Optical Atomic Clocks—from Dream to Reality

Recent developments in atomic physics and laser technology, especially techniques for laser cooling and the manipulation of atoms, have enabled the realization of so-called Cesium fountain atomic clocks with relative accuracy approaching 4 x 10-16.

 

figure

The changing definition of the “second”: (Left) 1s = 1/86,400 of a solar day; (center) 1s = 1/31,556,925.9747 of the tropical year; (right) 1s = 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atoms.

Time and timekeeping are among the most important aspects of human society. It is hard to imagine what life would be like without the presence of clocks, watches and cell phones to tell us what time it is.

For much of human history, time was based on the rotation of the Earth. It wasn’t until 1928 that the world had a definite and unambiguous time scale. That year, the International Astronomical Union recommended that the time measures from the various astronomical almanacs be used and called Universal Time. Still, there was no international agreement on the fundamental unit of time—the second—for the next couple of decades.

Finally, in the 1950s, the second was defined as 1/86,400 of a mean solar day. However, because the solar day is not exactly the same over the course of a year, the SI second was modified in 1956 to become the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours Ephemeris Time. This definition was ratified by the 11th General Conference on Weights and Measures in 1960.

An important next step was taken in 1967, when the second was made independent of geophysical phenomena. By that time, scientists had realized that the well-defined quantum energy states of an unperturbed atom provide an almost perfect and universal clock. By letting electromagnetic radiation excite such states, very sharp resonances could be used as frequency references to yield a much-improved definition of the second. At the 13th meeting of the General Conference of Weights and Measures, the second of atomic time was given its current definition: the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

Time research has played an important role in science. Indeed, 15 Nobel Prizes have been awarded in physics since the 1940s to people who have made significant contributions to atomic timekeeping. Most recently, John L. Hall and Theodor W. Hänsch shared half of the 2005 Nobel Prize in Physics for their work in high-precision laser-based spectroscopy and the development of the optical frequency comb technique, which yields ultra-precise measurements in both the frequency and time domains (Rev. Mod. Phys. 79, 1279 and Rev. Mod. Phys. 79, 1297).
The following equation can be used to describe the instability of a frequency standard based on an atomic transition:

σ(τ) ~ (Δf 0N) • (1/√τ ),

where Δν and ν0 are the line width and center frequency of the atomic transition, respectively. N is the number of atoms interacting with the electromagnetic field and τ is the measurement duration. It is obvious that the precision of the clock is strongly related to Δν/ν0. Transitions in the optical frequency region (ν0 ~ 1014-1015 Hz) have some five orders of magnitude higher frequency than those in the microwave region (ν0 ~ 1010 Hz).

Further, because many of those transitions also have very narrow line width, down to the sub-hertz, and even millihertz, level, scientists have long dreamt of building an optical clock. The combination of high frequency and narrow line width for optical clocks has resulted in predicted accuracy that is 100 to 1,000 times better than those for microwave clocks, which can reach values as low as 10-17 to 10-18.

 

figure

The principle of the optical clock: The laser frequency is locked on the atomic transition, and then divided precisely into the microwave region for counting.

With such high accuracy of time and frequency standards, the SI system of units could be further improved, and scientists could precisely measure the physics constants, search for possible drift, and test the fundamental physical theories. Optical clocks also offer potential applications for new and better satellite-based communication and positioning systems.

Similar to microwave clocks, the optical clock consists of two basic parts: an oscillator and a counter. The revolutionary discovery of the femtosecond laser frequency comb in 1999 made available a perfect “gear” for dividing optical frequencies down to microwave frequencies for simple counting. With this, the dream of building an optical clock took a giant step forward.

During the past six years, the frequencies of many atomic clock transitions have been measured with high precision in metrological laboratories around the world using the optical frequency comb technique. It is significant to note that the International Committee of Weights and Measures (CIPM) approved for the first time in 2006 four atomic transitions (Hg+, Sr+, Yb+ and Sr) in the optical frequency region as secondary representations of the SI second.

The General Conference for Weights and Measures (CGPM) will meet in October 2007, and the delegates from the members of the Convention of the Metre will make the final decision about the recommendation of the CIPM. The Convention of the Metre is a diplomatic treaty that gives authority to the CGPM, CIPM and the International Bureau of Weights and Measures (BIPM) to act in matters of world metrology, particularly concerning the demand for measurement standards of ever increasing accuracy, range and diversity.

 

 

figureConfiguration of an optical clock: The laser line width is narrowing by the well isolated optical cavity and corrected to stay at the center of the atomic transition. The optical frequency comb transfers the laser frequency precisely to other optical and microwave regions.

Construction of the optical clock

In an optical clock, a frequency stabilized laser has narrow line width at the sub-hertz level. The laser frequency v is tuned near the atomic clock transition precisely to determine the center frequency of the transition at v0. The servo system controls the laser frequency v so that v = v0. Then, v0 is divided precisely into the microwave region for counting. Therefore, the coherence, accuracy and stability are the same as the optical frequency.

In the most advanced devices, an optical lattice or ion trap provides the potential well to store the cooled atom species and isolate them to ensure minimal perturbation. The volume in which the atoms move in the optical lattice or trap is smaller than an optical wavelength, effectively eliminating Doppler shifts. In the case of the optical lattice, researchers have made use of the so-called “magic” wavelength—the wavelength for which the AC Stark shifts of both ground and upper energy levels of the atom clock transition in a strong-field-created optical lattice are exactly equal and thus cancel each other out, leading to high accuracy (Nature 435, 321).

Theoretical evaluations have shown that the uncontrolled frequency shifts of the clock transition can be reduced to a level of 10-17 to 10-18. Scientists have also investigated how to build a molecular optical clock.

To explore the extreme sharpness of selected optical atomic transitions, an exceptionally stable laser source with sub-hertz line width is required. To achieve such narrow band interrogation laser sources, a well-isolated, high-finesse optical cavity is kept under ultra-stable thermo-mechanical conditions and very low environmental noise. This cavity is used to narrow the laser line width by a servo system.

The most convenient way to transfer the laser light to the cooled atoms is to use optical fiber. However, the fluctuation of the light path in fiber adds the phase noise on the light that broadens the laser line width, so additional steps must be taken. To this end, researchers have developed phase noise cancellation schemes. Recent techniques can reduce the additional broadened line width to the millihertz level, which is good enough to transmit light for building an optical clock (Opt. Lett. 19, 1777).

Once the narrow bandwidth interrogation laser is resonant with the transition of the atoms, and its frequency is continuously corrected to stay at the center of the atomic transition, the high stability of the atomic transition is transferred to the laser. As a result, the laser frequency is accurate and stable and constitutes the oscillator of the optical clock.

In order to transfer the coherence, stability and accuracy of individual single optical frequency to other optical and microwave regions, where the frequency can be counted, the femtosecond laser frequency comb is an ideal tool. When the frequency of one comb component is phase-locked to that of the stabilized laser by the beating signal fb, the coherence, stability and accuracy of all comb components are the same as that of the stabilized laser. Currently, such experiments are being carried out with optical frequency standards in many laboratories around the world.

Recent achievements with optical clocks

 

figureThe trapped single 199Hg+ ion clock: The frequency of the trapped single Hg+ ion clock has been measured relative to the Cs microwave frequency standard using NIST’s broadband Ti:sapphire femtosecond laser frequency comb over the past six years.

The concept of the optical clock was first demonstrated using atoms and the femtosecond laser frequency comb in 2001. An optical frequency comb was phase-locked on an optical standard rather than a microwave standard. At that time, the cooled Ca atomic clock was compared with the trapped single Hg+ ion clock via the femtosecond laser frequency comb at the National Institute of Standards and Technology (NIST) in Boulder, Colo. The relative frequency instability observed was below 1 x 10-15 in the integrated time of a few hundred seconds, but still from 1 x 10-17 (Science 293, 825).

To find out if the results were limited by the comb, researchers compared four Ti:sapphire femtosecond laser frequency combs constructed by three different laboratories (NIST in the United States, BIPM in France and the East China Normal Universtiy in China) at NIST in 2003. The results of these comparisons demonstrated a frequency agreement between the four combs at the 10-19 level (Science 303, 1843). Additional comparisons were made from 2004 to 2005, confirming the earlier results and even showing a somewhat better reproducibility, below 1 x 10-19.

Researchers have recently developed another new tool: the fiber femtosecond laser frequency comb. Although its phase noise is slightly higher than the Ti:sapphire femtosecond laser frequency comb, it has the advantage of being compact, robust, reliable and economical. Scientists at the Physikalisch-Technische Bundesanstalt (PTB) in Germany have tested two Er fiber combs using single Yb+ ion transitions and found its uncertainty on the order of 10-18. Recently, the Er fiber femtosecond laser frequency comb was compared with a broadband Ti:sapphire femtosecond laser frequency comb at NIST. The frequency instability of the fiber comb can reach 6 x 10-17 at 1 s and 1 x 10-18 at 1,000 s (Nature Photon. 1, 283). This demonstrates that the homogeneity of the comb spectra from the fiber laser frequency comb corresponds or supersedes the needs for frequency conversion as part of an optical clock.

 

 

figureThe optical lattice clock with 87Sr atoms has been investigated in detail at three laboratories.

As mentioned earlier, the ultra-narrow line width laser is an indispensable building block of an optical clock. The line width of sub-hertz levels was achieved by using a well-isolated, high-finesse, Fabry-Perot cavity in 1999 (Phys. Rev. Lett. 82, 3799). Two cavity mirrors are optically connected to the ends of a cavity spacer, which is made of an extra-low thermal expansion material. The cavity is mounted inside an evacuated chamber, which is temperature-stabilized. The table to support the evacuated chamber is suspended by vertical strands of surgical tubing stretched to about 3 m. The tubing protects the cavity from vibration noise from the environment.

Scientists constructed two independent stabilized laser systems with a detected line width as low as 0.6 Hz using a Pound-Drever-Hall frequency servo scheme (Appl. Phy. B 31, 97). Such lasers have been used to probe a narrow transition in a trapped single Hg+ ion at 1.06 x 1015 Hz, which has been measured relative to the Cs standard over the past six years using comb technology. The accuracy of the frequency measurements at 1.06 x 1015 Hz has been improved from 10 Hz to 1 Hz.

At the PTB, researchers have studied frequency standards based on a trapped, single Yb+ ion (Phys. Rev. Lett. 94, 230801), and scientists have also studied standards based on a trapped single Sr+ ion at the National Physics Laboratory (NPL) in London (Science 306, 1355) and the National Research Council of Canada (Phys. Rev. Lett. 95, 033001). The results prove these ions to be interesting candidates for future optical clocks. Two single Yb+ ion systems have been compared with agreement of the sub-Hertz level at the PTB. The measurement of clock frequency of a single Sr+ ion has the uncertainty of one Hertz level at the NPL. Recently, researchers at NIST have compared trapped single Al+ and Hg+, and have demonstrated an instability of 4 x 10-17 (20th European Frequency and Time Forum, Braunschweig, Germany).

The Pound-Drever-Hall frequency servo scheme can lock the laser frequency very tightly to a high-finesse cavity. Consequently, the fluctuations of the cavity length limit the line width of a stabilized laser. Scientists at NIST, JILA, PTB and NPL have developed a new concept for the design of high-finesse cavities, which makes the cavity length essentially insensitive to environmental vibration (Appl. Phys. B 83, 531; Phys. Rev. A. 75, 011801(R)). Using this new concept, researchers at JILA at the University of Colorado have mounted the optical axis of the cavity in the vertical direction and supported the cavity mechanically at the horizontal plane of the mass center of the cavity body (Opt. Lett. 30, 1815).

In such an arrangement, a vertical acceleration induces the same length fluctuation, but it is of opposite sign for the lower and upper part of the cavity, giving much reduced sensitivity to vertical vibrations. Using this concept to design the cavity, researchers can narrow the laser line width to the sub-hertz level with a very compact system. With such a cavity, a stabilized diode laser at 689 nm showed a sub-hertz line width and was used to observe a 2 Hz line width of cooled Sr atoms in an optical lattice (Science 314, 1430; Opt. Lett. 32, 641).

The clock transition frequency of Sr atoms based on spin-forbidden transition has been measured in JILA in the United States, LNE-SYRTE in France, and AIST and Tokyo University in Japan. The agreement among the results was within a few Hz using a comb referenced to the Cs clock (Phys. Rev. Lett. 96, 033003; Phys. Rev. Lett. 97, 130801; J. Phys. Soc. Japan 75, 10, 104302; Phys. Rev. Lett. 98, 083002). A comparison between lattice-trapped cooled Sr atoms at JILA and a trapped single Hg+ in NIST is also under way.

More national laboratories are expected to build Sr and other optical clocks. This will allow for extended comparison activities and a strong uncertainty evaluation, which is a prerequisite if such clocks are to begin to contribute to real time scales.

Linking optical clocks for future time distribution

Optical clocks are being built and investigated in many laboratories around the world. Since the revolutionary discovery of the comb, the accuracy of the optical clock transition frequency measurements has dramatically improved and is in some cases estimated to be better than the current definition of the second based on the cesium 133 atom transition at microwave frequencies. The next major challenge is to find ways to link optical clocks located at different sites so that researchers can accurately compare their frequencies to provide evidence for the individual uncertainty budgets.

One of the more promising approaches for linking sites, at least over continental distances, is to use telecommunications fiber systems to transfer optical frequency standards and link the optical clocks at different locations. A recent review article discusses various techniques for ultrastable signal transfer to remote locations and reviews results by researchers at JILA (Rev. Sci. Instrum. 78, 021101). In a European collaboration, scientists from PTB transferred ultra-frequency-stable laser light at 1,542 nm over telecommunication fiber links in Paris from the LNE-SYRTE to the Laboratoire de Physique des Lasers using fiber phase noise cancellation techniques (CLEO 2007). They attained an instability in the transfer below 6 x 10-18 for a distance of 86 km and less than 2 x 10-17 over 211 km (integration time was about 8,000 s). This is the first demonstration of an optical carrier phase link over a distance of more than 100 km.

Some 50 years after the invention of the laser, which made highly coherent light available, we are today on the brink of turning another dream into reality: realizing an optical second.

[ Long-Sheng Ma is with the State Key Laboratory of Precision Spectroscopy, Physics Department of East China Normal University in Shanghai, China. ]


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Optical Atomic Clocks—from Dream to Reality

Recent developments in atomic physics and laser technology, especially techniques for laser cooling and the manipulation of atoms, have enabled the realization of so-called Cesium fountain atomic clocks with relative accuracy approaching 4 x 10-16.

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