Section 8: Atomic Clocks
The words "Atomic Clock" occasionally appear on wall clocks, wristwatches, and desk clocks, though in fact none of these devices are really atomic. They are, however, periodically synchronized to signals broadcast by the nation's timekeeper, the National Institute of Standards and Technology (NIST). The NIST signals are generated from a time scale controlled by the frequency of a transition between the energy states of an atom—a true atomic clock. In fact, the legal definition of the second is the time for 9,192,631,770 cycles of a particular transition in the atom 133Cs.
Figure 31: Isidor Isaac Rabi pioneered atomic physics in the U.S. during the 1930s, invented magnetic resonance, and first suggested the possibility of an atomic clock.
Source: © Trustees of Columbia University in the City of New York. More info
Columbia University physicist Isidor Isaac Rabi first suggested the possibility that atoms could be used for time keeping. Rabi's work with molecular beams in 1937 opened the way to broad progress in physics, including the creation of the laser as well as nuclear magnetic resonance, which led to the MRI imaging now used in hospitals. In 1944, the same year he received the Nobel Prize, he proposed employing a microwave transition in the cesium atom, and this system has been used ever since. The first atomic clocks achieved an accuracy of about 1 part in 1010. Over the years, their accuracy has been steadily improved. Cesium-based clocks now achieve accuracy greater than 1 part in 1015, 10,000 times more accurate than their predecessors, which is generally believed to be close to their ultimate limit. Happily, as will be described, a new technology for clocks based on optical transitions has opened a new frontier for precision.
A clock is a device in which a motion or event occurs repeatedly and which has a mechanism for keeping count of the repetitions. The number of counts between two events is a measure of the interval between them, in units of the period of the atomic transition frequency. If a clock is started at a given time—that is, synchronized with the time system—and kept going, then the accumulated counts define the time. This statement actually encapsulates the concept of time in physics.
In a pendulum clock, the motion is a swinging pendulum, and the counting device is an escapement and gear mechanism that converts the number of swings into the position of the hands on the clock face. In an atomic clock, the repetitious event is the quantum mechanical analogy to the physical motion of an atom: the frequency for a transition between two atomic energy states. An oscillator is adjusted so that its frequency matches the transition frequency, effectively making the atom the master of the oscillator. The number of oscillation cycles—the analogy to the number of swings of a pendulum—is counted electronically.
The quality of a clock—essentially its ability to agree with an identical clock—depends on the intrinsic reproducibility of the periodic event and the skill of the clock maker in counting the events. A cardinal principle in quantum mechanics is that all atoms of a given species are absolutely identical. Consequently, any transition frequency could form the basis for an atomic clock. The art lies in identifying the transition that can be measured with the greatest accuracy. For this, a high tick rate is desirable: It would be difficult to compare the rates of two clocks that ticked, for instance, only once a month. As the definition of the second reveals, cesium-based clocks tick almost 10 billion times per second.
Atomic clocks and the uncertainty principle
The precision with which a atomic transition can be measured is fundamentally governed by the uncertainty principle. As explained in Section 6, because of the time-energy uncertainty principle, there is an inherent uncertainty in the measurement of a frequency (which is essentially an energy) that depends on the length of the time interval during which the measurement is made. To reduce the uncertainty in the frequency measurement, the observation time should be as long as possible.
Figure 32: Schematic diagram of an atomic fountain clock.
Source: © NIST/Jeffrey Aarons. More info
In an atomic clock, the observation time is the time during which the atoms interact with the microwave radiation as they make the transition. Before the advent of ultracold atoms and atom trapping, this time was limited by the speed of the atoms as they flew through the apparatus. However, the slow speed of ultracold atoms opened the way for new strategies, including the possibility of an atomic fountain. In an atomic fountain, a cloud of cold atoms is thrust upward by a pulse of light. The atoms fly upward in the vacuum chamber, and then fall downward under the influence of gravity. The observation time is essentially the time for the atoms to make a roundtrip. For a meter-high fountain, the time is about one second.
The quality of an atomic clock depends on how well it can approach ideal measurement conditions. This requires understanding and controlling the many sources of error that can creep in. Errors arise from noise in the measurement process, perturbations to the atomic system by magnetic fields and thermal (blackbody) radiation, energy level shifts due to interactions between the atoms, and distortions in the actual measurement process. The steady improvement in the precision of atomic clocks has come from incremental progress in identifying and controlling these effects.
The cesium fountain clock
The cesium clock operates on a transition between two energy states in the electronic ground state of the atom. As mentioned in Section 7, the ground state of an alkali metal atom is split into two separate energy levels in a magnetic field. Even in the absence of an external magnetic field, however, the ground state is split in two. This splitting arises from a magnetic interaction between the outermost in the atom electron and the atom's nucleus, known as the hyperfine interaction. The upper hyperfine state can in principle radiate to the lower state by spontaneous emission, but the lifetime for this is so long—thousands of years—that for all purposes, both states are stable. The transition between these two hyperfine states is the basis of the cesium clock that defines the second.
The cesium fountain clock operates in a high vacuum so that atoms move freely without colliding. Cesium atoms from a vapor are trapped and cooled in a magneto-optical trap. The trap lasers both cool the atoms and "pump" them into one of the hyperfine states, state A. Then, the wavelength of the trap laser beam pointing up is tuned to an optical transition in the atoms, giving the cloud a push by photon recoil. The push is just large enough to send the atoms up about one meter before they fall back down. The atoms ascend through a microwave cavity, a resonant chamber where the atoms pass through the microwave field from an oscillator. The field is carefully controlled to be just strong enough that the atoms make "half a transition," which is to say that if one observed the states of the atoms as they emerged from the cavity, half would be in hyperfine state A and half would be in state B. Then the atoms fly up, and fall back. If the frequency is just right, the atoms complete the transition as they pass through the cavity, so that they emerge in state B. The atoms then fall through a probe laser, which excites only those that are in state B. The fluorescence of the excited atoms is registered on a detector. The signal from the detector is fed back to control the frequency of the microwave oscillator, so as to continuously stay in tune with the atoms.
Figure 33: This apparatus houses the NIST F1 cesium fountain clock, which is the primary time and frequency standard of the United States.
Source: © NIST. More info
If we plot the signal on the detector against the frequency of the oscillator, we end up with what is known as a resonance curve. The pattern, called a Ramsey resonance curve, looks suspiciously like two-slit interference. In fact, it is an interference curve, but the sources interfere not in space but in time. There are two ways for an atom to go to state B from state A: by making the transition on the way up or on the way down. The final amplitude of the wavefunction has contributions from both paths, just as the wavefunction in two-slit interference has contributions from paths going through each of the slits. This method of observing the transition by passing the atom through a microwave field twice is called the "separated oscillatory field method" and its inventor, Norman F. Ramsey, received the Nobel Prize for it in 1989.
A useful figure of quality for atomic clocks is the ratio of its frequency to the uncertainty in its frequency, . For a given value of , the higher the frequency, the better the clock. With atom-cooling techniques, there are many possibilities for keeping atoms close to rest so that is small. Consequently, clocks operating at optical frequencies, in the petahertz (1015 Hz) region, are potentially much more accurate than cesium-based clocks that operate in the gigahertz (109 Hz) region. However, two impediments have delayed the advent of optical clocks. Fortunately, these have been overcome, and optical clock technology is moving forward rapidly.
The first impediment was the need for an incredibly stable laser to measure the atomic signal. In order to obtain a signal from the atoms, the laser must continue oscillating smoothly on its own during the entire time the atoms are being observed. The requirement is formidable: a laser oscillating at a frequency of close to 1015 Hz that fluctuates less than 1 Hz. Through a series of patient developments over many years, this challenge has been met.
The second impediment to optical clocks was the problem of counting cycles of light. Although counting cycles of an oscillating electric field is routine at microwave frequencies using electronic circuitry, until recently there was no way to count cycles at optical frequencies. Fortunately, a technology has been invented. Known as the "frequency comb," the invention was immediately recognized as revolutionary. The inventors, Theodor W. Hänsch and John L. Hall, were awarded the Nobel Prize in 2005 "for their contributions to the development of laser-based precision spectroscopy including the optical frequency-comb technique."
Figure 34: The heart of a next-generation optical clock.
Source: © Ion Storage Group, NIST. More info
Optical clocks are only in the laboratory stage but progress is rapid. One type of clock employs ions stored in electromagnetic traps, similar to the trap used in Figure 1; another employs neutral atoms confined in an optical lattice such as in Figure 2. Figure 34 shows a state-of-the-art ion-based clock at NIST. A pair of such clocks has recently demonstrated a relative accuracy greater than one part in 1017. Making these clocks into practical devices is an interesting engineering challenge.
In the new world of precise clocks, transmitting timing signals and comparing clocks in different locations presents a major challenge. Transmissions through the atmosphere or by a satellite relay suffer bad atmospheric fluctuations. The signals can be transmitted over optical fibers, but fibers can introduce timing jitter from vibrations and optical nonlinearities. These can be overcome for distances of tens of kilometers by using two-way monitoring techniques, but methods for extending the distances to thousands of kilometers have yet to be developed. However, there is an even more interesting impediment to comparing clocks at different locations. The gravitational redshift explained in Unit 3 changes the rates of clocks by 1 part in 1016 for each meter of altitude, near Earth's surface. Clocks are approaching the regime of parts in 1018. To compare clocks in different locations, the relative altitudes would need to be known to centimeters. Earth's surface is constantly moving by tens of centimeters due to tides, weather, and geological processes. This presents not merely a practical problem but also a conceptual problem, for it forces us to realize that time and gravity are inextricably interlinked. Because of this, the view that time is essentially the clicks on a clock begins to seem inadequate.
Payoffs from basic research
When Isidor Isaac Rabi proposed the possibility of an atomic clock, he had a scientific goal in mind: to observe the effect of gravity on time—the gravitational redshift—predicted by Einstein's theory of general relativity. The quest to confirm Einstein's prediction motivated the field. Today, the gravitational redshift has not only been observed, but also measured to high precision. However, the biggest impacts of atomic clocks were totally unforeseen. Global Positioning System (GPS) is one of these.
The GPS is a network of satellites positioned so that several of them are essentially always in view. A receiver calculates its location from information transmitted by the satellites about their time and position at each instant. The satellites carry one or more atomic clocks whose times are periodically updated by a master atomic clock in a ground station. The GPS system is a miracle of engineering technology: sophisticated satellites, integrated electronics and advanced communications, information processing, geodesy, and orbital mechanics. But without atomic clocks, there would be no GPS. Furthermore, with the precision inherent in the GPS system, the gravitational redshift is not only detectable, but to overlook it would cause catastrophic navigational errors.
Figure 35: This VLBI image of jets from a black hole could not have been produced without atomic clocks.
Source: © Steven Tingay, Curtin University, Australia. More info
Atomic clocks have applications in fundamental science as well. The technique of very long baseline radio interferometry (VLBI) permits Earth to be converted to a giant radio telescope. Signals from radio observatories on different continents can be brought together and compared to provide the angular resolution of an Earth-sized dish. To do this, however, the astronomical radio signals must first be recorded against the signal from an atomic clock. The records are then brought together and their information is correlated. VLBI can reveal details less than a millionth of a degree, the highest resolution achieved in all of astronomy.
Although Einstein's theory of gravity is one of the most abstract subjects in science, the search to study it led to the invention of GPS and the creation of VLBI. This history illustrates, if illustration is needed, that the pursuit of basic knowledge is a worthy goal for scientists and a wise investment for society.