Microwave Frequency Standards Research Articles

Spectral Properties of THz Quantum-Cascade Lasers: Frequency Noise, Phase-Locking and Absolute Frequency Measurement

Quantum cascade lasers combine desirable features, namely high optical power and compactness, as no other coherent source in the field of THz generation. While their maximum operating temperature is progressively increasing, getting close to the range accessible by Peltier cooling, their range of application is expanding into new fields, such us molecular spectroscopy and their use as local oscillators. These applications would benefit from the investigation and improvement of the laser coherence properties. In this contribution we report the exploitation of electro-optic coherent detection based on a near-IR frequency comb to measure the frequency noise of a free running 2.5 THz quantum cascade laser. An intrinsic linewidth quantum limit of ~230 Hz has been measured, in good agreement with the Schawlow-Townes theoretical prediction. The same detection scheme is then exploited to phase-lock the quantum cascade laser line to a multiple of the comb tooth spacing, while a second comb allows to precisely measure the THz frequency. Such a dual frequency comb experimental setup thus yields a narrow line THz emission traceable to a microwave frequency standard.

Terahertz Comb Spectroscopy Traceable to Microwave Frequency Standard

The fine-structured spectrum of a terahertz (THz) frequency comb has been observed using asynchronous-optical-sampling THz time-domain spectroscopy with an extended time window covering multiple THz pulses. Fourier transformation of 10 consecutive THz pulses enables us to obtain the spectrum of THz comb mode having a linewidth of 25 MHz at intervals of 250 MHz. Further expansion of time window up to 100 consecutive THz pulses reduces the linewidth of THz comb mode down to 2.5 MHz while conserving interval of 250 MHz. The observed THz comb mode can be used as a precise and accurate frequency marker for broadband THz spectroscopy because it is phase-locked to a microwave frequency standard by laser control. The spectroscopy of pharmaceutical tablets and low-pressure molecular gas is used to demonstrate the utility of this approach, indicating a spectral resolution of 250 MHz. The proposed method enables frequency calibration of the THz spectrometer based on a microwave frequency standard.

Ab initiocalculations of transition amplitudes and hyperfineAandBconstants of Ga iii

In this paper, the $E1$, $E2$, and $M1$ transition amplitudes are calculated along with the hyperfine $A$ and $B$ constants of doubly ionized gallium using the relativistic coupled-cluster approach. Electron correlations and the Gaunt interactions are considered to all orders using the coupled-cluster theory in a relativistic framework and their contributions are discussed explicitly in the calculations of all these amplitudes. Some interesting features of the correlation effects on the Gaunt interactions are noticed in the calculations of the hyperfine constants. The lifetimes of some low-lying states are also calculated using the transition amplitudes obtained by the present theory and the experimental transition energies. The calculated $E1$ transition amplitudes and lifetimes are in good agreement with the results obtained by the other theories and experiment. The hyperfine splitting of the ground states of ${}^{71}$Ga iii and ${}^{69}$Ga iii are found to be about 35 and 27.5 GHz, respectively, which shows the importance of these isotopes for the possible use of microwave frequency standards. The calculated hyperfine constants are associated with linewidth estimations of some transition lines in the visible and ultraviolet regions of electromagnetic spectrum.

Cooling and Crystallization of Trapped 113Cd+ Ions for Atomic Clock

We report recent experimental progress toward a trapped 113Cd+ ion microwave frequency standard. With laser cooling, a large number of trapped cadmium ions are cooled to crystallization and the temperature of the ion crystal is measured to be 16±3 mK. The second order Doppler frequency shift, a main limiting factor of the atomic clock's performance, is estimated to be less than 1 × 10−16.

Experimental Determination (∼mHz) of the Ground-State Hyperfine Separation of Trapped 199Hg+ in a Hyperbolic Paul Trap

The Ramsey fringes on the ground-state hyperfine transition of 199Hg+ (ΔF = 1, ΔmF = 0) ions trapped in a hyperbolic Paul trap are firstly observed with the method of time-separated oscillatory fields. The full width at half maximum of central Ramsey fringes is about 25 mHz and the corresponding quality factor Q of the line is greater than 1012 for the trapped 199Hg+ microwave frequency standard. The hyperfine transition frequency shifted by magnetic field is also measured by the high-resolution Ramsey fringes. The final result is Δνh f s = 40507347997.3(0.5) Hz, which is corrected to zero magnetic field.

Introduction to the special issue on the 2011 Joint IEEE International Frequency Control Symposium and European Frequency and Time Forum

The 8 invited and 17 contributed papers in this special issue focus on the following topical areas covered at the 2011 Joint IEEE International Frequency Control Symposium and European Frequency and Time Forum, held in San Francisco, California: 1) Materials and Resonators; 2) Oscillators, Synthesizers, and Noise; 3) Microwave Frequency Standards; 4) Sensors and Transducers; 5) Timekeeping and Time and Frequency Transfer; and 6) Optical Frequency Standards.

Blackbody radiation shift, multipole polarizabilities, oscillator strengths, lifetimes, hyperfine constants, and excitation energies in Hg+

Excitation energies of the [Xe]$4{f}^{14}5{d}^{10}ns$, [Xe]$4{f}^{14}5{d}^{10}n{p}_{j}$, [Xe]$4{f}^{14}5{d}^{10}n{d}_{j}$, [Xe]$4{f}^{14}5{d}^{10}{n}^{\ensuremath{'}}{f}_{j}$, and [Xe]$4{f}^{14}5{d}^{10}{n}^{\ensuremath{'}}{g}_{j}$ states in Hg${}^{+}$ are evaluated ($n\ensuremath{\le}10$, ${n}^{\ensuremath{'}}\ensuremath{\le}9$, and $[\mathrm{Xe}]=1{s}^{2}2{s}^{2}2{p}^{6}3{s}^{2}3{p}^{6}3{d}^{10}4{s}^{2}4{p}^{6}4{d}^{10}5{s}^{2}5{p}^{6}$). First-, second-, third-, and all-order Coulomb energies and first- and second-order Coulomb-Breit energies are calculated. Reduced matrix elements, oscillator strengths, and transition rates are determined for electric-dipole transitions, including the $ns$ ($n=6$--11), $np$ ($n=6$--10), $nd$ ($n=6$--10), $nf$ ($n=5$--9), and $ng$ ($n=5$--9) states. Lifetime values are determined for all above-mentioned states. The ground state $E1$, $E2$, and $E3$ polarizabilities are evaluated. The hyperfine structure in ${}^{199}$Hg${}^{+}$ and ${}^{201}$Hg${}^{+}$ ions is investigated. The hyperfine $A$ and $B$ values are determined for the first low-lying levels up to $n$ $=$ 7. The quadratic Stark effect on hyperfine structure levels of ${}^{199}$Hg${}^{+}$ and ${}^{201}$Hg${}^{+}$ ground states is investigated. The calculated shift for the ${}^{199}$Hg${}^{+}$ ($F$ $=$ 1, $M$ $=$ 0) $\ensuremath{\leftrightarrow}$ ($F$ $=$ 0, $M$ $=$ 0) transition is $\ensuremath{-}$0.0597(2) Hz/(kV/cm)${}^{2}$, in agreement with previous theoretical result $\ensuremath{-}$0.060(3) Hz/(kV/cm)${}^{2}$. These calculations provide a theoretical benchmark for comparison with experiment and theory and provide values of blackbody radiation shifts for microwave frequency standards with ${}^{199}$Hg${}^{+}$ and ${}^{201}$Hg${}^{+}$ ions.

Ultracold atoms and precise time standards

Experimental techniques of laser cooling and trapping, along with other cooling techniques, have produced gaseous samples of atoms so cold that they are, for many practical purposes, in the quantum ground state of their centre-of-mass motion. Such low velocities have virtually eliminated effects such as Doppler shifts, relativistic time dilation and observation-time broadening that previously limited the performance of atomic frequency standards. Today, the best laser-cooled, caesium atomic fountain, microwave frequency standards realize the International System of Units (SI) definition of the second to a relative accuracy of ≈3×10(-16). Optical frequency standards, which do not realize the SI second, have even better performance: cold neutral atoms trapped in optical lattices now yield relative systematic uncertainties of ≈1×10(-16), whereas cold-trapped ions have systematic uncertainties of 9×10(-18). We will discuss the current limitations in the performance of neutral atom atomic frequency standards and prospects for the future.

Widely tunable THz synthesizer

The generation of cw-THz radiation by photomixing is particularly suited to the high resolution spectroscopy of gases; nevertheless, until recently, it has suffered from a lack of frequency metrology. Frequency combs are a powerful tool that can transfer microwave frequency standards to optical frequencies and a single comb has permitted accurate (10−8) THz frequency synthesis with a limited tuning range. A THz synthesizer composed of three extended cavity laser diodes phase locked to a frequency comb has been constructed and its utility for high resolution gas phase spectroscopy demonstrated. The third laser diode allows a larger tuning range of up to 300 MHz to be achieved without the need for large frequency excursions, while the frequency comb provides a versatile link to be established from any traceable microwave frequency standard. The use of a single frequency comb as a reference for all of the cw-lasers eliminates the dependency of synthesized frequency on the carrier envelope offset frequency. This greatly simplifies the frequency comb stabilization requirements and leads to a reduced instrument complexity.

Widely and continuously tunable terahertz synthesizer traceable to a microwave frequency standard

We constructed a widely and continuously tunable terahertz frequency synthesizer traceable to a hydrogen maser linked to coordinated universal time. Photomixing of two optical frequency synthesizers, linked to the hydrogen maser via dual optical frequency combs, gave this THz synthesizer frequency uncertainty of 10⁻¹². To demonstrate the potential of wide and continuous tunability in the THz synthesizer, we tuned its output frequency up to 50 GHz discretely and 1.26 GHz continuously in the F-band while maintaining the unprecedented frequency uncertainty by using a uni-traveling-carrier photodiode as a photomixer. This THz synthesizer will be a powerful tool for broadband, high-precision THz spectroscopy and THz frequency metrology.

Analytical solution of microwave transition spectral lines for 87Rb atoms in a Hanle configuration

This paper theoretically investigates the microwave transition spectrum of 87Rb atomic D1 line with specially prepared atomic state in a Hanle configuration. The approximate analytical results have shown that the 0–0 transition spectral line has the highest contrast and can be applied to microwave frequency standards.

Formation of Ramsey fringes based on pulsed coherent light storage

We propose a new scheme of microwave frequency standards based on pulsed coherent optical information storage. Unlike the usual frequency reference where the Ramsey fringe is printed on the population of a certain state, we print the Ramsey fringe on the coherence. Then the coherence is detected in the form of a retrieval light. The central line of the Ramsey fringe can be used as a frequency reference in an absorption-cell-based atomic frequency standard. This scheme is free of light shifts as the interrogating process is separated from the optical pumping processes, and the cavity pulling effect is negligible due to the low Q requirement. Encoding the Ramsey interference into the retrieval light pulse has the merit of high signal to noise ratio and the estimated frequency stability of shot noise limit is about $2\times10^{-14}$ in 1 second, this scheme is promising for building small, compact and stable atomic frequency standards.

Full Stabilization of a Microresonator-Based Optical Frequency Comb

We demonstrate control and stabilization of an optical frequency comb generated by four-wave mixing in a monolithic microresonator with a mode spacing in the microwave regime (86 GHz). The comb parameters (mode spacing and offset frequency) are controlled via the power and the frequency of the pump laser, which constitutes one of the comb modes. Furthermore, generation of a microwave beat note at the comb's mode spacing frequency is demonstrated, enabling direct stabilization to a microwave frequency standard.

Gravitational redshift at INRIM

The gravitational redshift is one of the main biases in the comparison of primary frequency standards; even if it is not a limit for the present accuracy of the microwave frequency standards such as Cs beam or fountain clocks, it could be a challenge for the forthcoming generation of atomic optical clocks. In this article we report the evaluation of the gravitational redshift with respect to the Geoid reference at Istituto Nazionale di Ricerca Metrologica (INRIM) laboratories, with an accuracy of 1 × 10−17 in terms of relative frequency. The evaluation is based on GPS/levelling measurements and on the use of both a local and a global model for the Earth Geoid; the main limitation to the accuracy is given by the Geoid reference potential itself.

Hydrogenlike Highly Charged Ions for Tests of the Time Independence of Fundamental Constants

Hyperfine transitions in the electronic ground state of cold, trapped hydrogenlike highly charged ions have attractive features for use as frequency standards because the majority of systematic frequency shifts are smaller by orders of magnitude compared to many microwave and optical frequency standards. Frequency measurements of these transitions hold promise for significantly improved laboratory tests of local position invariance of the electron and quark masses.

Femtosecond frequency comb and optical frequency measurement of 532 nm Nd:YAG laser

In this paper we report on the Ti:sapphire mode-locked femtosecond laser based optical frequency comb apparatus and developed by NIM its application in optical frequency measurement of the I2 stabilized 532nm Nd∶YAG laser installed in NIM. The measurement result of 127I2 R(56)32-10 hyperfine transition is 563260223512991±20 (Hz), with a relative frequency uncertainty of 3.6×10-14. To our knowledge，this result is the first optical frequency measurement in China which is referenced directly to the Cs microwave frequency standard.

Cold atom clocks and applications

This paper describes advances in microwave frequency standards using laser-cooled atoms at BNM-SYRTE. First, recent improvements of the 133Cs and 87Rb atomic fountains are described. Thanks to the routine use of a cryogenic sapphire oscillator as an ultra-stable local frequency reference, a fountain frequency instability of 1.6 × 10−14 τ−1/2 where τ is the measurement time in seconds is measured. The second advance is a powerful method to control the frequency shift due to cold collisions. These two advances lead to a frequency stability of 2 × 10−16 at 50 000 s for the first time for primary standards. In addition, these clocks realize the SI second with an accuracy of 7 × 10−16, one order of magnitude below that of uncooled devices. In a second part, we describe tests of possible variations of fundamental constants using 87Rb and 133Cs fountains. Finally we give an update on the cold atom space clock PHARAO developed in collaboration with CNES. This clock is one of the main instruments of the ACES/ESA mission which is scheduled to fly on board the International Space Station in 2008, enabling a new generation of relativity tests.

Advances in atomic fountains

This article describes the work performed at BNM-SYRTE (Observatoire de Paris) in the past few years, toward the improvement and the use of microwave frequency standards using laser-cooled atoms. First, recent improvements of the 133Cs and 87Rb atomic fountains are described. An important advance is the achievement of a fractional frequency instability of 1.6 × 10 −14 τ − 1 / 2 where τ is the measurement time in seconds, thanks to the routine use of a cryogenic sapphire oscillator as an ultra-stable local frequency reference. The second advance is a powerful method to control the frequency shift due to cold collisions. These two advances lead to a fractional frequency in stability of 2 × 10 −16 at 50 000 s between two independent primary standards. In addition, these clocks realize the SI second with an accuracy of 7 × 10 −16 , one order of magnitude below that of uncooled devices. Tests of fundamental physical laws constitute an important field of application for highly accurate atomic clocks. In a second part, we describe tests of possible variations of fundamental constants using 87Rb and 133Cs fountains. The third part is an update on the cold atom space clock PHARAO developed in collaboration with CNES. This clock is one of the main instruments of the ACES/ESA mission which will fly on board the International Space Station in 2007-2008, enabling a new generation of relativity tests. To cite this article: S. Bize et al., C. R. Physique 5 (2004).

Delivery of high-stability optical and microwave frequency standards over an optical fiber network

Optical and radio frequency standards located in JILA and National Institute of Standards and Technology (NIST) laboratories have been connected through a 3.45-km optical fiber link. An optical frequency standard based on an iodine-stabilized Nd:YAG laser at 1064 nm (with an instability of ∼4×10-14 at 1 s) has been transferred from JILA to NIST and simultaneously measured in both laboratories. In parallel, a hydrogen maser-based radio frequency standard (with an instability of ∼2.4×10-13 at 1 s) is transferred from NIST to JILA. Comparison between these frequency standards is made possible by the use of femtosecond frequency combs in both laboratories. The degradation of the optical and rf standards that are due to the instability in the transmission channel has been measured. Active noise cancellation is demonstrated to improve the transfer stability of the fiber link.

The Dick effect for an optical frequency standard

We present an analysis of the frequency stability degradation of an optical atomic frequency standard which is operated sequentially, and that is caused by the frequency noise of the laser used to interrogate the clock transition. This is an extension to optical frequencies of the ‘Dick effect’ already studied in atomic microwave frequency standards. It is shown that the simple concept of laser linewidth is not the relevant parameter to estimate the frequency stability degradation. Rather, the details of the laser frequency noise spectral density must be accounted for together with the parameters of the interrogation method. We compute the optical Dick effect in the case of