) to harmonic wavelengths from 780 nm in the near infrared to 317 nm in the ultraviolet (UV). The observed SHG conversion efficiency is as high as 4.6% (mW)-1. This broadband PM technique opens a new way for nonlinear optics applications in WGM resonators. This work is also the first reported continuous wave UV generation by direct SHG in a WGM resonator, Comment: 8 pages

An optical comb is shown to arise from a whispering gallery mode resonator pumped by two optical frequencies. Two externally excited modes couple due to Kerr nonlinearity to initially empty modes and give rise to new frequency components. This thresholdles process is much more efficient than the previously reported single-pump four-wave mixing. As a result, a few milliwatt pump is sufficient to generate strong secondary fields, that efficiently generate higher-order frequency components and so on, in a cascade process leading to an optical comb., Comment: 4 pages, 6 figures

We describe a practical implementation of a (semi-deterministic) photon gun based on stimulated Raman adiabatic passage pumping and the strong enhancement of the photonic density of states in a photonic band-gap material. We show that this device allows {\em deterministic} and {\em unidirectional} production of single photons with a high repetition rate of the order of 100kHz. We also discuss specific 3D photonic microstructure architectures in which our model can be realized and the feasibility of implementing such a device using ${Er}^{3+}$ ions that produce single photons at the telecommunication wavelength of $1.55 \mu$m., Comment: 4 pages, 4 EPS figures

The goal of this research is to determine and study a physical system that will enable a fast and intrinsically two-photon detector, which would be of interest for quantum information and metrology applications. We consider two types of two-photon processes that can be observed using a very faint, but quantum-correlated biphoton field. These are optical up-conversion and an external photoelectric effect. We estimate the correlation enhancement factor for the biphoton light compared to coherent light, report and discuss the preliminary experimental results., Comment: 18 pages, 10 figures, proceeding of Physics of Quantum Electronics 2002, to appear in J.Mod.Opt

The state of the signal-idler photon pair of spontaneous parametric down conversion(SPDC) is a typical nonlocal entangled pure state with zero entropy. The precise correlation of the subsystems is completely described by the state. However, it is an experimental choice to study only one subsystem and to ignore the other. What can we learn about the measured subsystem and the remaining parts? Results of this kind of measurements look peculiar. The experiment confirms that the two subsystems are both in mixed states with entropy greater than zero. One can only obtain statistical knowledge of the subsystems in this kind of measurement., Comment: 14 pages, 2 eps figures

Development of innovative aerospace technologies is critical for our nation to meet its goals to explore and under-stand the Earth, our solar system, and the universe. The spectacular success of many recent NASA missions hinges on the extensive technological innovations that NASA has been supporting for the past decades. To sustain this successful tradition it is very important to identify and stimulate the scientific research that may turn into a viable technology in the decades yet to come. Investment in innovative low-TRL research stimulates the growth of the scientific knowledge and enhances the technical capabilities in a way that answers the new questions and responds to new requirements.

An optical resonator fabricated from a uniaxial birefringent crystal, such as beta barium borate. The crystal is cut with the optical axis not perpendicular to a face of the cut crystal. In some cases the optical axis lies in the plane of the cut crystal face. An incident (input) electromagnetic signal (which can range from the infrared through the visible to the ultraviolet) is applied to the resonator. An output signal is recovered which has a frequency that is an integer multiple of the frequency of the input signal. In some cases a prism is used to evanescently couple the input and the output signals to the resonator.

would like to summarize that our "Ghost Imaging of Space Objects" NIAC research effort was successful. As anticipated, its main return has been the newly acquired knowledge and the understanding of the pathways that lead from this knowledge to its applications in observational astronomy. During this research we came across several fundamental insights that were not expected at the beginning. We came to realize that the ghost imaging of dark objects using background thermal light can be treated as a special case of Hanbury Brown and Twiss intensity interferometry in combination with the Babinet's principle for higher-order observables. Extensive recent work performed in this field by other research groups worldwide might seem to detract from the conceptual originality and novelty of our approach; but at the same time it serves as an encouraging indication that the chosen approach is acknowledged in the broader science community as promising. This newly found synergy, acknowledged in the CTA newsletter from May 2014 reporting on the Workshop on Hanbury Brown and Twiss interferometry in Nice, makes us confident that our published and otherwise disseminated results will be integrated into a larger-scale on-going research effort aimed at performing astronomy observations of both bright and dark objects with unparalleled resolution. While we are satisfied with acceptance of our results by the international research community as a contribution to the field of intensity interferometry as well as to the on-going mission-oriented projects, we also have been aiming at receiving support to continue and advance this research at JPL. Several proposals have been submitted in pursuit of this goal. Three of them are still under consideration, and we expect to learn about the funding decisions soon. These new projects would leverage the results of this NIAC study and extend it along well-defined directions that have been discussed above. Shifting the main paradigm of our approach towards intensity interferometry entailed another important realization, that the actual imaging of dark objects, in a sense of mapping the column optical density distribution, is possible by using known numerical techniques, such as the Gerchberg-Saxton approach. This insight was also unanticipated in the beginning and caused a shift of the research focus from the initial plan. While this focus shift has been well-justified and fruitful, it has left several issues unexplored. Some of these issues, too, are included in the future research proposals.

While a variety of techniques exist to monitor trace gases, methods relying on absorption of laser light are the most commonly used in terrestrial applications. Cavity-enhanced absorption techniques typically use high-reflectivity mirrors to form a resonant cavity, inside of which a sample gas can be analyzed. The effective absorption length is augmented by the cavity's high quality factor, or Q, because the light reflects many times between the mirrors. The sensitivity of such mirror-based sensors scales with size, generally making them somewhat bulky in volume. Also, specialized coatings for the high-reflectivity mirrors have limited bandwidth (typically just a few nanometers), and the delicate mirror surfaces can easily be degraded by dust or chemical films. As a highly sensitive and compact alternative, JPL is developing a novel trace gas sensor based on a monolithic optical resonator structure that has been modified such that a gas sample can be directly injected into the cavity. This device concept combines ultra-high Q optical whispering gallery mode resonators (WGMR) with microfabrication technology used in the semiconductor industry. For direct access to the optical mode inside a resonator, material can be precisely milled from its perimeter, creating an open gap within the WGMR. Within this open notch, the full optical mode of the resonator can be accessed. While this modification may limit the obtainable Q, calculations show that the reduction is not significant enough to outweigh its utility for trace gas detection. The notch can be milled from the high- Q crystalline WGMR with a focused ion beam (FIB) instrument with resolution much finer than an optical wavelength, thereby minimizing scattering losses and preserving the optical quality. Initial experimental demonstrations have shown that these opened cavities still support high-Q whispering gallery modes. This technology could provide ultrasensitive detection of a variety of molecular species in an extremely compact and robust package. With this type of modified WGMR, one can inject a gas sample into the open gap, allowing highly sensitive trace molecule detection within a roughly 1-cm volume. Other critical components of the instrument, such as the detector and a semiconductor laser, could be directly packaged with the resonator so as to not significantly increase the size of the device. Besides its low mass, volume, and power consumption, the monolithic design makes these resonators intrinsically robust devices, capable of handling significant temperature excursions, without moving parts to wear out or delicate coatings that can be easily damaged. A sensor could integrate with microfluidics technology for a chip-scale device. It could be mounted to the end of a deployable arm, or inserted into a borehole. Also, a network of individual sensors could be dispersed to monitor conditions over a wide region

We derive an approximation to the intensity covariance function of two scanning pinhole detectors, facing a distant source (e.g., a star) being occluded partially by an absorptive object (e.g., a planet). We focus on using this technique to identify or image an object that is in the line-of-sight between a well-characterized source and the detectors. We derive the observed perturbation to the intensity covariance map due to the object, showing that under some reasonable approximations it is proportional to the real part of the Fourier transform of the source's photon-flux density times the Fourier transform of the object's intensity absorption. We highlight the key parameters impacting its visibility and discuss the requirements for estimating object-related parameters, e.g., its size, velocity or shape. We consider an application of this result to determining the orbit inclination of an exoplanet orbiting a distant star. Finally, motivated by the intrinsically weak nature of the signature, we study its signal-to-noise ratio and determine the impact of system parameters.

For a given inertial frame of reference, the software combines the spacecraft orbits with the spacecraft attitude quaternions, and rotates the body-fixed reference frame of a particular spacecraft to the inertial reference frame. The conversion assumes that the two spacecraft are aligned with respect to the mutual line of sight, with a parameterized time tag. The software is implemented in Python and is completely open source. It is very versatile, and may be applied under various circumstances and for other related purposes. Based on the solid linear algebra analysis, it has an extra option for compensating the linear pitch. This software has been designed for simulation of the calibration maneuvers performed by the two spacecraft comprising the GRAIL mission to the Moon, but has potential use for other applications. In simulations of formation flights, one needs to coordinate the spacecraft orbits represented in an appropriate inertial reference frame and the spacecraft attitudes. The latter are usually given as the time series of quaternions rotating the body-fixed reference frame of a particular spacecraft to the inertial reference frame. It is often desirable to simulate the same maneuver for different segments of the orbit. It is also useful to study various maneuvers that could be performed at the same orbit segment. These two lines of study are more timeand labor-efficient if the attitude and orbit data are generated independently, so that the part of the data that has not been changed can be recycled in the course of multiple simulations.

Great progress has been made in both micromechanical resonators and micro-optical resonators over the past decade, and a new field has recently emerged combining these mechanical and optical systems. In such optomechanical systems, the two resonators are strongly coupled with one influencing the other, and their interaction can yield detectable optical signals that are highly sensitive to the mechanical motion. A particularly high-Q optical system is the whispering gallery mode (WGM) resonator, which has many applications ranging from stable oscillators to inertial sensor devices. There is, however, limited coupling between the optical mode and the resonator s external environment. In order to overcome this limitation, a novel type of optomechanical sensor has been developed, offering great potential for measurements of displacement, acceleration, and mass sensitivity. The proposed hybrid device combines the advantages of all-solid optical WGM resonators with high-quality micro-machined cantilevers. For direct access to the WGM inside the resonator, the idea is to radially cut precise gaps into the perimeter, fabricating a mechanical resonator within the WGM. Also, a strategy to reduce losses has been developed with optimized design of the cantilever geometry and positions of gap surfaces.

This software implements digital control of a WGM (whispering-gallerymode) resonator temperature based on the dual-mode approach. It comprises one acquisition (dual-channel) and three control modules. The interaction of the proportional-integral loops is designed in the original way, preventing the loops from fighting. The data processing is organized in parallel with the acquisition, which allows the computational overhead time to be suppressed or often completely avoided. WGM resonators potentially provide excellent optical references for metrology, clocks, spectroscopy, and other applications. However, extremely accurate (below micro-Kelvin) temperature stabilization is required. This software allows one specifically advantageous method of such stabilization to be implemented, which is immune to a variety of effects that mask the temperature variation. WGM Temperature Tracker 2.3 (see figure) is a LabVIEW code developed for dual-mode temperature stabilization of WGM resonators. It has allowed for the temperature stabilization at the level of 200 nK with one-second integration time, and 6 nK with 10,000-second integration time, with the above room-temperature set point. This software, in conjunction with the appropriate hardware, can be used as a noncryogenic temperature sensor/ controller with sub-micro-Kelvin sensitivity, which at the time of this reporting considerably outperforms the state of the art.

The most accurate astronomical data is available from space-based observations that are not impeded by the Earth's atmosphere. Such measurements may require spectral samples taken as long as decades apart, with the 1 cm/s velocity precision integrated over a broad wavelength range. This raises the requirements specifically for instruments used in astrophysics research missions -- their stringent wavelength resolution and accuracy must be maintained over years and possibly decades. Therefore, a stable and broadband optical calibration technique compatible with spaceflights becomes essential. The space-based spectroscopic instruments need to be calibrated in situ, which puts forth specific requirements to the calibration sources, mainly concerned with their mass, power consumption, and reliability. A high-precision, high-resolution reference wavelength comb source for astronomical and astrophysics spectroscopic observations has been developed that is deployable in space. The optical comb will be used for wavelength calibrations of spectrographs and will enable Doppler measurements to better than 10 cm/s precision, one hundred times better than the current state-of-the- art.

Ring Image Analyzer software analyzes images to recognize elliptical patterns. It determines the ellipse parameters (axes ratio, centroid coordinate, tilt angle). The program attempts to recognize elliptical fringes (e.g., Newton Rings) on a photograph and determine their centroid position, the short-to-long-axis ratio, and the angle of rotation of the long axis relative to the horizontal direction on the photograph. These capabilities are important in interferometric imaging and control of surfaces. In particular, this program has been developed and applied for determining the rim shape of precision-machined optical whispering gallery mode resonators. The program relies on a unique image recognition algorithm aimed at recognizing elliptical shapes, but can be easily adapted to other geometric shapes. It is robust against non-elliptical details of the image and against noise. Interferometric analysis of precision-machined surfaces remains an important technological instrument in hardware development and quality analysis. This software automates and increases the accuracy of this technique. The software has been developed for the needs of an R&TD-funded project and has become an important asset for the future research proposal to NASA as well as other agencies.

Low-current, high-impedance microelectronic devices can be affected by electric current shot noise more than they are affected by Nyquist noise, even at room temperature. An approach to implementing a sub-shot noise current source for powering such devices is based on direct conversion of amplitude-squeezed light to photocurrent. The phenomenon of optical squeezing allows for the optical measurements below the fundamental shot noise limit, which would be impossible in the domain of classical optics. This becomes possible by affecting the statistical properties of photons in an optical mode, which can be considered as a case of information encoding. Once encoded, the information describing the photon (or any other elementary excitations) statistics can be also transmitted. In fact, it is such information transduction from optics to an electronics circuit, via photoelectric effect, that has allowed the observation of the optical squeezing. It is very difficult, if not technically impossible, to directly measure the statistical distribution of optical photons except at extremely low light level. The photoelectric current, on the other hand, can be easily analyzed using RF spectrum analyzers. Once it was observed that the photocurrent noise generated by a tested light source in question is below the shot noise limit (e.g. produced by a coherent light beam), it was concluded that the light source in question possess the property of amplitude squeezing. The main novelty of this technology is to turn this well-known information transduction approach around. Instead of studying the statistical property of an optical mode by measuring the photoelectron statistics, an amplitude-squeezed light source and a high-efficiency linear photodiode are used to generate photocurrent with sub-Poissonian electron statistics. By powering microelectronic devices with this current source, their performance can be improved, especially their noise parameters. Therefore, a room-temperature sub-shot noise current source can be built that will be beneficial for a very broad range of low-power, low-noise electronic instruments and applications, both cryogenic and room-temperature. Taking advantage of recent demonstrations of the squeezed light sources based on optical micro-disks, this sub-shot noise current source can be made compatible with the size/power requirements specific of the electronic devices it will support.

Optical sidebands have been generated with relative frequency tens to hundreds of GHz by using optical sidebands that are generated in a cascade process in high-quality optical resonators with Kerr nonlinearity, such as whispering gallery mode (WGM) resonators. For this purpose, the WGM resonator needs to be optically pumped at two frequencies matching its resonances. These two optical components can be one or several free spectral ranges (FSRs), equal to approximately 12 GHz, in this example, apart from each other, and can be easily derived from a monochromatic pump with an ordinary EOM (electro-optic modulation) operating at half the FSR frequency. With sufficient nonlinearity, an optical cascade process will convert the two pump frequencies into a comb-like structure extending many FSRs around the carrier frequency. This has a demonstratively efficient frequency conversion of this type with only a few milliwatt optical pump power. The concept of using Kerr nonlinearity in a resonator for non-degenerate wave mixing has been discussed before, but it was a common belief that this was a weak process requiring very high peak powers to be observable. It was not thought possible for this approach to compete with electro-optical modulators in CW applications, especially those at lower optical powers. By using the high-Q WGM resonators, the effective Kerr nonlinearity can be made so high that, using even weak seeding bands available from a conventional EOM, one can effectively multiply the optical sidebands, extending them into an otherwise inaccessible frequency range.

Recently, there has been a considerable effort to study the Casimir and van der Waals forces, enabled by the improved ability to measure small forces near surfaces. Because of the continuously growing role of micro- and nanomechanical devices, the focus of this activity has shifted towards the ability to control these forces. Possible approaches to manipulating the Casimir force include development of composite materials, engineered nanostructures, mixed-phase materials, or active elements. So far, practical success has been limited. The role of geometrical factors in the Casimir force is significant. It is known, for example, that the Casimir force between two spherical shells enclosed one into the other is repulsive instead of normal attractive. Unfortunately, nanosurfaces with this topology are very difficult to make. A more direct approach to manipulating and neutralizing the Casimir force is using external mechanical or electromagnetic forces. Unfortunately, the technological overhead of such an approach is quite large. Using electromagnetic compensation instead of mechanical will considerably reduce this overhead and at the same time provide the degree of control over the Casimir force that mechanical springs cannot provide. A mechanical analog behind Casimir forces is shown.

Optical combs generated by a monolithic resonator with Kerrmedium can be used in a number of applications, including orbital clocks and frequency standards of extremely high accuracy, such as astronomy, molecular spectroscopy, and the like. The main difficulty of this approach is the relatively high pump power that has to be used in such devices, causing undesired thermorefractive effects, as well as stimulated Raman scattering, and limiting the optical comb quality and utility. In order to overcome this problem, this innovation uses a different approach to excitation of the nonlinear oscillations in a Kerr-nonlinear whispering gallery mode (WGM) resonator and generation of the optical comb. By coupling to the resonator two optical pump frequencies instead of just one, the efficiency of the comb source can be increased considerably. It therefore can operate in a lowerpower regime where the undesirable effects are not present. This process does not have a power threshold; therefore, the new optical component can easily be made strong enough to generate further components, making the optical comb spread in a cascade fashion. Additionally, the comb spacing can be made in an arbitrary number of the resonator free spectral ranges (FSR). The experimental setup for this innovation used a fluorite resonator with OMEGA= 13.56 GHz. This material has very low dispersion at the wavelength of 1.5 microns, so the resonator spectrum around this wavelength is highly equidistant. Light was coupled in and out of the resonator using two optical fibers polished at the optimal coupling angle. The gap between the resonator and the fibers, affecting the light coupling and the resonator loading, was controlled by piezo positioners. The light from the input fiber that did not go into the resonator reflected off of its rim, and was collected by a photodetector. This enabled observation and measurement of the (absorption) spectrum of the resonator. The input fiber combined light from two lasers centered at around 1,560 nanometers. Both laser frequencies were simultaneously scanned around the selected WGMs of the same family. However, they were separated by one, two, three, or ten FSRs. This was achieved by fine-tuning each laser frequency offset until the selected resonances overlap on the oscilloscope screen. The resonator quality factor Q = 7 x 10(exp 7) was relatively low to increase the linewidth and, therefore, the duty cycle of both lasers simultaneously coupled into their WGMs. The optical spectrum analyzer (OSA) connected to the output fiber was continuously acquiring data, asynchronously with the laser scan. The instrument was set to retain the peak power values; therefore, a trace recorded for a sufficiently long period of time reflected the situation with both lasers maximally coupled to the WGMs.

A method of shifting and fixing an optical frequency of an optical resonator to a desired optical frequency, and an optical resonator made by such a method are provided. The method includes providing an optical resonator having a surface and a refractive index, and obtaining a coating composition having a predetermined concentration of a substance and having a refractive index that is substantially similar to the refractive index of the optical resonator. The coating composition inherently possesses a thickness when it is applied as a coating. The method further includes determining a coating ratio for the surface of the optical resonator and applying the coating composition onto a portion of the surface of the optical resonator based upon the determined coating ratio.

A differential temperature sensor system and method of determining a temperature shift of an optical resonator and its surroundings are provided. The differential temperature sensor system includes a light generating device capable of generating a beam having a carrier frequency, a modulator capable of modulating the beam with a sideband frequency, and an optical resonator capable of supporting an ordinary mode and an extraordinary mode. The system includes an ordinary mode-lock setup capable of locking the carrier frequency of the beam to the ordinary mode of the optical resonator and an extraordinary mode-lock setup capable of locking the sideband frequency of the beam to the extraordinary mode of the optical resonator by providing a specific radio frequency to the modulator substantially corresponding to a frequency shift between the ordinary mode and the extraordinary mode of the optical resonator resulting from a temperature change of the optical resonator. A processor precisely calculates the differential temperature based upon the frequency shift between the ordinary mode and extraordinary mode of the optical resonator.