Cavity Phase Shift Research Articles

Development of a new tuning method for an radio frequency quadrupole accelerator

Tuning is a critical step in the low-power test of the radio frequency quadrupole (RFQ) accelerator. A 163 MHz RFQ for boron neutron capture therapy (BNCT) at Lanzhou University has been fully assembled. Its designed output energy is 2.6 MeV, and the designed output current in continuous wave mode is 30 mA. Before the feeding of high power, a low-power tuning was performed. First, based on the analysis of the tuning algorithm, a new tuning code capable of tuning the RFQ longitudinal field distribution to any desired target field distribution has been developed using Matlab. The tuning code mainly consisted of two parts: the data processing module and the tuning module, including sub-functions such as smoothing processing function and Fourier expansion function. Among them, the smoothing function based on the Gaussian distribution can effectively eliminate random errors in the measured voltage distribution, thereby optimizing the tuning procedure. Then, a new bead-pull system which can directly track the cavity phase shift was built. The bead-pull system was mainly composed of a vector network analyzer, a stepper motor, etc. Finally, the field unflatness of the RFQ was controlled below 1% after 4 times of tuning. The experiment also measured the radio-frequency performance of the RFQ cavity after installing the fixed copper tuners. The results showed that the RFQ operation frequency was 162.937 MHz, the unflatness of the quadrupole voltage was ±0.74%, and the asymmetry of the dipole voltage was ±1.19%, all of which met the requirements of beam dynamics.

Characteristics analysis of compact cesium atomic clock with magnetic state selection

This paper introduces a compact magnetic state-selection cesium atomic clock called LIP Cs-3000 and analyses its characteristics. The test results reveal that the ranges of the line width, peak-to-valley ratio and signal-to-noise ratio of Ramsey pattern are 340–410 Hz, 2–13 and 2,000–8,000 respectively. The corresponding distributions of these parameters are derived by using statistical methods. According to these results, some suggestions are put forward for the further development of the clock. It is also pointed out that the most important factor affecting the accuracy of LIP Cs-3000 atomic clock is the uncertainty of cavity phase shift. In addition, the method to estimate the lifetime of a clock has been proposed. In the end, the paper gives some environmental adaptability designs of the clock, which enable the clock to be used in complex environments.

First uncertainty evaluation of the cesium fountain primary frequency standard NMIJ-F2

We report the first uncertainty evaluation of NMIJ-F2, the second atomic fountain primary frequency standard at the National Metrology Institute of Japan. To improve the frequency stability, we increase the number of detected atoms to 9 × 105 using high-power cooling laser beams for vapor-loaded optical molasses and optical pumping into the Zeeman sublevel m F = 0. We also employ an ultra-stable cryogenic sapphire oscillator as a local oscillator to prevent the degradation of frequency stability due to the Dick effect. After correcting the collisional frequency shift by alternating atom densities, the frequency stability typically reaches 2.5 × 10−13(τ/s)−1/2. Its value is 1.9 × 10−16 after 20 days of measurement. Type B uncertainty is typically evaluated at 4.7 × 10−16; the largest contribution is from a distributed cavity phase shift, followed by a microwave leakage shift. In long-term comparison, the frequency of NMIJ-F2 is found to be consistent with that of the other primary and secondary frequency standards within the uncertainty.

Measuring atom positions in a microwave cavity to evaluate distributed cavity phase shifts

Distributed cavity phase (DCP) frequency shifts are a leading systematic effect in atomic fountain frequency standards. They originate from the phase variations of the field in the microwave cavity combined with different positions of the atoms in the cavity on the ascent and descent. Here we demonstrate techniques to precisely determine the position of the cloud of atoms in the microwave cavity, using either the approximately linear variation of the transverse components of the microwave field or the quadratic variation of the longitudinal microwave field amplitude in the cavity. We also show that shifting the initial position of the atoms gives a significantly higher sensitivity to DCP variations than the often-used tilting of fountains. A demonstrated centring precision of order 50 μm will enable DCP frequency shift uncertainties to be reduced to less than 10–17 and thereby contribute insignificantly to the accuracy budget of a standard. These techniques to vertically align a fountain are straightforward to automate for routine operation and require a negligible fraction of the standard’s averaging time.

Microwave Detection of Electron-Phonon Interactions in a Cavity-Coupled Double Quantum Dot.

Quantum confinement leads to the formation of discrete electronic states in quantum dots. Here we probe electron-phonon interactions in a suspended InAs nanowire double quantum dot (DQD) that is electric-dipole coupled to a microwave cavity. We apply a finite bias across the wire to drive a steady state population in the DQD excited state, enabling a direct measurement of the electron-phonon coupling strength at the DQD transition energy. The amplitude and phase response of the cavity field exhibit oscillations that are periodic in the DQD energy level detuning due to the phonon modes of the nanowire. The observed cavity phase shift is consistent with theory that predicts a renormalization of the cavity center frequency by coupling to phonons.

Ozone Cross-Section Measurement by Gas Phase Titration.

Elevated values of ground-level ozone damage health, vegetation, and building materials and are the subject of air quality regulations. Levels are monitored by networks using mostly ultraviolet (UV) absorption instruments, with traceability to standard reference photometers, relying on the UV absorption of ozone at the 253.65 nm line of mercury. We have redetermined the ozone cross-section at this wavelength based on gas phase titration (GPT) measurements. This is a well-known chemical method using the reaction of ozone (O3) with nitrogen monoxide (NO) resulting in nitrogen dioxide (NO2) and oxygen (O2). The BIPM GPT facility uses state-of-the-art flow measurement, chemiluminescence for NO concentration measurements, a cavity phase shift analyzer (CAPS) for NO2 measurements, and a UV ozone analyzer. The titration experiment is performed over the concentration range 100-500 nmol/mol, with NO and NO2 reactants/calibrants diluted down from standards with nominal mole fractions of 50 μmol/mol. Accurate measurements of NO, NO2, and O3 mole fractions allow the calculation of ozone absorption cross section values at 253.65 nm, and we report a value of 11.24 × 10-18 cm2 molecule-1 with a relative expanded uncertainty of 1.8% (coverage factor k = 2) based on nitrogen monoxide titration values and a value of 11.22 × 10-18 cm2 molecule-1 with a relative expanded uncertainty of 1.4% (coverage factor k = 2) based on nitrogen dioxide titration values. The excellent agreement between these values and recently published absorption cross-section measurements directly on pure ozone provide strong evidence for revising the conventionally accepted value of ozone cross section at 253.65 nm.

First accuracy evaluation of NIST-F2

We report the first accuracy evaluation of NIST-F2, a second-generation laser-cooled caesium fountain primary standard developed at the National Institute of Standards and Technology (NIST) with a cryogenic (liquid nitrogen) microwave cavity and flight region. The 80 K atom interrogation environment reduces the uncertainty due to the blackbody radiation shift by more than a factor of 50. Also, the Ramsey microwave cavity exhibits a high quality factor (>50 000) at this low temperature, resulting in a reduced distributed cavity phase shift. NIST-F2 has undergone many tests and improvements since we first began operation in 2008. In the last few years NIST-F2 has been compared against a NIST maser time scale and NIST-F1 (the US primary frequency standard) as part of in-house accuracy evaluations. We report the results of nine in-house comparisons since 2010 with a focus on the most recent accuracy evaluation. This paper discusses the design of the physics package, the laser and optics systems and the accuracy evaluation methods. The type B fractional uncertainty of NIST-F2 is shown to be 0.11 × 10−15 and is dominated by microwave amplitude dependent effects. The most recent evaluation (August 2013) had a statistical (type A) fractional uncertainty of 0.44 × 10−15.

Photonic Microcantilevers With Interferometric Bragg Grating Interrogation

Germanosilicate glass microcantilevers are fabricated featuring an integrated Fabry-Perot interferometer. Direct UV writing of single-mode planar waveguides and Bragg gratings is combined with physical micromachining, using a precision dicing saw, to realize glass microcantilevers on a silicon platform. The device presented here has a wavelength shift force sensitivity of 330 nm/N, which is calibrated using a surface profilometer measurement and is an order of magnitude better than current state-of-the-art Bragg-grating-based sensors. The device also shows an approximately tenfold increase in amplitude modulation compared with a similar device architecture utilizing a single Gaussian-apodized Bragg grating. By forming the Fabry-Perot cavity around the point of greatest strain, we reduce the unwanted effects of grating chirp as the cantilever is deflected and relate the performance to a mechanical model that relates cavity phase shift to deflection.

Progress in atomic fountains at LNE-SYRTE

We give an overview of the work done with the Laboratoire National de Métrologie et d'Essais-Systèmes de Référence Temps-Espace (LNE-SYRTE) fountain ensemble during the last five years. After a description of the clock ensemble, comprising three fountains, FO1, FO2, and FOM, and the newest developments, we review recent studies of several systematic frequency shifts. This includes the distributed cavity phase shift, which we evaluate for the FO1 and FOM fountains, applying the techniques of our recent work on FO2. We also report calculations of the microwave lensing frequency shift for the three fountains, review the status of the blackbody radiation shift, and summarize recent experimental work to control microwave leakage and spurious phase perturbations. We give current accuracy budgets. We also describe several applications in time and frequency metrology: fountain comparisons, calibrations of the international atomic time, secondary representation of the SI second based on the (87)Rb hyperfine frequency, absolute measurements of optical frequencies, tests of the T2L2 satellite laser link, and review fundamental physics applications of the LNE-SYRTE fountain ensemble. Finally, we give a summary of the tests of the PHARAO cold atom space clock performed using the FOM transportable fountain.

Comment on ‘Accurate rubidium atomic fountain frequency standard’

We discuss the treatment of distributed cavity phase, microwave lensing and microwave leakage in the paper by Ovchinnikov and Marra (2011 Metrologia 48 87–100). The paper neglects the potential distributed cavity phase shifts from linear phase gradients and quadrupolar phase variations. Only azimuthally symmetric phase variations were analysed and an incorrect model was used for these. The paper also omits an uncertainty due to microwave lensing, which must be included. Finally, we describe additional measurements that could clarify the model used to analyse the frequency shifts due to microwave leakage.

Improved accuracy of the NPL-CsF2 primary frequency standard: evaluation of distributed cavity phase and microwave lensing frequency shifts

We evaluate the distributed cavity phase (DCP) and microwave lensing frequency shifts, which were the two largest sources of uncertainty for the NPL-CsF2 caesium fountain clock. We report measurements that confirm a detailed theoretical model of the microwave cavity fields and the frequency shifts of the clock that they produce. The model and measurements significantly reduce the DCP uncertainty to 1.1 × 10−16. We derive the microwave lensing frequency shift for a cylindrical cavity with circular apertures. An analytic result with reasonable approximations is given, in addition to a full calculation that indicates a shift of 6.2 × 10−17. The measurements and theoretical models we report, along with improved evaluations of collisional and microwave leakage induced frequency shifts, reduce the frequency uncertainty of the NPL-CsF2 standard to 2.3 × 10−16, nearly a factor of two lower than its most recent complete evaluation.

Cold atom space clock with counter-propagating atoms

We discuss the feasibility of realizing a cold atom space clock with counter-propagating cold atoms in microgravity. The design of the space clock is based on an atomic beam clock with Ramsey cavity, except that magneto-optical trap (MOT) is placed at each side. Cold atoms are launched simultaneously from the MOTs at both sides of the clock and they move at the counter-direction towards each other. The velocity of the launched atoms is precisely controlled to Ramsauer-Townsend resonance so that no additional collision frequency shift takes place. Such configuration can efficiently cancel the frequency shift resulting from cavity phase shift and increase the signal-to-noise ratio (SNR).

Compensation of systematic errors in a compact atomic beam frequency standard due to evanescent field inside a Ramsey cavity

Systematic errors due to evanescent field inside an E-plane type Ramsey cavity are corrected by introducing an extended square pulse profile in our Ramsey spectral analysis. This procedure is crucial for the proper operation of thermal beam based atomic frequency standards with short cavities. By accounting for the spatial extent of the field inside the cavity, the method enables a correct calculation of transition probability for atoms at the interaction region. The authors demonstrate that the systematic errors in quadratic Doppler and end-to-end cavity phase shifts can be reduced by an order of magnitude.

Passive Phasing in a Coherent Laser Array

A coherent array of fiber lasers in a self-Fourier cavity is described and analyzed. With individual regenerative feedback added to each fiber laser, the integrated gain in each individual fiber is a function of its cold cavity phase shift (fiber length). This results in a gain-dependent phase shift due to the Kramers-Kronig relations, and has been shown to partially compensate for the random differences in fiber lengths often encountered in coherent fiber arrays. A coupled cavity analysis of the active gain elements and the passive external cavity is performed and a self-consistent fundamental supermode determined. The output phase distribution of the array is determined based on a random distribution in fiber lengths. The Strehl ratio of this phase distribution is calculated and compared to experimental data.

Reevaluation of the Optically Pumped Cesium Frequency Standard NRLM-4 With an H-Bend Ring Cavity

The largest source of uncertainty of the optically pumped cesium (Cs) frequency standard (NRLM-4), i.e., the distributed cavity phase shift, was reduced by replacing the microwave cavity with a new ring-type one. An H-bend-type ring cavity is adopted for the first time. Due to the novel cavity and the improvement of the Cs beam alignment, the distributed cavity phase shift was significantly reduced from 2 x 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-14</sup> to 1.4 x 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup> . The frequency stability was measured to be 8 x 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-13</sup> tau <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1/2</sup> . The total uncertainty was reevaluated to be 6.7 x 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup> , which is four times better than the previous value.

A Movable-Cavity Cold Atom Space Clock

We present an experimental scheme of a cold atom space clock witha movable cavity. By using a single microwave cavity, we find that theclock has a significant advantage, i.e. the longitudinal cavity phaseshift is eliminated. A theoretical analysis has been carried out interms of the relation between the atomic transition probability and thevelocity of the moving cavity by taking into account the velocitydistribution of cold atoms. The requirements for the microwave powerand its stability for atomic π/2 excitation at differentmoving velocities of the cavity lead to the determination of the properworking parameters of the rubidium clock in frequency accuracy10−17. Finally, the mechanical stability for the scheme isanalysed and the ways of solving the possible mechanical instability ofthe device are proposed.

Numerical Simulation of Distributed Cavity Phase Shift in Atomic Fountain Frequency Standard

The spatial phase variations in feeding a microwave cavity with asymmetrical amplitudes and phases were calculated using the finite element method (FEM) that was applied to the three-dimensional (3D) model of the microwave cavity developed at the National Metrology Institute of Japan (NMIJ)/AIST. The distributed cavity phase shift (DCPS) in an atomic fountain frequency standard was calculated for atomic interaction with the position-dependent amplitudes and phases inside the cavity. The tolerances of asymmetry in the phases and amplitudes of microwaves were determined in order to achieve an uncertainty of 5×10-16 with respect to the DCPS.

Measurement of dynamic end-to-end cavity phase shifts in cesium-fountain frequency standards

We have measured a previously unobserved systematic frequency shift in our cesium-fountain frequency standard, NIST-F1. This shift, predicted theoretically previously, mimics the well-known end-to-end phase shift in atomic beam standards when synchronous thermal transients are present. Detuning the microwave cavity several megahertz from resonance reduces this effect to the deltaf/f = 1o(-16) level.

Measurement of dynamic end-to-end cavity phase shifts in cesium-fountain frequency standards

Measurement of dynamic end-to-end cavity phase shifts in cesium-fountain frequency standards

Characterization of the Brazilian Cs atomic-frequency standard: evaluation of major shifts

As part of a programme to implement scientific time and frequency metrology in Brazil, the caesium-beam frequency standard of the Instituto de Física de São Carlos has been improved in order to obtain greater accuracy. Our most recent evaluation shows an Allan standard deviation of σy(τ) = (1.8 ± 0.2) × 10-11τ-0.5, corresponding to an improvement of two orders of magnitude over our previous evaluation. Estimates of the main shifts of the frequency standard, such as second-order Doppler shift, end-to-end cavity phase shift, and Rabi frequency value, have been performed employing two different methods that allow the results to be extracted from the Ramsey pattern.