Measurement of the electric quadrupole moment of the 4d2D5/2 level in 88Sr+

Atomic Quadrupole Moment Measurement Using Dynamic Decoupling

We present a method that uses dynamic decoupling of a multilevel quantum probe to distinguish small frequency shifts that depend on m_{j}^{2}, where m_{j}^{2} is the angular momentum of level |j⟩ along the quantization axis, from large noisy shifts that are linear in m_{j}, such as those due to magnetic field noise. Using this method we measured the electric-quadrupole moment of the 4D_{5/2} level in ^{88}Sr^{+} to be 2.973_{-0.033}^{+0.026}ea_{0}^{2}. Our measurement improves the uncertainty of this value by an order of magnitude and thus helps mitigate an important systematic uncertainty in ^{88}Sr^{+} based optical atomic clocks and verifies complicated many-body quantum calculations.

Direct comparison of a Ca+ single-ion clock against a Sr lattice clock to verify the absolute frequency measurement

Optical frequency comparison of the (40)Ca(+) clock transition ν(Ca)((2)S(1/2-)(2D(5/2), 729 nm) against the (87)Sr optical lattice clock transition ν(Sr) ((1)S(0)-(3)P(0), 698 nm) has resulted in a frequency ratio ν(Ca) / ν(Sr) = 0.957 631 202 358 049 9(2 3). The rapid nature of optical comparison allowed the statistical uncertainty of frequency ratio ν(Ca) / ν(Sr) to reach 1 × 10(-15) in 1000s and yielded a value consistent with that calculated from separate absolute frequency measurements of ν(Ca) using the International Atomic Time (TAI) link. The total uncertainty of the frequency ratio using optical comparison (free from microwave link uncertainties) is smaller than that obtained using absolute frequency measurement, demonstrating the advantage of optical frequency evaluation. We note that the absolute frequency of (40)Ca(+) we measure deviates from other published values by more than three times our measurement uncertainty.

High-accuracy optical clock based on the octupole transition in 171Yb+

We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition (2)S(1/2)(F=0)→(2)F(7/2)(F=3) in a single trapped (171)Yb(+) ion. The extraordinary features of this transition result from the long natural lifetime and from the 4f(13)6s(2) configuration of the upper state. The electric-quadrupole moment of the (2)F(7/2) state is measured as -0.041(5)ea(0)(2), where e is the elementary charge and a(0) the Bohr radius. We also obtain information on the differential scalar and tensorial components of the static polarizability and of the probe-light-induced ac Stark shift of the octupole transition. With a real-time extrapolation scheme that eliminates this shift, the unperturbed transition frequency is realized with a fractional uncertainty of 7.1×10(-17). The frequency is measured as 642 121 496 772 645.15(52) Hz.

Generation of 656 nm coherent red-light by frequency-doubled Nd:YLiF4/β-BaB2O4 laser for a compact silver atoms optical clock

We describe an efficient continuous-wave diode-pumped Nd:YLiF4 laser oscillating on the σ-polarized 4F3/2-4I13/2 transition at λω = 1312 nm. With a simple linear cavity laser, we reached an intracavity power of 310 W at λ = 1312 nm for 16 W of absorbed pump power (λp ~ 806 nm). A 0.25 W of tunable radiation (λ2ω = 656−658 nm) was obtained by intracavity second-harmonic generation (SHG) with a 5 × 5 × 7 mm3β-BaB2O4 crystal. Up to 10 mW of tunable single-frequency operation was observed using a 200 μm thin fused silica intracavity solid etalon. The optimal waist for a maximum conversion efficiency has been calculated theoretically using Boyd and Kleiman model. For the 1312–656 nm SHG, we found a walk-off parameter B = 8.99 and an optimal waist of 25 μm. Comparing to the experimental measurement of the optimal waist, we found a relative discrepancy of 2.84 × 10-2. This laser is dedicated to the spectroscopic study of silver atoms trapped in a buffer-gas-free paraffin coated Pyrex cell that will be used in a compact atomic optical clock.

Frequency measurement of the 2S(1/2)-2D(3/2) electric quadrupole transition in a single 171Yb+ ion

We report on precision laser spectroscopy of the 2S(1/2)(F = 0)-2D(3/2) (F = 2, m(F) = 0) clock transition in a single ion of 171Yb+. The absolute value of the transition frequency, determined using an optical frequency comb referenced to a hydrogen maser, is 688358979309310 +/- 9 Hz. This corresponds to a fractional frequency uncertainty of 1.3 x 10(-14).

Magic wavelength to make optical lattice clocks insensitive to atomic motion

In a standing wave of light, a difference in spatial distributions of multipolar atom-field interactions may introduce atomic-motion dependent clock uncertainties in optical lattice clocks. We show that the magic wavelength can be defined so as to eliminate the spatial mismatch in electric dipole, magnetic dipole, and electric quadrupole interactions for specific combinations of standing waves by allowing a spatially constant light shift arising from the latter two interactions. Experimental prospects of such lattices used with a blue magic wavelength are discussed.

‘Designer atoms’ for quantum metrology

Entanglement is recognized as a key resource for quantum computation and quantum cryptography. For quantum metrology, the use of entangled states has been discussed and demonstrated as a means of improving the signal-to-noise ratio. In addition, entangled states have been used in experiments for efficient quantum state detection and for the measurement of scattering lengths. In quantum information processing, manipulation of individual quantum bits allows for the tailored design of specific states that are insensitive to the detrimental influences of an environment. Such 'decoherence-free subspaces' (ref. 10) protect quantum information and yield significantly enhanced coherence times. Here we use a decoherence-free subspace with specifically designed entangled states to demonstrate precision spectroscopy of a pair of trapped Ca+ ions; we obtain the electric quadrupole moment, which is of use for frequency standard applications. We find that entangled states are not only useful for enhancing the signal-to-noise ratio in frequency measurements--a suitably designed pair of atoms also allows clock measurements in the presence of strong technical noise. Our technique makes explicit use of non-locality as an entanglement property and provides an approach for 'designed' quantum metrology.

Single-atom optical clock with high accuracy

For the past 50 years, atomic standards based on the frequency of the cesium ground-state hyperfine transition have been the most accurate time pieces in the world. We now report a comparison between the cesium fountain standard NIST-F1, which has been evaluated with an inaccuracy of about 4 x 10(-16), and an optical frequency standard based on an ultraviolet transition in a single, laser-cooled mercury ion for which the fractional systematic frequency uncertainty was below 7.2 x 10(-17). The absolute frequency of the transition was measured versus cesium to be 1,064,721,609,899,144.94 (97) Hz, with a statistically limited total fractional uncertainty of 9.1 x 10(-16) the most accurate absolute measurement of an optical frequency to date.

Electric quadrupole moments of the D states of alkaline-earth-metal ions

The electric quadrupole moment for the 4d(2)D(5/2) state of (88)Sr(+); one of the most important candidates for an optical clock, has been calculated using the relativistic coupled-cluster theory. This is the first application of this theory to determine atomic electric quadrupole moments. The result of the calculation is presented and the important many-body contributions are highlighted. The calculated electric quadrupole moment is (2.94 +/- 0.07)ea(2)(0), where a(o) is the Bohr radius and the electronic charge while the measured value is (2.6 +/- 0.3) ea(2)(0). This is so far the most accurate determination of the electric quadrupole moment for the above mentioned state. We have also calculated the electric quadrupole moments for the metastable 4d(2)D(3/2) state of 88(Sr(+) and for the 3d(2)D(3/2.5/2) and 5d(2)D(3/2.5/2) states of (43)Ca(+) and (138)Ba(+), respectively.

Electric quadrupole shift cancellation in single-ion optical frequency standards

The electric quadrupole shift is presently the most significant source of uncertainty on the systematic shifts for several single-ion optical frequency standards. We present a simple method for cancelling this shift based on measurements of the Zeeman spectrum of the clock transition. This method is easy to implement and yields very high cancellation levels. A fractional uncertainty of 5 x 10(-18) for the canceled quadrupole shift is estimated for a measurement of the absolute frequency of the 5s (2)S(1/2)-4d (2)D(5/2) clock transition of 88Sr+.

Sub-Hertz optical frequency comparisons between two trapped 171Yb+ ions

We compare the frequencies of the 6s2S(1/2)(F = 0)-->5d2D(3/2)(F = 2) reference transition in 171Yb+ for two single ions stored in independent traps. The quadrupole moment of the 5d2D(3/2) state is measured to be 9.32(48) x 10(-40) C m2 and from the quadratic Stark shift the relevant scalar and tensor polarizabilities are determined to be alphaS(S(1/2)) - alphaS(D(3/2)) = -6.9(1.4) x 10(-40) J m2/V2 and alphaT(D(3/2)) = -13.6(2.2) x 10(-40) J m2/V2, respectively. In the absence of external perturbations we find a mean frequency difference between the two trapped ions of 0.26(42) Hz, corresponding to a relative difference of 3.8(6.1) x 10(-16). This is comparable to the agreement found in the most accurate comparisons between cesium fountain clocks.

Measurement of the (199)Hg+ 5d9 6s2 (2)D(5/2) electric quadrupole moment and a constraint on the quadrupole shift

The electric-quadrupole moment of the (199)Hg+ 5d9 6s2 (2)D(5/2) state is measured to be theta(D,5/2) = -2.29(8) x 10(-40) C m2. This value was determined by measuring the frequency of the (199)Hg+ 5d10 6s (2)S(1/2) --> 5d9 6s2 (2)D(5/2) optical clock transition for different applied electric-field gradients. An isolated, mechanically stable optical cavity provides a frequency reference for the measurement. We compare the results with theoretical calculations and discuss the implications for the accuracy of an atomic clock based upon this transition. We now expect that the frequency shift caused by the interaction of the quadrupole moment with stray electric-field gradients will not limit the accuracy of the Hg+ optical clock at the 10(-18) level.

Hertz-Level Measurement of the Optical Clock Frequency in a Single 88Sr+ Ion

The frequency of the 5s 2S(1/2)-4d 2D(5/2) electric quadrupole clock transition in a single, trapped, laser-cooled 88Sr+ ion has been measured by using an optical frequency comb referenced to a cesium fountain primary frequency standard. The frequency of the transition is measured as 444,779,044,095,484.6 (1.5) hertz, with a fractional uncertainty within a factor of 3 of that of the cesium standard. Improvements required to obtain a cesium-limited frequency measurement are described and are expected to lead to a 88Sr+ optical clock with stability and reproducibility exceeding that of the primary cesium standard.