Bidirectional microwave and optical signal dissemination.

We describe a technique to disseminate highly stable microwave and optical signals from physically separated frequency standards to multiple locations. We demonstrate our technique by transferring the frequency stability performance of a microwave frequency reference to the repetition-rate stability of an optical frequency comb in a different location. The stabilized optical frequency comb becomes available in both locations for measurements of both optical and microwave signals. We show a microwave frequency stability of 4×10(-15) in both locations for integration times beyond 100 s. The control system uses only a standard Ethernet connection.

Direct terrestrial test of Lorentz symmetry in electrodynamics to 10(-18).

Lorentz symmetry is a foundational property of modern physics, underlying the standard model of particles and general relativity. It is anticipated that these two theories are low-energy approximations of a single theory that is unified and consistent at the Planck scale. Many unifying proposals allow Lorentz symmetry to be broken, with observable effects appearing at Planck-suppressed levels; thus, precision tests of Lorentz invariance are needed to assess and guide theoretical efforts. Here we use ultrastable oscillator frequency sources to perform a modern Michelson-Morley experiment and make the most precise direct terrestrial test to date of Lorentz symmetry for the photon, constraining Lorentz violating orientation-dependent relative frequency changes Δν/ν to 9.2±10.7 × 10(-19) (95% confidence interval). This order of magnitude improvement over previous Michelson-Morley experiments allows us to set comprehensive simultaneous bounds on nine boost and rotation anisotropies of the speed of light, finding no significant violations of Lorentz symmetry.

Atomic fountain clock with very high frequency stability employing a pulse-tube-cryocooled sapphire oscillator.

The frequency stability of an atomic fountain clock was significantly improved by employing an ultra-stable local oscillator and increasing the number of atoms detected after the Ramsey interrogation, resulting in a measured Allan deviation of 8.3 × 10(-14)τ(-1/2)). A cryogenic sapphire oscillator using an ultra-low-vibration pulse-tube cryocooler and cryostat, without the need for refilling with liquid helium, was applied as a local oscillator and a frequency reference. High atom number was achieved by the high power of the cooling laser beams and optical pumping to the Zeeman sublevel m(F) = 0 employed for a frequency measurement, although vapor-loaded optical molasses with the simple (001) configuration was used for the atomic fountain clock. The resulting stability is not limited by the Dick effect as it is when a BVA quartz oscillator is used as the local oscillator. The stability reached the quantum projection noise limit to within 11%. Using a combination of a cryocooled sapphire oscillator and techniques to enhance the atom number, the frequency stability of any atomic fountain clock, already established as primary frequency standard, may be improved without opening its vacuum chamber.

Invited article: Dielectric material characterization techniques and designs of high-Q resonators for applications from micro to millimeter-waves frequencies applicable at room and cryogenic temperatures.

Dielectric resonators are key elements in many applications in micro to millimeter wave circuits, including ultra-narrow band filters and frequency-determining components for precision frequency synthesis. Distributed-layered and bulk low-loss crystalline and polycrystalline dielectric structures have become very important for building these devices. Proper design requires careful electromagnetic characterization of low-loss material properties. This includes exact simulation with precision numerical software and precise measurements of resonant modes. For example, we have developed the Whispering Gallery mode technique for microwave applications, which has now become the standard for characterizing low-loss structures. This paper will give some of the most common characterization techniques used in the micro to millimeter wave regime at room and cryogenic temperatures for designing high-Q dielectric loaded cavities.

Optimum design of a high-Q room- temperature whispering-gallery-mode X-band sapphire resonator.

A process for optimal design of a room-temperature whispering-gallery-mode sapphire resonator has been developed. In particular, design rules were determined to enable choice of the optimum azimuthal mode number and resonator radius for a given resonance frequency. The coupling probe design was investigated and it was found that straight antenna probes aligned radially and positioned in the mid-plane of the resonator gave the highest unloaded Q-factors because of minimized probe losses. We noted that when coupling through this technique (as compared with a perpendicularly positioned probe) the mode standing wave pattern would lock to some asymmetry in the crystal resonator itself and not to the probe. This was confirmed by noting that the coupling could be altered over a significant range by merely rotating the resonator. Following these optimal design rules, we were able to measure the Q-factors of quasi-TE and quasi-TM modes with high precision in four cylindrical sapphire resonators at room temperature. From this analysis, the highest attainable Q-factor is expected to be (2.1 ± 0.1) x 10(5) at 9 GHz in a quasi-TM mode.

High-power solid-state sapphire whispering gallery mode maser.

We present new results on a cryogenic solid-state maser frequency standard, which relies on the excitation of whispering gallery (WG) modes within a doped monocrystalline sapphire resonator (alpha-Al2O3). Included substitutively within the highest purity HEMEX-grade sapphire crystal lattice are Fe2+ impurities at a concentration of parts per million, an unavoidable result of the manufacturing process. Mass conversion of Fe2+ to Fe3+ ions was achieved by thermally annealing the sapphire in air. Above-threshold maser oscillation was then excited in the resonator at zero applied DC magnetic field by pumping high-Q WG modes coincident in frequency with the electron spin resonance (ESR) energy levels of the Fe3+ spin population. A 2 stage annealing process was undertaken for a sapphire resonator with exceptionally low Fe3+ concentration, resulting in an improvement of 6 orders of magnitude in output power for this particular crystal, and exceeding the previous best implementation of our scheme in another crystal by nearly 20 dB. This represents an output signal 7 orders of magnitude more powerful than a typical commercial hydrogen maser. At this power level, we estimate a limit on the frequency stability of order 1 x 10(-17)/square root(tau) due to the Schawlow-Townes fundamental thermal noise limit.

Long-term operation and performance of cryogenic sapphire oscillators.

Cryogenic sapphire oscillators (CSO) developed at the University of Western Australia (UWA) have now been in operation around the world continuously for many years. Such oscillators, due to their excellent spectral purity are essential for interrogating atomic frequency standards at the limit of quantum projection noise; otherwise aliasing effects will dominate the frequency stability due to the periodic sampling between successive interrogations of the atomic transition. Other applications, which have attracted attention in recent years, include tests on fundamental principles of physics, such as tests of Lorentz invariance. This paper reports on the long-term operation and performance of such oscillators. We compare the long-term drift of some different CSOs. The drift rates turn out to be linear over many years and in the same direction. However, the magnitude seems to vary by more than one order of magnitude between the oscillators, ranging from 10(14) per day to a few parts in 10(13) per day.

Second generation 50 K dual-mode sapphire oscillator.

Low-temperature, high-precision sapphire resonators exhibit a turning point in mode frequency-temperature dependence at around 10 K. This, along with sapphire's extremely low dielectric losses at microwave frequencies, results in oscillator fractional frequency stabilities on the order of 10(-15). At higher temperatures the lack of a turning point makes single-mode oscillators very sensitive to temperature fluctuations. By exciting two quasi-orthogonal whispering gallery (WG) modes in a single sapphire resonator, a turning point in the frequency-temperature dependence can be found in the beat frequency between the two modes. A temperature control technique based on mode frequency temperature dependence has been used to maintain the sapphire at this turning point and the fractional frequency instability of the beat frequency has been measured to be at a level of 4.3 X 10(-14) over 1 s, dropping to 3.5 X 10(-14) over 4 s integration time.

Room temperature measurement of the anisotropic loss tangent of sapphire using the whispering gallery mode technique.

The anisotropic loss tangent has been determined in monocrystalline sapphire for components parallel and perpendicular to the crystal axis, using the whispering gallery (WG) mode method. The Q-factors of quasi-TE and quasi-TM modes were measured precisely in four cylindrical sapphire resonators at room temperature, from which was determined a maximum attainable Q-factor of (2.1 +/- 0.2) x 10(5) at 9 GHz in a quasi-TM mode. Sapphire dielectric material from three different manufacturers was compared over the 270-345 K temperature range and the 5-16 GHz frequency range.

Designs of a microwave TE011 mode cavity for a space borne H-maser.

Method of Lines and Finite Element Analysis investigations have been performed to optimize parameters in a TE011 mode cavity resonator suitable for a spaceborne hydrogen maser. We report on designs that were explored to find a global maximum in the important design parameters for the microwave cavity used in a hydrogen maser. The criteria sought in this exercise were both the minimization of the total volume of the cavity and the maximization of the product of the z-component of the magnetic energy filling factor and the cavity TE011 mode Q-factor (Q.eta). Different configurations were studied. They were a sapphire tube in a copper cylinder, a sapphire tube in a copper cylinder with Bragg reflectors, and spherical copper cavities both empty and sapphire-lined on the inside cavity surface. At 320 K, the simulations resulted in an optimum product Q.eta = 4.9 x 10(4), with an inner cavity radius of 80 mm and unity aspect ratio. This represents a 54% improvement over an earlier design. The expected increase in the product Q . eta) with the inclusion of Bragg reflectors to the sapphire tube was not achieved. Moreover, the z-component of the magnetic energy filling factor was greatly reduced due to an increase in the radial magnetic field. The sapphire-lined spherical cavity showed no better performance than an equivalent-sized empty copper spherical cavity. For the empty cavity the simulations resulted in the product Q.eta = 4.4 x 10(4). The empty spherical cavity resonator is not suitable for the spaceborne hydrogen maser as the total volume in this case is 33% larger than that of the optimized sapphire tube resonator.

Distributed bragg reflector resonators with cylindrical symmetry and extremely high Q-factors.

A simple non-Maxwellian method is presented that allows the approximate solution of all the dimensions of a multilayered dielectric TE0qp mode cylindrical resonant cavity that constitutes a distributed Bragg reflection (DBR) resonator. The analysis considers an arbitrary number of alternating dielectric and free-space layers of cylindrical geometry enclosed by a metal cylinder. The layers may be arranged along the axial direction, the radial direction, or both. Given only the aspect ratio of the cavity, the desired frequency and the dielectric constants of the material layers, the relevant dimensions are determined from only a set of simultaneous equations, and iterative techniques are not required. The formulas were verified using rigorous method of lines (MoL) calculations and previously published experimental work. We show that the simple approximation gives dimensions close to the values of the optimum Bragg reflection condition determined by the rigorous analysis. The resulting solution is more compact with a higher Q-factor when compared to other reported cylindrical DBR structures. This is because it properly takes into account the effect of the aspect ratio on the Bragg antiresonance condition along the z-axis of the resonator. Previous analyses assumed the propagation in the z-direction was independent of the aspect ratio, and the layers of the Bragg reflector were a quarter of a wavelength thick along the z-direction. When the aspect ratio is properly taken into account, we show that the thickness of the Bragg reflectors are equivalent to the thickness of plane wave Bragg reflectors (or quarter wavelength plates). Thus it turns out that the sizes of the reflectors are related to the free-space propagation constant rather than the propagation constant in the z-direction.

Spherical Bragg reflector resonators.

In this paper we introduce the concept of the spherical Bragg reflector (SBR) resonator. The resonator is made from multiple layers of spherical dielectric, loaded within a spherical cavity. The resonator is designed to concentrate the energy within the central region of the resonator and away from the cavity walls to minimize conductor losses. A set of simultaneous equations is derived, which allows the accurate calculation of the dimensions of the layers as well as the frequency. The solution is confirmed using finite-element analysis. A Teflon-free space resonator was constructed to prove the concept. The Teflon SBR was designed at 13.86 GHz and exhibited a Q-factor of 22,000, which agreed well with the design values. This represents a factor of 3.5 enhancement over a resonator limited by the loss-tangent of Teflon. Similarly, SBR resonators constructed with low-loss materials could achieve Q-factors of the order of 300,000.

Whispering-gallery mode technique applied to the measurement of the dielectric properties of Langasite between 4 K and 300 K.

We report new measurements of dielectric properties of Lanthanum gallium silicate (Langasite or LGS) conducted with the whispering-gallery mode technique at microwave frequencies and between 4.2 K and 300 K. The real part of the permittivity tensor of LGS presents two components having temperature coefficients of opposite sign. This unique property enables the design of a temperature compensated resonator that may be useful in building stable microwave oscillators or filters. We report also the first measurements of the two independent components of the imaginary part of the permittivity tensor. It appears LGS is a relatively high-loss dielectric material compared with sapphire or quartz.

The microwave characterization of single crystal lithium and calcium fluoride at cryogenic temperatures.

The whispering-gallery mode method is used for very accurate permittivity and dielectric loss measurements of single crystal lithium fluoride (LiF) and calcium fluoride (CaF2) over the temperature range of 4.5 K to 300 K. The absolute uncertainty in the real part of permittivity was estimated to be less than 0.1%, and it was limited principally by uncertainty in dimensions of the samples. Dielectric losses were measured with uncertainties of about 10% limited by the accuracy of Q-factor measurements. The measured materials exhibited dielectric losses between 2-4 x 10(-7) near 5 K. The relative permittivity was evaluated as 6.502 (4.9 K) to 6.844 (296 K) at 17.5 GHz for CaF2 and 8.534 (4.6 K) to 9.063 (300 K) at 13.5 GHz for LiF.

High-Q whispering modes in empty spherical cavity resonators.

This work presents the study of high-order modes in spherical cavity resonators. In general there are resonant mode families, degenerate in frequency, that "whisper" around the spherical surface. We call these whispering spherical (WS) mode sets. Each set includes the well-known whispering gallery (WG) mode, which propagates like a ray around the azimuth. Also, we identify a new mode, which we label the whispering longitudinal (WL) mode. This mode propagates as a wave front along the longitudinal direction. The rest of the degenerate set propagates like a combination of the WG and WL modes. We show that transverse electric WS modes have high geometric factors, greater than 2000, which increase linearly with frequency. This is an order of magnitude greater than that of a TM010 cylindrical resonator. Also, Q-factors as high as 65,000 at 13.3 GHz were measured at room temperature.

Simple design rules for optimal design of dielectric temperature-compensated sapphire resonators.

It has been shown that the use of two dielectric crystals with opposite temperature coefficient of permittivity allows the realization of a resonator with a zero temperature coefficient of frequency. By using sapphire and rutile materials, which have low-loss tangents, some compensated resonators with very high Q-factors have been realized. In this work we develop rules that greatly simplify the design of a dielectric-compensated resonator. We show that the optimum design for compensation at a specific temperature may be determined by simply selecting the aspect ratio of the sapphire resonator.

New method to build a high stability sapphire oscillator from the temperature compensation of the difference frequency between modes of orthogonal polarization.

A new method to construct a high stability sapphire oscillator is presented (patent pending). The method relies on the anisotropic fractional temperature coefficients of frequency (TCF) of orthogonally polarized modes. We show that it is possible to design a resonator with transverse electric and magnetic modes at different frequencies, but with the same TCF in units hertz per kelvin, resulting in temperature compensation of the difference frequency. Compensation was demonstrated between 50 to 77 K by measuring the difference frequency of two microwave oscillators frequency locked to orthogonally polarized whispering gallery modes. Curvature of the compensation points was measured to be 1 to 3 x 10(-8) K(-2) between 50 and 77 K. This technique enables the construction of temperature compensated oscillators at any temperature and does not require dielectric, paramagnetic, or mechanical compensation techniques. Considering the above parameters, we show that it is possible to construct oscillators with fractional frequency instability at tau = 1s, of order 7.6 x 10(-15) at solid nitrogen temperature (approximately 50 K).

Cryogenic dual-mode resonator for a fly-wheel oscillator for a caesium frequency standard.

A dual-mode, sapphire-loaded cavity (SLC) resonator has been designed and optimized with the aid of finite element software. The resonance frequency was designed to be near the frequency of a Cs atomic frequency standard. Experimental tests are shown to agree very well with calculations. The difference frequency of two differently polarized modes is shown to be a highly sensitive temperature sensor in the 50 to 80 K temperature range. We show that an oscillator based on this resonator has the potential to operate with fractional frequency instability below 10(-14) for measurement times of 1 to 100 seconds. This is sufficient to operate an atomic clock at the quantum projection noise limit.

High Q-factor Bragg-reflection sapphire-loaded cavity TE01delta mode resonators.

An innovative method of enhancing the quality factor of TE01delta cavity resonators with a dielectric tube made of monolithic sapphire is presented. Very high Q-factor is achieved by employing a Bragg reflection technique. A TE01delta mode in a copper cavity was measured to have a Q-factor of 1 x 10(5) at 8.78 GHz and 290 K. This is only 30% less than the limit due to the loss tangent of the dielectric material. The technique confines electromagnetic energy in the sapphire dielectric and in the vacuum well away from the cavity walls, thus reducing the surface losses in the copper shield. The technique offers some significant advantages over other methods. One advantage is the very low spurious mode density, which can improve filter and resonator design capabilities. Another is the small compact design, with a single sapphire piece, as compared to previously published Bragg reflection techniques. Finite element simulations and experimental data for this method were compared and found to be in very good agreement. The cavity dimensions were optimized to achieve maximum quality factor.