Single-ion Optical Frequency Standards Research Articles

Er:fiber-based femtosecond frequency comb stabilized to an Yb+ single-ion optical frequency standard

An erbium fiber-based femtosecond optical frequency comb stabilized to an Yb+ single-ion optical frequency standard was created. For the first time, a combination of an extra-cavity acousto-optic frequency modulator with fiber outputs and an intracavity electro-optic phase modulator based on a KTP crystal were used to stabilize offset frequency and one of the optical components of the Er:fiber femtosecond comb. As a result a locking bandwidth of 30 kHz for the optical comb offset frequency has been obtained. It is shown that the relative instability introduced by the stabilization and measurement systems into the output radio frequencies (in addition to the instability of the reference optical signal) is no worse than 5 × 10−14 for averaging times of 1 s and 2 × 10−16 for averaging times of 400 s.

A comparison of two 40Ca+ single-ion optical frequency standards at the 5 × 10−17 level and an evaluation of systematic shifts

A comparison of two optical frequency standards and a detailed study of the systematic frequency shifts of each 40Ca+ single-ion optical frequency standard is presented. The methods used for the systematic shift evaluation of the comparison measurements are also provided. One of the ion traps runs at a chosen operating frequency of 24.7 MHz, determined by the differential scalar polarizability of the clock transition, at which frequency the rf-induced Stark shifts and second-order Doppler shifts cancel each other, yielding a great suppression in the combined micromotion shifts. After compensating for the micromotion, the two optical frequency standards both reach an uncertainty level of a few parts in 10−17, which is more than an order of magnitude smaller compared to a few years ago. The dominant source of uncertainty is the blackbody radiation shift after minimizing the micromotion-induced shifts. The blackbody radiation shift is evaluated by controlling and measuring the temperature at the trap center. With a measurement over one month, the frequency difference between the two clocks is measured to be 3.2 × 10−17 with a measurement uncertainty of 5.5 × 10−17, considering both the statistical (1.9 × 10−17) and the systematic (5.1 × 10−17) uncertainties. Due to improvement of the clock laser and better control of the optical and electromagnetic field geometry and the laboratory conditions, a fractional stability of 7 × 10−17 in 20,000 s of averaging time is achieved. The absolute frequency of the 40Ca+ 4 s2S1/2–3d 2D5/2 clock transition is measured as 411 042 129 776 401.7 (1.1) Hz, with a fractional uncertainty of 2.7 × 10−15 using the GPS satellites as a link to the SI second. Details of the method used for the systematic shift evaluation of the measurements are given.

Laser system for Doppler cooling of ytterbium ion in an optical frequency standard

A laser system for Doppler cooling of ytterbium ion on the transition in a single-ion optical frequency standard is developed. The second harmonic of a semiconductor laser with a wavelength of is used for cooling. The laser frequency is doubled in a nonlinear BiBO crystal embedded in a ring resonator, which also serves as a reference for laser frequency stabilisation. Second-harmonic power of is generated at a wavelength of . Diode laser radiation is modulated by an electro-optic modulator at to generate a sideband exciting the hyperfine component of the cooling transition that is not excited by resonant cooling light. The sideband relative intensity of a few percent proved to be sufficient to reduce the ion dwelling time in the state to less than and increase the cooling efficiency.

Recent Progress of Single-Ion Optical Frequency Standards

Recent progress of single-ion optical frequency standards is reported. Based on clock transitions in single ions trapped and laser-cooled in ion traps, measurements with fractional uncertainties down to the 10−18 level have been achieved. Overview of the measurements reported so far is described. New attempts to overcome the limitations of the measurements are also reviewed.

Potential of electric quadrupole transitions in radium isotopes for single-ion optical frequency standards

We explore the potential of the electric quadrupole transitions 7s {sup 2}S{sub 1/2}-6d {sup 2}D{sub 3/2}, 6d {sup 2}D{sub 5/2} in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive {sup A}Ra{sup +} candidates, with A= 223-229, are identified. In particular, we show that the transition 7s {sup 2}S{sub 1/2} (F=2,m{sub F}=0)-6d {sup 2}D{sub 3/2} (F=0,m{sub F}=0) at 828 nm in {sup 223}Ra{sup +}, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of 10{sup -17}. With more experimental effort, the {sup 223,225,226}Ra{sup +} clocks could be pushed to a projected performance reaching the 10{sup -18} level.

A narrow linewidth and frequency-stable probe laser source for the 88Sr+ single ion optical frequency standard

In this paper, we describe in detail a narrow linewidth and frequency-stable laser source used to probe the 5s2S1/2–4d2D5/2 clock transition of the 88Sr+ optical frequency standard. The performance of the laser system is investigated with studies of its frequency drift rates and with high resolution spectra of the 88Sr+ clock transition. The observed short-term drift rates are typically in the range of 10 to 23 mHz/s, and the current long-term drift rate is 13.9(3) mHz/s. The laser stability, after subtraction of linear drifts, reaches 5×10−16 at an averaging time of 3000 s. This high level of stability is attributed for the most part to stabilization of the reference cavity at the temperature where the coefficient of linear thermal expansion crosses zero. An upper bound for the laser linewidth is given by the observation of a Fourier-transform limited resonance of 4.3 Hz (Δν/ν=1×10−14) on the 88Sr+ clock transition. The effective averaging time during the linewidth measurements was about 100 s.

$^{171}\hbox{Yb}^{+}$ Single-Ion Optical Frequency Standard at 688 THz

Two <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">171</sup> Yb <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> single-ion optical frequency standards operating at 688 THz (436 nm) are compared in order to investigate systematic frequency shifts in the subhertz range. In the absence of externally applied perturbations, a mean relative frequency difference of 3.8 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-16</sup> is observed. Using a femtosecond frequency comb generator based on an Er <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> -doped fiber laser, the frequency of the <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">171</sup> Yb <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> standard is measured with a relative systematic uncertainty of 3.1 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup> and a statistical uncertainty of 0.6 - 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup>

Laser frequency stabilization to a single ion

A fundamental limit to the stability of a single-ion optical frequency standard is set by quantum noise in the measurement of the internal state of the ion. We discuss how the interrogation sequence and the processing of the atomic resonance signal can be optimized in order to obtain the highest possible stability under realistic experimental conditions. A servo algorithm is presented that stabilizes a laser frequency to the single-ion signal and that eliminates errors due to laser frequency drift. Numerical simulations of the servo characteristics are compared to experimental data from a frequency comparison of two single-ion standards based on a transition at 688 THz in 171Yb+. Experimentally, an instability σy(100 s) = 9 × 10−16 is obtained in the frequency difference between both standards.

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+.

Towards an indium single-ion optical frequency standard

A narrow transition of a single laser-cooled ion, stored in a radio-frequency trap,can serve as a reference for a frequency standard of very high accuracy andstability. For the implementation of such a system, we study the 5s2 1S0–5s5p 3P0transition in In+, at a wavelength of 237 nm. This resonance has a linewidth of 0.8Hz, with systematic frequency shifts expected to be at the mHz level. A fractionalresolution of 1.3 × 10−13 has been so far achieved, limited by the frequency instabilityof the clock laser used to excite the line. The absolute frequency of the 1S0–3P0transition was measured using the frequency comb of a mode-locked fs laser, andas a reference a methane-stabilized He–Ne laser at 3.4 μm, which was calibratedagainst an atomic caesium fountain clock. The transition frequency wasdetermined as 1267 402 452 899.92 (0.23) kHz, the uncertainty being limited by theuncertainty of the He–Ne standard. The short-term frequency stability of theclock laser was recently greatly improved. With a new laser set-up a linewidth < 4Hz (FWHM) for integration times up to 26 s was achieved, using laserplatforms which actively isolate from external mechanical vibrations.

Measurement of the lifetime of the3d2D5/2state in40Ca+

We report a measurement of the lifetime of the 3d 2D_{5/2} metastable level in 40Ca+, using quantum jumps of a single cold calcium ion in a linear Paul trap. The 4s S_{1/2} - 3d D_{5/2} transition is significant for single-ion optical frequency standards, astrophysical references, and tests of atomic structure calculations. We obtain tau = 1.168 +- 0.007 s from observation of nearly 64,000 quantum jumps during approximately 32 hours. Our result is more precise and significantly larger than previous measurements. Experiments carried out to quantity systematic effects included a study of a previously unremarked source of systematic error, namely excitation by the broad background of radiation emitted by a semiconductor diode laser. Combining our result with atomic structure calculations yields 1.20 +- 0.01 s for the lifetime of 3d D_{3/2}. We also use quantum jump observations to demonstrate photon anti-bunching, and to estimate background pressure and heating rates in the ion trap.