Clockmakers and Atomic Time

One day, when I was a young boy, my grandfather asked me to follow him into his garage. I watched curiously as he retrieved a small round object from the dark recesses of the garage. As he held the object in a shaft of light streaming from a small window, the object became recognizable as a pocket watch. "I want you to have this," he said. I lifted the watch from his hands as if it were pure gold. Even though the watch had little value, it became one of my most treasured possessions. As far as I know, my grandfather was not aware of my fascination with clocks and time. Nevertheless, he had an innate sense of the sort of things I might like. As a boy, I marveled at the inner workings of clocks, and I often pondered the nature of time.

Despite our lack of understanding of time, there is nothing to prevent us from measuring it. Measuring time relies upon a regular sequence of events. But how can we tell whether the sequence of events is regularly spaced in time in the first place? It seems that in order to construct a clock, we need to have a clock! The only way out of this quandary is to assume that time flows at a constant rate. This may seem obvious, but it is a necessary assumption for clocks to work -- and to make sense of our world.

Since ancient times, clockmakers have implicitly invoked this assumption. Some of the earliest clocks were simple mechanical devices. The mechanisms in the devices were made to oscillate with a "natural period." The unique period of a particular clock corresponds to a unique unit of time. We merely count the periods to see how much time has elapsed.

Beyond manmade clocks, we are surrounded by natural clocks: beating hearts, the changing phases of the moon, and radio pulses from rotating neutron stars just to name a few. Whether clocks are manmade or natural, they all have a common feature: they are based on a regular sequence of events. The accuracy of the clock depends on the regularity of the events.

Ever since the first manmade clock was built, humans have worked to create clocks of ever increasing accuracy. This is not a pointless ambition -- since the earliest manmade clocks, humans have relied upon them for coordinating events and warfare. As technology evolved, humans became increasingly dependent on accurate time keeping. Modern transportation, energy distribution, telecommunications, and computer networks would all grind to a halt without precise clocks. Many scientific experiments cannot be done without extremely precise time measurements. Space missions and navigation depend on extraordinarily accurate clocks. Consider the global positioning system, which is comprised of a network of orbiting satellites. The satellites require onboard clocks that are much more accurate than "normal clocks," because timing errors on the order of one part in a billion can give rise to position errors of several meters.

Currently, atomic clocks are the most accurate clocks that humans make. Like any other clock, atomic clocks rely on a regular sequence of events. Inside an atomic clock, quantum transitions between two energy levels of an atom occur at regular time intervals. This can happen, for instance, when a group of identical atoms are subjected to an electromagnetic field oscillating at a specific frequency. Under this special condition, the electromagnetic field stimulates quantum transitions between two specific energy levels.

One way of creating such a system is to trap a group of identical atoms inside a resonant cavity. If there are no energy losses, which there always are in real systems, then a perpetual sequence of atomic transitions ensues. The periodicity of the transitions (events) is extremely stable because the atomic energy levels are well defined. A signal stabilized by the natural period can be used to regulate an external clock. The stability of a clock is often expressed in terms of the accumulated time errors Δt measured over an average time interval T.

Atomic clocks are capable of measuring time with a precision of one part in a billion or greater. A particular type of quantum transition known as a "hyperfine transition" is especially suited for atomic clocks. Hyperfine transitions refer to interactions between the magnetic field of the nucleus and the magnetic field of an orbiting electron. Atomic clocks generally make use of hyperfine transitions of the outer or valence electron in hydrogen-1, cesium-133, and rubidium-87 atoms.

Only a handful of laboratory atomic clocks maintain the "time standard," known as Coordinated Universal Time (UTC), for the entire civil world. UTC is sometimes loosely referred to as Greenwich Mean Time (GMT) or Zulu time. Occasionally, leap seconds are added to UTC at irregular intervals in order to compensate for irregularities in the Earth's orbital and rotational periods. In addition to maintaining the time standard, many other atomic clocks are synchronized to the UTC time standard. Laboratory atomic clocks can be quite large (the size of an automobile). Modern cesium atomic clocks are so accurate, that they would gain or lose only one second in 1.4 million years!

For most applications, large laboratory cesium clocks are impractical. This is especially true for GPS and telecommunications satellites. The weight and size constraints pose serious challenges to atomic clock designers. The challenges have been met, to some extent, with rubidium vapor cell clocks (or simply Rb clocks). Remarkably, Rb clocks can be made smaller than a coffee cup. The National Institute of Standards and Technology and other groups are testing chip scale atomic clocks that have sizes on the order of a few millimeters. The smaller atomic clocks do not have the accuracy of their larger laboratory cousins, but they are nevertheless surprisingly accurate. In fact, the Rb clocks onboard GPS satellites are so stable that they develop an error of only half a nanosecond after three hours of running.

Researchers continue to push the limits of technology on atomic clocks. New scientific experiments and future applications demand accuracies which have not yet been attained. Future applications will require extremely small chip scale atomic clocks. To provide a perspective on contemporary research efforts, I surveyed the patent and journal literature for the latest publications on atomic clocks. In the remaining paragraphs, I point out a few recent developments related to atomic clocks.

A fair number of publications are concerned with reducing the size of atomic clocks. For example, the Sarnoff Corporation recently filed a patent application for a chip scale atomic clock (click here for patent). The clock has a vapor cell containing cesium atoms. Hyperfine end transitions are used to stabilize the frequency of the local oscillator. By using end transitions, the cesium vapor density can be increased. The higher vapor density increases the signal-to-noise ratio of the output signal. Radio frequency waves are used to directly interrogate the end-state transition. Unfortunately, the end resonance is accompanied by a first order magnetic field dependence. To get around this problem, a Zeeman end resonance is simultaneously used to stabilize the magnetic field.

Another design for a chip scale atomic clock has been patented by the Intel Corporation (click here for patent). The Intel clock is small enough to fit within a cubic millimeter. The heart of the clock consists of cesium or rubidium atoms which are deposited in a layer over a substrate. Hyperfine transitions occur in the deposited atoms. As with most atomic clocks, the atoms are spin-polarized by a magnetic field. A giant magneto-resistive effect sensor can be used to detect the hyperfine transitions. In various embodiments, the atomic clock could have dimensions ranging from less than a millimeter to a little over a micrometer.

A Japanese group recently built an extremely stable cesium optical atomic clock with a 9.19 GHz microwave output signal (click here for article). The microwave output signal is stabilized by the atomic clock. The long-term stability is reported to be as high as Δt/T = 8.0 x 10^-14 over an averaging time of t = 5000 seconds. By coupling a mode-locked fiber laser to the microwave output signal, an optical pulse train can be generated with the same stability. The optical pulse train could then conceivably serve as frequency standard throughout the world via fiber optic networks.

Significant research efforts on atomic clocks have focused on coherent population trapping (CPT). Most efforts are concerned with CPT atomic clocks that use ⁸⁷Rb atoms. However, a Chinese group has focused on improving clock stability by using CPT resonance with ⁸⁵Rb atoms (click here for article). The group reports that the frequency stability of the ⁸⁵Rb CPT clock is improved by reducing the effect of light shift. Experimental tests reveal short-term frequency stability on the order of 10^-10 seconds. The long term frequency stability is 1.5 x 10^-11 seconds over an averaging time of t = 8000 seconds. This is comparable to ⁸⁷Rb CPT clocks. The very high stability and low power demands of these prototype clocks could open the door for future low cost chip scale atomic ⁸⁵Rb CPT clocks.

Further advances in CPT clocks are evident in a recent US patent application (click here for patent). The application is concerned with a method for modulating an atomic clock signal. The method employs two amplitude pulse modulated laser beams which are directed into a cavity containing either cesium or rubidium atoms (the interactive region). Due to the complexity of the modulation method, the reader is encouraged to read the patent application. However, it should be mentioned that a notable claim alludes that the method is particularly suitable for the industrial production of miniaturized clocks whose interactive cell volumes are less than a few cubic millimeters.

For many applications, atomic clocks must operate continuously for very long periods. This is particularly true for spacecraft. A Caltech group recently built an atomic clock designed to withstand the rigors of deep space navigation and science (click here for article). The atomic clock is based on mercury ions that are shuttled between a quadrupole and a 16-pole rf trap. A vacuum tube contains the trap. The device exhibited short term stability of Δt/T = 1 x 10^-13 over an averaging time of t = 1 second. There was no measurable degradation of the ion trapping lifetime or short-term stability after operating under a vacuum for nearly two years.

To learn more about the physical principles of atomic clocks, a nice treatise can be found in The Quantum Beat: The Physical Principles of Atomic Clocks, by F.G. Major. (click here for book)

[1] T. Hirayama, M. Yoshida, M Nakazawa, A Cs optical atomic clock with a mode-locked fiber laser, Rec. Electr. Commun. Eng. Conversazione, 76, 290-291, 2008.

[2] A.M. Braun, J.H. Abeles, W.K. Chan, M. Kwakernaak, T.J. Davis, Batch-Fabricated, RF-Interrogated, End Transition, Chip-Scale Atomic Clock, US Patent Application 20070247241/US-A1, Applicant: Sarnoff Corporation, Filed on 04-18-2004.

[3] Lu Liu, Guo Tao, Ke Deng, Xin-yuan Liu Xu-Zong Chen, Zhong Wang, Frequency Stability of Atomic Clocks based on Coherent Population Trapping Resonance in 85RB, Chinese Physics Letters, 24, 7, 1883-1885, 2007.

[4] N. E. Dimarcq, S.S. Guerandel, T.P Zanon, D.P. Holleville, Method For Modulating an Atomic Clock Signal With Coherent Population Trapping and Corresponding Atomic Clock, US Patent Application 20070200643/US-A1, Filed on 03-29-2005.

[5] E.C. Hannah, M.A. Brown, Atomic Clock, US Patent 7,142,066, Assignee: Intel Corporation, Filed on 12-30-2005.

[6] J.D. Prestage, S.K. Chung, L. Lim, L. Thanh, Hg Ion Atomic Clock For Deep Space Navigation and Science, Proc. SPIE 6673, 1, 1-8, 2007.

[7] Fouad G. Major, The Quantum Beat: The Physical Principles of Atomic Clocks, Springer, 1998.

Nerac Analyst James J. Marie, Ph.D., assists companies with prior art assessments including patentability studies, patent invalidity investigations, and technology assessments. He has worked with a wide range of companies on projects such as robotics technology assessment for an automotive company to prior art research on jet engine components for a major aerospace company. He also assists the energy industry on nuclear power, solar energy, and energy conversion technology projects.