Atomic Clocks: an Application of Spectroscopy in the Last Installment of This Column (1), I Talked About Clocks As the First Scientific Instrument

14 Spectroscopy 21(1) January 2007 www.spectroscopyonline.com The Baseline Atomic Clocks: An Application of Spectroscopy In the last installment of this column (1), I talked about clocks as the first scientific instrument. What do clocks have to do with spectroscopy? Actually, the world’s most accurate clocks, atomic clocks, are based upon a spectroscopic transition of cesium or other elements, making spectroscopy a fundamental tool in our measurements of the natural universe. David W. Ball ime is one of the seven fundamental quantities in Originally, a second was defined as part of a minute, nature. I made a case in the last installment of this which was part of an hour, which was in turn defined as T column (1) that mechanical devices for measuring part of a day. Thus, 1 s was 1/(60 ϫ 60 24), or 1/86,400 time — clocks — might be considered the world’s first sci- of a day. However, even by the 17th century, defining the entific instruments. Clocks are ubiquitous because the day itself was difficult. Was the day based upon the position measurement of time is a fundamental activity that is im- of the sun (the solar day) or the position of distant stars portant to computer users, pilots, and lollygaggers alike. (the sidereal day)? At what latitude (that is, position toward the north or south) is a day measured? Over time it was rec- The Second ognized that measuring time accurately was a challenge. Quantities of time are expressed in a variety of units that In 1660, the Royal Society proposed that a second be de- we teach our grade-schoolers, but the IUPAC-approved termined by the half-period (that is, one swing) of a pendu- fundamental unit of time is the second (abbreviated “s” not lum of a given length. That given length was very close to “sec”). Units such as minute, hour, day, and year, as well as what became 1 m, suggesting a relationship between the prefix-modified units such as millisecond, nanosecond, and standard unit of length and the standard unit of time. How- megasecond, are all based directly upon the second; derived ever, it was recognized that the period of a pendulum of units such as the newton (where 1 N = 1 kg·m2/s) and joule given length varied with position on the Earth’s surface. (1 J = 1 N/s = 1 kg·m2/s2) also are based upon the second. Nonetheless, the concept of a “seconds pendulum” was use- (Interestingly, within the SI system of units, the units for ful through the 18th century in France, England, and the time greater than second — minute, hour, day, and so forth Americas, with the length of the pendulum varying be- — are the only units not based upon powers of 10 times the tween 99.0 and 99.4 cm, depending upon location and basic unit. What was once referred to as the “metric system” often specified to five decimal places. is now properly referred to as the “SI system” of units, with In 1956, it was finally recognized that the rotation of the “SI” coming from the French phrase “système international Earth was too inconstant to use in the definition of a sec- d’unités,”or “international system of units.”) Ultimately, it ond. Instead, the revolution of the Earth about the Sun was becomes fundamentally important to be able to determine used. In 1960, the Eleventh General Conference on Weights exactly how long a second is. and Measures (Conférence générale des poids et mesures, 16 Spectroscopy 22(1) January 2007 www.spectroscopyonline.com The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine F = levels of the ground state of the caesium- 133 atom. 5 In 1997, this was amended with the 82.9 MHz 7 2P 4 statement: 3/2 66.5 MHz This definition refers to a caesium 49.9 MHz 3 atom at rest at a temperature of 0 K. 2 This amendment was required to compensate for thermal variations in the frequency of the transition. At this point, the way to identify a second’s worth of time is to count 9,192,631,770 658,155,873 MHz wavelengths of light coming from the hyperfine levels of cesium-133. This, by the way, corresponds to a wavelength of 3.2612256 cm, which lies in the microwave region of the electromagnetic 4 spectrum, nearer to the infrared region 6 2S than the radiowave region. The ability 1/2 9,192.631770 MHz to measure a second, then, is based 3 upon our ability to measure this partic- ular spectroscopic transition of 133Cs. Figure 1: Electronic energy levels of 133Cs (nuclear spin I = 7/2), which are involved in the Why cesium (or, as preferred by definition of the second. (Vertical axis is not to scale.) The labels on the left are term symbols of IUPAC, caesium)? Several reasons: 2S+1 1 ● Cesium has a relatively low boiling the form LJ, where S = /2 (for a single electron), L represents the orbital angular momentum quantum number of the electronic state, and J is the total electronic angular momentum (1/2 for point of 941.4 K (668.3 °C), so the lower electronic state, 3/2 for the upper electronic state). The total atomic angular obtaining cesium in the vapor phase momentum quantum number F goes from I + J → I – J in integral steps, resulting in two states (F is relatively easy. In fact, an operat- = 7/2 + 1/2 = 4 and 7/2 – 1/2 = 3) for the ground electronic state and four states for the upper ing temperature of only 80 °C is electronic state (F = 5, 4, 3, and 2). For ease of comparison, all frequencies are expressed in required to generate enough Cs megahertz. (Adapted from reference 2.) vapor for some atomic clocks to operate. ● Cesium is a fairly heavy atom (133 CGPM) ratified a new definition of the the Earth’s motion about the Sun. amu), meaning that its thermal unit second: Enter spectroscopy. velocity at any temperature is low, 1/31,556,925.9747 of the tropical year In the late 1940s and through the increasing measurement times and for 1900 January 0 at 12 hours 1950s, work on atomic clocks pro- decreasing Doppler effects on its ephemeris time gressed. Early atomic clocks were de- spectrum. “Ephemeris time” is an older time veloped at the U.S. National Bureau of ● Cesium has a single valence elec- scale based upon the positions of ce- Standards (now the National Institute tron, and in some respects, the elec- lestial bodies. Because the length of the of Standards and Technology, or tronic spectrum of cesium can be “tropical year” (a year as measured NIST) and the National Physical Labo- approximated loosely as a one-elec- going from one point to the same ratory (NPL) in the UK. Atomic clocks tron system, like atomic hydrogen. point on the celestial ecliptic) varies essentially are masers (microwave am- ● Natural cesium exists as one iso- over long periods of time as well as on plification by stimulated emission of tope, having mass number 133. the starting and ending points of the radiation) that have extremely stable Hence, any sample of naturally ecliptic, a “mean tropical year” is the outputs. They have been based upon occurring cesium is isotopically average of all points over one solar hydrogen, rubidium, or cesium, al- pure and its spectrum is uncontami- year, and the imaginary tropical year though the cesium atomic clocks are nated by any isotope effect. starting at 1900 January 0, 1200 hours the ones upon which the modern defi- ● Cesium has a relatively large nuclear formed the basis for the second. nition of the second is based. spin I of 7/2. Nuclei of other ele- In 1967, based upon the work of as- ments have this or even higher spin Spectroscopic Definition of Second tronomers from NPL and the United (for example, 138La has a spin of 5), Even this definition, however, was States Naval Observatory (USNO), the but they suffer by not having the problematic because of variations in second was redefined as: other advantages of cesium. 18 Spectroscopy 22(1) January 2007 www.spectroscopyonline.com The Atomic Clock How does an atomic clock work? Older atomic clocks were based upon beams of cesium atoms, with the atoms moving at several hundred me- ters per second. The most modern atomic clock at NIST uses what is called an atomic fountain. Figure 2 shows a general schematic of the clock (3,4). Initially, a cloud of cesium vapor is introduced into a vacuum chamber. Six perpendicularly placed infrared lasers are used to capture a small cloud of cesium atoms at their intersection; the repeated rebounds of photons from all directions slow the gas-phase cesium atoms to near absolute zero (the phrase “optical molasses” is some- times used to describe the conditions experienced by the cesium atoms). Ap- proximately 100 million atoms are captured. At this point, atoms popu- late the F = 3 and F = 4 states, which also have quantized z-components of angular momentum ranging from mF = –3 to 3 for the F = 3 state, and from mF = –4 to 4 for the F = 4 state. Only the mF = 0 states are useful, so atoms not in this state must be eliminated. The atoms are then pushed up by the two vertical lasers, and then all of the lasers are turned off. The atoms drift up about 1 m under the influence of gravity, passing through a microwave cavity.

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