Black-body Shift Research Articles

An optical atomic clock using 4DJ states of rubidium

Abstract We analyze an optical atomic clock using two-photon 5 S 1 / 2 → 4 D J transitions in rubidium. Four one- and two-color excitation schemes to probe the 4 D 3 / 2 and 4 D 5 / 2 fine-structure states are considered in detail. We compare key characteristics of Rb 4 D J and 5 D 5 / 2 two-photon clocks. The 4 D J clock features a high signal-to-noise ratio due to two-photon decay at favorable wavelengths, low dc electric and magnetic susceptibilities, and minimal black-body shifts. Ac Stark shifts from the clock interrogation lasers are compensated by two-color Rabi-frequency matching. We identify a ‘magic’ wavelength near 1060 nm, which allows for in-trap, Doppler-free clock-transition interrogation with lattice-trapped cold atoms. From our analysis of clock statistics and systematics, we project a quantum-noise-limited relative clock stability at the 10 − 13 / τ ( s ) -level, with integration time τ in seconds, and a relative accuracy of ∼ 10 − 13 . We describe a potential architecture for implementing the proposed clock using a single telecom clock laser at 1550 nm, which is conducive to optical communication and long-distance clock comparisons. Our work could be of interest in efforts to realize small and portable Rb clocks and in high-precision measurements of atomic properties of Rb 4 D J -states.

The use of various materials as a metal component in a metamaterial thermophotovoltaic emitter

Thermophotovoltaics (TPV) is a process by which photons emitted by a heat emitter are converted into electrical energy by a photovoltaic cell. Selective heat emitters that can survive temperatures at or above 1000°C have the potential to significantly improve the energy conversion efficiency of a PV cell by limiting the emission of photons with energies below the band gap energy of a photovoltaic cell.
 Waste heat can be a valuable source of energy if we can find a way to harvest it efficiently. Deviations from ideal absorption and ideal blackbody behavior lead to light losses. For selective emitters, any light emitted at wavelengths outside the bandgap energy of the photovoltaic system may not be efficiently converted, reducing efficiency. In particular, it is difficult to avoid emission associated with phonon resonance for wavelengths in the deep infrared, which cannot be practically converted. An ideal emitter would not emit light at wavelengths other than the bandgap energy, and much TFP research is devoted to designing emitters that approximate better this narrow emission spectrum.
 TPV systems usually consist of a heat source, a radiator and a waste heat removal system. TFV cells are placed between the emitter, often a metal or similar block, and the cooling system, often a passive radiator.
 Efficiency, heat resistance and cost are the three main factors for choosing a TPF emitter. The efficiency is determined by the absorbed energy relative to the incoming radiation. High temperature operation is critical because efficiency increases with operating temperature. As the temperature of the emitter increases, the radiation of the black body shifts toward shorter waves, which allows for more efficient absorption by photocells. This paper demonstrates the feasibility of using materials such as platinum, gold, and nichrome as a metal component in a metamaterial emitter with respect to their absorption and thermal stability.

Narrow-line Cooling and Determination of the Magic Wavelength of Cd.

We experimentally and theoretically determine the magic wavelength of the (5s^{2})^{1}S_{0}-(5s5p)^{3}P_{0} clock transition of ^{111}Cd to be 419.88(14) and 420.1(7)nm. To perform Lamb-Dicke spectroscopy of the clock transition, we use narrow-line laser cooling on the ^{1}S_{0}-^{3}P_{1} transition to cool the atoms to 6 μK and load them into an optical lattice. Cadmium is an attractive candidate for optical lattice clocks because it has a small sensitivity to blackbody radiation and its efficient narrow-line cooling mitigates higher order light shifts. We calculate the blackbody shift, including the dynamic correction, to be fractionally 2.83(8)×10^{-16} at 300K, an order of magnitude smaller than that of Sr and Yb. We also report calculations of the Cd ^{1}P_{1} lifetime and the ground state C_{6} coefficient.

Ca+40 ion optical clock with micromotion-induced shifts below 1×10−18

We recently reported a $^{40}{\mathrm{Ca}}^{+}$ optical clock comparison with an uncertainty at $5.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$, mainly limited by the excess micromotion shift. Here we report the progress made to reduce this shift and its uncertainty below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$ by precise measurement of the ``magic'' rf drive frequency ${\mathrm{\ensuremath{\Omega}}}_{0}$ at which the micromotion-induced scalar Stark shift and second-order Doppler shift cancel each other. ${\mathrm{\ensuremath{\Omega}}}_{0}$ is measured as $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}24.801(2)\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, and the differential static scalar polarizability $\mathrm{\ensuremath{\Delta}}{\ensuremath{\alpha}}_{0}$ of the $^{40}{\mathrm{Ca}}^{+}$ ion clock transition is measured as $\ensuremath{-}7.2677(21)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\phantom{\rule{0.28em}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}2}$. The blackbody radiation shift is then calculated to be 0.37913(12) Hz at 300 K considering the dynamic correction. The contribution of the blackbody shift coefficient to the uncertainty of the optical clock at room temperature has been reduced to the $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ level. With further improvements made to reduce the servo error, the total clock uncertainty is reduced to $2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$, limited by the blackbody radiation field evaluation.

Measurement of the Spin-Dipolar Part of the Tensor Polarizability of ^{87}Rb.

We report on the measurement of the contribution of the magnetic-dipole hyperfine interaction to the tensor polarizaility of the electronic ground state in ^{87}Rb. This contribution was isolated by measuring the differential shift of the clock transition frequency in ^{87}Rb atoms that were optically trapped in the focus of an intense CO_{2} laser beam. By comparing to previous tensor polarizability measurements in ^{87}Rb, the contribution of the interaction with the nuclear electric-quadrupole moment was isolated as well. Our measurement will enable better estimation of blackbody shifts in Rb atomic clocks. The methods reported here are applicable for future spectroscopic studies of atoms and molecules under strong quasistatic fields.

High-accuracy measurement of the differential scalar polarizability of a 88Sr+ clock using the time-dilation effect.

We report a high-accuracy measurement of the differential static scalar polarizability Δα(0) of the 5s(2)S(1/2)-4d(2)D(5/2) transition of the (88)Sr(+) ion. The high accuracy is obtained by comparing the micromotion-induced positive scalar Stark shift to the negative time-dilation shift. Measurement of the trap drive frequency where these shifts cancel is used to determine Δα(0) without the need to determine the electric field. Δα(0) is a critical parameter for the operation of frequency standards as it determines the blackbody radiation frequency shift coefficient, the largest source of uncertainty in the (88)Sr(+) ion clock. The measured value of Δα(0) is -4.7938(71) × 10(-40) J m(2)/V(2). Taking into account the dynamic correction, the blackbody shift at 300 K is 0.247,99(37) Hz. The contribution of the blackbody shift coefficient to the uncertainty of the ion standard has been reduced by a factor of 24, from 2 × 10(-17) to 8.3 × 10(-19). The revised total uncertainty of our reference standard is 1.2 × 10(-17), limited by the blackbody field evaluation. An additional benefit of the low uncertainty of Δα(0) is the ability to suppress, by a factor of about 200, the net micromotion frequency shifts.

Cs-based optical frequency measurement using cross-linked optical and microwave oscillators

We describe a measurement of the frequency of the 2S1/2(F = 0) - 2D3/2(F' = 2) transition of 171Yb+ at the wavelength 436 nm (frequency 688 THz), using a single Yb+ ion confined in a Paul trap and two caesium fountains as references. In one of the fountains, the frequency of the microwave oscillator that interrogates the caesium atoms is stabilized by the laser that excites the Yb+ reference transition with a linewidth in the hertz range. The stability is transferred to the microwave oscillator with the use of a fiber laser based optical frequency comb generator that also provides the frequency conversion for the absolute frequency measurement. The frequency comb generator is configured as a transfer oscillator so that fluctuations of the pulse repetition rate and of the carrier offset frequency do not degrade the stability of the frequency conversion. The phase noise level of the generated ultrastable microwave signal is comparable to that of a cryogenic sapphire oscillator. For fountain operation with optical molasses loaded from a laser cooled atomic beam source, we obtain a stability corresponding to a fractional Allan deviation of $4.1\times 10^{-14}\ (\tau/\text{s})^{-1/2}$. With the molasses loaded from thermal vapor and an averaging time of 65 h, we measure the frequency of the Yb+ transition with a relative statistical uncertainty of $2.8\times10^{-16}$ and a systematic uncertainty of $5.9\times10^{-16}$. The frequency was also simultaneously measured with the second fountain that uses a quartz-based interrogation oscillator. The unperturbed frequency of the Yb+ transition is realized with an uncertainty of $1.1\times10^{-16}$ that mainly results from the uncertainty of the blackbody shift at the operating temperature near 300 K. The transition frequency of 688 358 979 309 307.82(36) Hz, measured with the two fountains, is in good agreement with previous results.

Evaluation of systematic shifts of the88Sr+single-ion optical frequency standard at the10−17level

An ion trap of the end-cap design was built recently at the National Research Council of Canada for improved control of the ${}^{88}$Sr${}^{+}$ single-ion optical frequency standard systematic shifts. The uncertainty on the micromotion-induced shifts is smaller by more than four orders of magnitude when compared to our previous trap system and reaches a fractional frequency uncertainty of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$. To obtain this low uncertainty level, the micromotion is minimized with trim electrodes and the trap is operated at a special frequency at which there is anticorrelation between the second-order Doppler and Stark shifts. This choice of operating frequency, determined by the differential scalar polarizability of the clock transition, yields a suppression by a factor of $\ensuremath{\approx}$28 in the combined micromotion shifts. Like many optical frequency standards, the dominant source of uncertainty in the new trap is the blackbody radiation shift. Its uncertainty has been reduced by an order of magnitude with a recent theoretical evaluation of the differential scalar polarizability of the clock transition. The fractional blackbody shift uncertainty, estimated using a model of the blackbody field at the ion, is $2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. The otherwise dominant electric quadrupole shift is reduced to below the $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ level with a cancellation method based on the average frequency of several pairs of Zeeman components. This method also cancels the tensor Stark shift and simplifies the description of the frequency shifts that are quantization-axis dependent. This paper provides a detailed description of the ${}^{88}$Sr${}^{+}$ optical frequency standard uncertainty evaluation and the methods used to make the standard robust against changes in the trap environment. The total fractional frequency uncertainty of the ${}^{88}$Sr${}^{+}$ ion for our current system is estimated at $2.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. We also discuss the uncertainty evaluation of a recently reported measurement of the ${}^{88}$Sr${}^{+}$ $S$-$D$ clock transition made over a 2-month period by comparison with a maser referenced to the SI second. The frequency measured is $444\phantom{\rule{0.16em}{0ex}}779\phantom{\rule{0.16em}{0ex}}044\phantom{\rule{0.16em}{0ex}}095\phantom{\rule{0.16em}{0ex}}485.5(9)$ Hz, with an uncertainty limited by the evaluation of the maser frequency.

Magnetic blackbody shift of hyperfine transitions for atomic clocks

We derive an expression for the magnetic blackbody shift of hyperfine transitions such as the cesium primary reference transition which defines the second. The shift is found to be a complicated function of temperature, and has a ${T}^{2}$ dependence only in the high-temperature limit. We also calculate the shift of ground-state ${p}_{1/2}$ hyperfine transitions which have been proposed as new atomic clock transitions. In this case interaction with the ${p}_{3/2}$ fine-structure multiplet may be the dominant effect.

Reexamining blackbody shifts for hydrogenlike ions

We investigate blackbody-induced energy shifts for low-lying levels of atomic systems, with a special emphasis on transitions used in current and planned high-precision experiments on atomic hydrogen and ionized helium. Fine-structure- and Lamb-shift-induced blackbody shifts are found to increase with the square of the nuclear charge number, whereas blackbody shifts due to virtual transitions decrease with increasing nuclear charge as the fourth power of the nuclear charge. We also investigate the decay width acquired by the ground state of atomic hydrogen, due to interaction with blackbody photons. The corresponding width is due to an instability against excitation to higher excited atomic levels, and due to blackbody-induced ionization. These effects limit the lifetime of even the most fundamental, a priori absolutely stable, ``asymptotic'' state of atomic theory, namely, the ground state of atomic hydrogen.

A Novel Technique for Blackbody Shift Evaluation in Cs With a Fountain Standard

The uncertainty in the evaluation of the frequency shift caused in the Cs hyperfine transition by the alternating current Stark effect due to blackbody radiation is presently the dominant term in the accuracy budget of Cs fountain frequency standards. The bias is calculated with a formula wherein it is proportional to a coefficient beta. The latter must be known to the nearest 1% if the accuracy goal is in the low 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-16</sup> . This, in turn, has required 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-16</sup> uncertainty in frequency measurements used to evaluate beta. The novel technique discussed here relaxes this latter requirement by shifting the burden to the short-term stability of the experiment, hence allowing that kind of accuracy on beta even if the accuracy of the standard is lower. The method is based on fast temperature cycling of the drift tube while keeping everything else at a constant temperature. In this way, all frequency biases, other than the one under study, are rejected as common mode in a differential measurement, and the uncertainty on the relative shift can be better than the accuracy of the frequency standard

Subkilohertz absolute-frequency measurement of the 467-nm electric octupole transition in171Yb+

The {sup 2}S{sub 1/2}(F=0){yields}{sup 2}F{sub 7/2}(F=3,m{sub F}=0) transition at 467 nm in a single trapped, laser-cooled ion of {sup 171}Yb{sup +} has been measured to be f{sub Yb{sup +}}=642 121 496 771.26(23) kHz using a femtosecond laser frequency comb generator. The measurement is limited by measurement statistics and by the ac Stark shift, both related to the 4.5 kHz linewidth of the probe laser at the time. The systematic shifts of the transition, including ac Stark, second-order Zeeman, quadrupole, and blackbody shifts, have been evaluated.

Stark shifts due to black-body radiation

The free energy of the system consisting of a harmonically bound electron coupled via dipole interaction with the radiation field is calculated exactly at finite temperature. A temperature-dependent shift in the free energy, Delta F0= pi e2(kT)2/3h(cross)mc3 is identified. The shift in the energy, however, is opposite in sign, in disagreement with previous calculations. It is pointed out that, for weak binding, these results can be applied to a Rydberg electron. The Hollberg-Hall (1984) measurements of the black-body shift in high Rydberg states of rubidium are consistent with these results.

A new transient temperature emissometer

An emissometer is described which measures the temperature dependent total hemispherical emittance of flat samples coated with a selective surface. The construction of the instrument is such that heat losses occur only through radiation and then only from the surface under investigation. The emittances of several selective surfaces are measured and compared with other results on the same, or similar surfaces. These are measured in both other calorimeters and in instruments using reflectance methods. It is found that different calorimetric methods give close agreement, as do different reflectance methods. However, reflectance results tend to be about one third lower than those obtained through calorimetry. This seems to indicate that normal emittance and hemispherical emittance should not be equated for selective surfaces. There also appears to be a marked difference in the temperature dependence of emittance, depending on whether the measurements are made in a calorimeter or calculated from theoretical black body shifts applied to spectral reflectance curves.