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14 Spectroscopy 21(1) January 2007 www.spectroscopyonline.com

The Baseline Atomic : 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 of the natural universe.

David W. Ball

ime is one of the seven fundamental quantities in Originally, a was defined as part of a , . I made a case in the last installment of this which was part of an , which was in turn defined as T column (1) that mechanical devices for measuring part of a . Thus, 1 s was 1/(60 60 24), or 1/86,400 — clocks — might be considered the world’s first sci- of a day. However, even by the 17th , defining the entific instruments. Clocks are ubiquitous because the day itself was difficult. Was the day based upon the of time is a fundamental activity that is im- of the sun (the solar day) or the position of distant 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 is the second (abbreviated “s” not lum of a given . That given length was very close to “sec”). Units such as minute, hour, day, and , as well as what became 1 m, suggesting a relationship between the prefix-modified units such as , , 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 of units such as the (where 1 N = 1 kg·m2/s) and 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 “ 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 the tween 99.0 and 99.4 cm, depending upon location and basic unit. What was once referred to as the “” 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 of 9,192,631,770 peri- ods of the radiation corresponding to the transition between the two hyperfine F = levels of the of the - 133 . 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 of 0 K. 2 This amendment was required to compensate for thermal variations in the 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 coming from the hyperfine levels of cesium-133. This, by the way, corresponds to a wavelength of 3.2612256 cm, which lies in the mi- crowave 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 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 symbols of IUPAC, caesium)? Several reasons: 2S+1 1 ● Cesium has a relatively low boiling the form LJ, where S = /2 (for a single ), L represents the orbital 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 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. at any temperature is low, 1/31,556,925.9747 of the In the late 1940s and through the increasing measurement times and for 1900 January 0 at 12 1950s, on atomic clocks pro- decreasing Doppler effects on its 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 ( am- ● Natural cesium exists as one iso- over long periods of time as well as on plification by stimulated emission of tope, having 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, , 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 How does an work? Older atomic clocks were based upon beams of cesium , 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 (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 mi- crowave cavity. A short burst from the Figure 2: General diagram of a cesium fountain-based atomic clock. (Source: NIST.) drives the atoms having F = 4 and mF = 0 (using the Dirac bra-ket notation, labeled the ● Cesium has a fair-sized nuclear a |4,0 state) into the |3,0 state by way magnetic . These last two 2 of stimulated emission. Then, a burst properties lead to: of radiation from an 852-nm laser ● Cesium has an unusually large energy levels based upon the interac- causes absorption from the F = 4 state hyperfine splitting in its ground tion of the vectors; to the F = 5 state, essentially heating state, caused by the magnetic inter- the energy change is calculated by up the atoms and removing them of the spin from the with a called the thermally. The atoms of cesium are unpaired 6s1 valence electron and constant. now essentially all in the |3,0 state. the I = 7/2 nucleus. It is the transition from the ground The cloud of atoms then passes 2 It is this hyperfine structure that state, labeled 6 S1/2 (F = 3), to the first through a microwave cavity tuned 2 causes the diagram that is hyperfine , 6 S1/2 (F = 4), (hopefully) to 9192631770 Hz. They involved in the definition of the sec- that is involved in the definition of the absorb the microwave radiation to ond. Figure 1 shows a diagram of the second. It is worth noting that, with transfer to the |4,0 state. They are electronic energy levels of the Cs such a relatively low energy, even at 80 then hit again by the 852-nm laser, atom. The interaction of the magnetic °C there are a significant number of transfer to the F = 5 excited state, and dipole moment of 133Cs (due to its atoms in the F = 4 state due to thermal fluoresce back to the F = 4 state. The nonzero spin) and the magnetic dipole population. fluorescence is detected optically. moment of the orbiting 6s1 valence The process is repeated multiple electron causes the formation of new times until the fluorescence output is 20 Spectroscopy 22(1) January 2007 www.spectroscopyonline.com maximized. It is at this point that the Conclusion 2006. microwave cavity is tuned to the “cor- The defining of the units we use to (4) S.R. Jefferts, J. Shirley, T.E. Parker, T.P. rect” frequency. characterize the physical universe has Heavner, D.M. Meekhof, C. Nelson, F. Because the fountaining motion of to be among the most fundamental Levi, G. Costanzo, A. De Marchi, R. the cesium atoms is slow (about 4 m/s) work a scientist can do. Spectroscopists Drullinger, L. Hollberg, W.D. Lee, and and the atoms themselves are cooled should take some pride in knowing F.L. Walls, 39, 321 (2002). by the optical molasses to only a few that the tools of their trade are instru- (5) S.A. Diddams, J.C. Bergquist, S.R. Jef- microkelvins, the atoms interact with mental in determining the value of the ferts, and C.W. Oates, 306, the microwave field for about a second. unit used to measure time. Interested 1318 (2004). This allows for a very narrow linewidth readers are urged to consult the refer- (6) S.R. Jefferts, T.P. Heavner, and E.A. Don- for the measured transition, allowing ences and the works cited within for ley, Jpn. J. Appl. Phys. 43, 2803 04). for a v/v of less than 1015 — a very additional information. accurate measurement. This corre- David W. Ball is sponds to an accuracy of 1 s in about Acknowledgment a professor of chem- 31.7 million . Modern atomic Thanks to Dr. Steve Jefferts of the istry at Cleveland State clocks are so accurate that the greatest NIST Time and Frequency Division in University in Ohio. errors are thought to arise from colli- Boulder, Colorado, for technical assis- Many of his “Baseline” sions between cesium atoms, uncer- tance. columns have been tainties in the local gravitational field, reprinted in book form and effects due to ambient blackbody References by SPIE Press as The radiation (that is, the fact that the (1) D.W. Ball, Spectroscopy 21(12), 87–95 Basics of Spectroscopy, clock itself is operating mostly at room (2006). available through the SPIE Web Bookstore at temperature). New atomic clocks are (2) J.F. Milligan, Am. J. Phys. 42, 883 www.spie.org. His most recent book, Field being designed to minimize these ef- (1974). Guide to Spectroscopy (published in May fects, which might ultimately include (3) Available online at 2006), is available from SPIE Press. He can operation of the clock in a micro- or http://tf.nist.gov/timefreq/cesium/fou be reached at [email protected]; his web- nongravity environment (5,6). ntain.htm. Accessed November 1, site is academic.csuohio.edu/ball.

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