Modern Michelson-Morley experiment using cryogenic optical resonators

An ultra-low vibration cryostat with split design

The development of cryogenic technology promotes frontier scientific discoveries, while the device performance is often limited by vibration of cryostats. We present the design and implementation of a split-type, ultra-low vibration cryostat using a pulse tube cryocooler. Methods of gas-liquid helium mixture damping, non-contact heat exchangers, soft connections, and vibration isolating foundation are used together to suppress vibration. These innovations reduce background vibrations at the sample area to 5 × 10-7 m/s2/Hz1/2 (7 × 10-9 m/Hz1/2) @ 1-10 Hz in all directions and effectively suppress vibration harmonics of the pulse tube frequency with a suppression ratio up to 23 dB. In addition, with a low heat leakage design, the 2.2 L large sample area can be cooled down to below 4 K in 36 h, and the temperature fluctuation is 0.03 mK under active control. The performance of ultra-low vibration and fast cooling of a large sample space to below 4 K is outstanding among the reported low-vibration cryostats, which meets the demands of advanced cryogenic applications.

Cryogenic sapphire optical reference cavity with crystalline coatings at 1 × 10-16 fractional frequency instability

The frequency stability of a laser locked to an optical reference cavity is fundamentally limited by thermal noise in the cavity length. These fluctuations are linked to material dissipation, which depends on both the temperature of the optical components and the material properties. Here, the design and experimental characterization of a sapphire optical cavity operated at 10 K with crystalline coatings at 1069 nm is presented. Theoretical estimates of the thermo-mechanical noise indicate a thermal noise floor below 4.5 × 10-18. Major technical noise contributions including vibrations, temperature fluctuations, and residual amplitude modulation are characterized in detail. The short-term performance is measured via a three-cornered hat analysis with two other cavity-stabilized lasers, yielding a noise floor of 1 × 10-16. The long-term performance is measured against an optical lattice clock, indicating cavity stability at the level of 2 × 10-15 for averaging times up to 10 000 s.

Improved bounds on Lorentz violation from composite pulse Ramsey spectroscopy in a trapped ion

In attempts to unify the four known fundamental forces in a single quantum-consistent theory, it is suggested that Lorentz symmetry may be broken at the Planck scale. Here we search for Lorentz violation at the low-energy limit by comparing orthogonally oriented atomic orbitals in a Michelson-Morley-type experiment. We apply a robust radiofrequency composite pulse sequence in the 2F7/2 manifold of an Yb+ ion, extending the coherence time from 200 μs to more than 1 s. In this manner, we fully exploit the high intrinsic susceptibility of the 2F7/2 state and take advantage of its exceptionally long lifetime. We match the stability of the previous best Lorentz symmetry test nearly an order of magnitude faster and improve the constraints on the symmetry breaking coefficients to the 10−21 level. These results represent the most stringent test of this type of Lorentz violation. The demonstrated method can be further extended to ion Coulomb crystals.

Digital control of residual amplitude modulation at the 10-7 level for ultra-stable lasers

The stabilization of lasers on ultra-stable optical cavities by the Pound-Drever-Hall (PDH) technique is a widely used method. The PDH method relies on the phase-modulation of the laser, which is usually performed by an electro-optic modulator (EOM). When approaching the 10^-16 fractional frequency stability level, this technology requires an active control of the residual amplitude modulation (RAM) generated by the EOM in order to bring the frequency stability of the laser down to the thermal noise limit of the ultra-stable cavity. In this article, we report on the development of an active system of RAM reduction based on a free space EOM, which is used to perform PDH-stabilization of a laser on a cryogenic silicon cavity. A minimum RAM instability of 1.4 × 10^-7 is obtained by employing a digital servo that stabilizes the EOM DC electric field, the crystal temperature and the laser power. Considering an ultra-stable cavity with a finesse of 2.5 × 10⁵, this RAM level would contribute to the fractional frequency instability at the level of about 5 × 10^-19, well below the state of the art thermal noise limit of a few 10^-17.

Long-term stable optical cavity for special relativity tests in space

BOOST (BOOst Symmetry Test) is a proposed space mission to search for Lorentz invariance violations and aims to improve the Kennedy-Thorndike parameter constraint by two orders of magnitude. The mission consists of comparing two optical frequency references of different nature, an optical cavity and a hyperfine transition in molecular iodine, in a low Earth orbit. Naturally, the stability of the frequency references at the orbit period of 5400 s (f=0.18 mHz) is essential for the mission success. Here we present our experimental efforts to achieve the required fractional frequency stability of 7.4×10^-14 Hz ^-1/2 at 0.18 mHz (in units of the square root of the power spectral density), using a high-finesse optical cavity. We have demonstrated a frequency stability of (9±3)×10^-14 Hz ^-1/2 at 0.18 mHz, which corresponds to an Allan deviation of 10^-14 at 5400 s. A thorough noise source breakdown is presented, which allows us to identify the critical aspects to consider for a future space-qualified optical cavity for BOOST. The major noise contributor at sub-milli-Hertz frequency was related to intensity fluctuations, followed by thermal noise and beam pointing. Other noise sources had a negligible effect on the frequency stability, including temperature fluctuations, which were strongly attenuated by a five-layer thermal shield.

Ultrastable Silicon Cavity in a Continuously Operating Closed-Cycle Cryostat at 4 K

We report on a laser locked to a silicon cavity operating continuously at 4 K with 1×10^{-16} instability and a median linewidth of 17 mHz at 1542 nm. This is a tenfold improvement in short-term instability, and a 10^{4} improvement in linewidth, over previous sub-10-K systems. Operating at low temperatures reduces the thermal noise floor and, thus, is advantageous toward reaching an instability of 10^{-18}, a long-sought goal of the optical clock community. The performance of this system demonstrates the technical readiness for the development of the next generation of ultrastable lasers that operate with an ultranarrow linewidth and long-term stability without user intervention.

Self-organized synchronization of digital phase-locked loops with delayed coupling in theory and experiment

Self-organized synchronization occurs in a variety of natural and technical systems but has so far only attracted limited attention as an engineering principle. In distributed electronic systems, such as antenna arrays and multi-core processors, a common time reference is key to coordinate signal transmission and processing. Here we show how the self-organized synchronization of mutually coupled digital phase-locked loops (DPLLs) can provide robust clocking in large-scale systems. We develop a nonlinear phase description of individual and coupled DPLLs that takes into account filter impulse responses and delayed signal transmission. Our phase model permits analytical expressions for the collective frequencies of synchronized states, the analysis of stability properties and the time scale of synchronization. In particular, we find that signal filtering introduces stability transitions that are not found in systems without filtering. To test our theoretical predictions, we designed and carried out experiments using networks of off-the-shelf DPLL integrated circuitry. We show that the phase model can quantitatively predict the existence, frequency, and stability of synchronized states. Our results demonstrate that mutually delay-coupled DPLLs can provide robust and self-organized synchronous clocking in electronic systems.

Resonator with Ultrahigh Length Stability as a Probe for Equivalence-Principle-Violating Physics

In order to investigate the long-term dimensional stability of matter, we have operated an optical resonator fabricated from crystalline silicon at 1.5 K continuously for over one year and repeatedly compared its resonance frequency f_{res} with the frequency of a GPS-monitored hydrogen maser. After allowing for an initial settling time, over a 163-day interval we found a mean fractional drift magnitude |f_{res}^{-1}df_{res}/dt|<1.4×10^{-20}/s. The resonator frequency is determined by the physical length and the speed of light and we measure it with respect to the atomic unit of time. Thus the bound rules out, to first order, a hypothetical differential effect of the Universe's expansion on rulers and atomic clocks. We also constrain a hypothetical violation of the principle of local position invariance for resonator-based clocks and derive bounds for the strength of space-time fluctuations.

Mathematical model of thermal shields for long-term stability optical resonators

Modern experiments aiming at tests of fundamental physics, like measuring gravitational waves or testing Lorentz Invariance with unprecedented accuracy, require thermal environments that are highly stable over long times. To achieve such a stability, the experiment including typically an optical resonator is nested in a thermal enclosure, which passively attenuates external temperature fluctuations to acceptable levels. These thermal shields are usually designed using tedious numerical simulations or with simple analytical models. In this paper, we propose an accurate analytical method to estimate the performance of passive thermal shields in the frequency domain, which allows for fast evaluation and optimization. The model analysis has also unveiled interesting properties of the shields, such as dips in the transfer function for some frequencies under certain combinations of materials and geometries. We validate the results by comparing them to numerical simulations performed with commercial software based on finite element methods.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

What do we know about Lorentz invariance?

The realization that Planck-scale physics can be tested with existing technology through the search for spacetime-symmetry violation brought about the development of a comprehensive framework, known as the gravitational standard-model extension (SME), for studying deviations from exact Lorentz and CPT symmetry in nature. The development of this framework and its motivation led to an explosion of new tests of Lorentz symmetry over the past decade and to considerable theoretical interest in the subject. This work reviews the key concepts associated with Lorentz and CPT symmetry, the structure of the SME framework, and some recent experimental and theoretical results.

Measurement and control of residual amplitude modulation in optical phase modulation

Residual amplitude modulation is one of the major sources of instability in ultra-sensitive optical detections based on frequency modulation. Using a MgO·LiNbO(3) electro-optic crystal, we systematically measure the temperature and polarization dependence of residual amplitude modulation and our experimental results are in good agreement with a previous theoretical analysis. After optical phase modulation, two independent arms including optical detection and frequency demodulation are employed to closely examine the instability of the residual amplitude modulation. Residual amplitude modulation below 25 ppm is obtained with an active cancellation scheme in which the crystal temperature is varied so as to zero the baseline drifts with different origins. Possible improvements for better suppression and stability are discussed.

Cavity bounds on higher-order lorentz-violating coefficients

We determine the sensitivity of a modern Michelson-Morley resonant-cavity experiment to higher-order nonbirefringent and nondispersive coefficients of the Lorentz-violating standard-model extension. Data from a recent year-long run of the experiment are used to place the first experimental bounds on coefficients associated with nonrenormalizable Lorentz-violating operators.

Laboratory test of the isotropy of light propagation at the 10(-17) level

We report on the results of a strongly improved test of local Lorentz invariance, consisting of a search for an anisotropy of the resonance frequencies of electromagnetic cavities. The apparatus comprises two orthogonal standing-wave optical cavities interrogated by a laser, which were rotated approximately 175 000 times over the duration of 13 months. The measurements are interpreted as a search for an anisotropy of the speed of light, within the Robertson-Mansouri-Sexl (RMS) and the standard model extension (SME) photon sector test theories. We find no evidence for an isotropy violation at a 1sigma uncertainty level of 0.6 parts in 10(17) (RMS) and 2 parts in 10(17) for seven of eight coefficients of the SME.

Thermoacoustic optical path length stabilization in a single-mode optical fiber

We present a simple technique to actively stabilize the optical path length in an optical fiber. A part of the fiber is coated with a thin, electrically conductive layer, which acts as a heater. The optical path length is thus modified by temperature-dependent changes in the refractive index and the mechanical length of the fiber. For the first time, we measure the dynamic response of the optical path length to the periodic changes of temperature and find it to be in agreement with our former theoretical prediction. The fiber's response to the temperature changes is determined by the speed of sound in quartz rather than by slow thermal diffusion. Making use of this fact, we succeeded in actively stabilizing the optical path length with a closed-loop bandwidth of 3.8 kHz.

Tests of relativity by complementary rotating Michelson-Morley experiments

We report relativity tests based on data from two simultaneous Michelson-Morley experiments, spanning a period of more than 1 yr. Both were actively rotated on turntables. One (in Berlin, Germany) uses optical Fabry-Perot resonators made of fused silica; the other (in Perth, Australia) uses microwave whispering-gallery sapphire resonators. Within the standard model extension, we obtain simultaneous limits on Lorentz violation for electrons (5 coefficients) and photons (8) at levels down to 10(-16), improved by factors between 3 and 50 compared to previous work.

Lorentz-violating electrodynamics and the cosmic microwave background

Possible Lorentz-violating effects in the cosmic microwave background are studied. We provide a systematic classification of renormalizable and nonrenormalizable operators for Lorentz violation in electrodynamics and use polarimetric observations to search for the associated violations.

Sensitive polarimetric search for relativity violations in gamma-ray bursts

We show that the recent measurements of linear polarization in gamma rays from GRB 930131 and GRB 960924 constrain certain types of relativity violations in photons to less than parts in 10(37), representing an improvement in sensitivity by a factor of 100,000.

Limits on Lorentz violation from synchrotron and inverse Compton sources

We derive new bounds on Lorentz violations in the electron sector from existing data on high-energy astrophysical sources. Synchrotron and inverse Compton data give precisely complementary constraints. The best bound on a specific combination of electron Lorentz-violating coefficients is at the 6 x 10(-20) level, and independent bounds are available for all the Lorentz-violating c coefficients at the 2 x 10(-14)level or better. This represents an improvement in some bounds by 14 orders of magnitude.

Cold atom clock test of Lorentz invariance in the matter sector

We report on a new experiment that tests for a violation of Lorentz invariance (LI), by searching for a dependence of atomic transition frequencies on the orientation of the spin of the involved states (Hughes-Drever type experiment). The atomic frequencies are measured using a laser cooled 133Cs atomic fountain clock, operating on a particular combination of Zeeman substates. We analyze the results within the framework of the Lorentz violating standard model extension (SME), where our experiment is sensitive to a largely unexplored region of the SME parameter space, corresponding to first measurements of four proton parameters and improvements by 11 and 13 orders of magnitude on the determination of four others. In spite of the attained uncertainties, and of having extended the search into a new region of the SME, we still find no indication of LI violation.

Phase-locked, low-noise, frequency agile titanium:sapphire lasers for simultaneous atom interferometers

We demonstrate a laser system consisting of a >1.6 W titanium:sapphire laser that is phase locked to another free-running titanium:sapphire laser at a wavelength of 852 nm with a phase noise of -138 dBc/Hz at 1 MHz from the carrier, using an intracavity electro-optic phase modulator. The residual phase variance is 2.5 x 10(-8) rad2 integrated from 1 Hz to 10 kHz. This system can phase-continuously change the offset frequency within 200 ns with frequency steps up to 4 MHz. Simultaneous atom interferometers can make full use of this ultralow phase noise in differential measurements, where influences from the vibration of optics are greatly suppressed in common mode.

Active sub-Rayleigh alignment of parallel or antiparallel laser beams

We measure and stabilize the relative angle of parallel and antiparallel laser beams to 5 nrad/(square root of)Hz resolution by comparing the phases of radio frequency beat notes on a quadrant photodetector. The absolute accuracy is 5.1 and 2.1 microrad for antiparallel and parallel beams, respectively, which is more than 6 and 16 times below the Rayleigh criterion.

Test of the isotropy of the speed of light using a continuously rotating optical resonator

We report on a test of Lorentz invariance performed by comparing the resonance frequencies of one stationary optical resonator and one continuously rotating on a precision air bearing turntable. Special attention is paid to the control of rotation induced systematic effects. Within the photon sector of the standard model extension, we obtain improved limits on combinations of 8 parameters at a level of a few parts in 10(-16). For the previously least well known parameter we find [EQUATION: SEE TEXT]. Within the Robertson-Mansouri-Sexl test theory, our measurement restricts the isotropy violation parameter [EQUATION: SEE TEXT]. corresponding to an eightfold improvement with respect to previous nonrotating measurements.

Test of Lorentz invariance in electrodynamics using rotating cryogenic sapphire microwave oscillators

We present the first results from a rotating Michelson-Morley experiment that uses two orthogonally orientated cryogenic sapphire resonator oscillators operating in whispering gallery modes near 10 GHz. The experiment is used to test for violations of Lorentz invariance in the framework of the photon sector of the standard model extension (SME), as well as the isotropy term of the Robertson-Mansouri-Sexl (RMS) framework. In the SME we set a new bound on the previously unmeasured kappa(ZZ)(e-) component of 2.1(5.7) x 10(-14), and set more stringent bounds by up to a factor of 7 on seven other components. In the RMS a more stringent bound of -0.9(2.0) x 10(-10) on the isotropy parameter, P(MM) = delta-beta + 1 / 2 is set, which is more than a factor of 7 improvement.

Long-distance frequency dissemination with a resolution of 10(-17)

We use a new technique to disseminate microwave reference signals along ordinary optical fiber. The fractional frequency resolution of a link of 86 km in length is 10(-17) for a one day integration time, a resolution higher than the stability of the best microwave or optical clocks. We use the link to compare the microwave reference and a CO2/OsO4 frequency standard that stabilizes a femtosecond laser frequency comb. This demonstrates a resolution of 3 x 10(-14) at 1 s. An upper value of the instability introduced by the femtosecond laser-based synthesizer is estimated as 1 x 10(-14) at 1 s.

Bound on Lorentz and CPT violating boost effects for the neutron

A search for an annual variation of a daily sidereal modulation of the frequency difference between colocated 129Xe and 3He Zeeman masers sets a stringent limit on boost-dependent Lorentz and CPT violation involving the neutron, consistent with no effect at the level of 150 nHz. In the framework of the general standard-model extension, the present result provides the first clean test for the fermion sector of the symmetry of spacetime under boost transformations at a level of 10(-27) GeV.

Vacuum Cerenkov radiation

Within the classical Maxwell-Chern-Simons limit of the standard-model extension, the emission of light by uniformly moving charges is studied confirming the possibility of a Cerenkov-type effect. In this context, the exact radiation rate for charged magnetic point dipoles is determined and found in agreement with a phase-space estimate under certain assumptions.

Subhertz-linewidth Nd:YAG laser

Light from a Nd:YAG laser at 1064 nm is independently stabilized to two Fabry-Perot etalons situated on separate vibration-isolation platforms. A heterodyne beat measurement shows their relative frequency stability to be at the part-in-10(15) level at 5 s and the relative linewidth to be less than 1 Hz.

Offset compensation by use of amplitude-modulated sidebands in optical frequency standards

We present a general method for continuously measuring and compensating for offsets (due to residual amplitude modulation, parasitic resonances, or electronic offset voltages, for example) in frequency stabilization systems. The spectral power distribution of the oscillator waveform is modified by amplitude-modulated sidebands, and the error signal is corrected to null the induced periodic lock-point shifts. We demonstrate significant improvements to the frequency stability of standards based on cryogenic optical resonators and molecular iodine.

Improved test of time dilation in special relativity

An improved test of time dilation in special relativity has been performed using laser spectroscopy on fast ions at the heavy-ion storage-ring TSR in Heidelberg. The Doppler-shifted frequencies of a two-level transition in 7Li+ ions at v=0.064c have been measured in the forward and backward direction to an accuracy of Deltanu/nu=1 x 10(-9) using collinear saturation spectroscopy. The result confirms the relativistic Doppler formula and sets a new limit of 2.2 x 10(-7) for deviations from the time dilation factor gamma(SR)=(1-v2/c2)(-1/2).