Atomic Clocks Meet Laser Cooling

Walter F. Buell and Bernardo Jaduszliwer

The Stealth bomber pilot flying under combat conditions as well as the weekend boater out for a sail can make use of the same technology—the Global Positioning System, or GPS, which provides three-dimensional positioning and navigation data. Once the province only of the military, civilian GPS receivers are now sold in sporting goods stores, offered as standard equipment on new cars, and packaged with cellular phones in consumer safety products.

Atomic Clocks in Space Systems

GPS consists of 24 satellites that orbit the Earth every 12 hours. The satellites send encoded radio signals that the GPS receiver uses to compute position. At the heart of GPS are the atomic clocks that provide the highly accurate time signals required for positioning. Atomic clocks are the most precise instruments modern technology can provide.

In fact, the current trend in defining new physical standards is using a time interval measurement whenever possible. For example, the standard unit of length, the meter, is no longer defined by reference to a metal rod kept in a vault, but rather by the defined speed of light and an atomic clock second. Today, the nation's primary atomic time and frequency standard is the NIST-7 cesium beam clock at the National Institute of Standards and Technology in Boulder, Colorado.

The Aerospace Corporation was an integral part of the team that created GPS and has been involved in atomic clock development for the last two decades. Scientists at Aerospace recently designed a laser-cooled atomic clock, specifically intended for space applications. The Aerospace atomic clock is compact, robust, requires relatively low power, and avoids problems associated with other proposed laser-cooled atomic clocks for space application. Aerospace estimates a factor of 100 improvement over the frequency stability of current space-qualified atomic beam clocks.

GPS is not the only space system to carry atomic clocks on board. Glonass, the Russian navigation satellite system, is equipped in a similar manner. Communication satellite systems such as Milstar require the robust timekeeping capabilities of atomic clocks in order to provide secure communications. As the competition for radio frequency bandwidth heats up, other communication systems, commercial as well as military, may have to rely on atomic clocks to provide accurate frequency and time onboard spacecraft. Currently the highest performance requirements on spacecraft clocks are placed by space navigation systems such as GPS, where an error of one-thousandth of a second in spacecraft time translates into a 200-mile error in user range measurement.

A Brief History of Atomic Beam Clocks

The development of atomic clock technology as such started during the 1950s, following ideas presented by Isidor Rabi in a 1945 public lecture. It was enabled by investigations in fundamental physics carried out during the first half of the century. The discovery of the electron spin, measurements of nuclear spins and magnetic moments, and the puzzle of the magnetic moment of the proton were some of the research topics providing scientific insights and the practical tool kit that eventually would be used in designing and building cesium atomic beam clocks (see sidebar, How a Cesium Beam Atomic Clock Works).

Louis Essen and J. V. L. Parry at the National Physics Laboratory in Great Britain, and Harold Lyons and coworkers at the National Bureau of Standards (NBS) in the United States, demonstrated the first laboratory cesium beam frequency standards in the mid-1950s. This work eventually led to the redefinition of the Standard International Second (SI second) in terms of the cesium hyperfine transition frequency, as measured by a cesium atomic beam clock.

In the meantime, Jerrold Zacharias, who had provided inspiration and technical advice for the NBS work, also led the National Company's effort to produce the first commercial atomic clock, the Atomichron, unveiled in 1956. This device, the direct ancestor of the cesium beam clocks flown onboard today's GPS satellites, had a frequency accuracy better than one part in 10¹⁰. Today's metrology cesium clocks measure frequency with an accuracy of 2–3 parts in 10¹⁴; this corresponds to an uncertainty of 2 nanoseconds per day or 1 second in 1,400,000 years.

What would happen if one of the original scientists working on the Atomichron had gone to sleep for 40 years, Rip Van Winkle-like, to wake up in front of a modern commercial atomic clock? He would be surprised by its small size and excited about its performance and reliability, but he would not have much difficulty recognizing each of the components of the physics package and understanding its role and operation. The changes between the physics package of the Atomichron and that of a GPS clock have been evolutionary in nature, and our sleepy scientist would find neither new atomic physics nor unrecognizable "tricks of the trade."

However, if he were to wake up 10 years from now, the situation might be very different. Once again, fundamental developments in physics over the last 15 years have provided us with the scientific understanding and the tool kit required to develop novel atomic clocks that have 2- to 3-orders of magnitude better performance than current ones. The enabling technology in this case is that of cooling and trapping atoms by optical techniques, and our sleepy scientist might have some difficulty understanding how they operate.

In modern atomic clocks the VCXO is frequency-locked to an atomic microwave resonance of center frequency _A and width . In order to detect the atomic system signal, the populations of the two atomic energy levels connected by the transition must be unequal.

What is an Atomic Clock?

Every clock consists of a periodic signal source and a counter. The performance of the clock is determined by the frequency stability of the periodic signal. The source of that periodic signal has changed over the centuries, from Galileo's use of his own pulse when studying the motion of falling objects to atomic microwave transitions in modern atomic clocks.

In modern atomic clocks the "atomic system" provides a very sharp frequency reference that is used to stabilize the frequency of a local oscillator (usually a very high-quality voltage-controlled quartz crystal oscillator, or VCXO). The frequency reference is, in most cases, a hyperfine transition in atoms having a single valence electron, such as hydrogen or the alkali metals. To provide the highest accuracy, the physics package of an atomic clock is designed so as to:

Allow the microwave interrogation of atoms as isolated as possible from each other and from any external perturbation
Provide a frequency reference having as small a frequency uncertainty as possible (that is, a high line Q). Ultimately, this requires long interrogation times
Provide the highest possible signal-to-noise ratio in the clock signal. This requires interrogating large numbers of atoms

The feedback loop that provides the frequency lock was developed during World War II for automatic frequency control of microwave oscillators used in radar, and was first used to frequency-lock the Atomichron.

Laser-Cooled Atomic Clocks

In the late 1940s Norman Ramsey introduced a novel microwave cavity design enabling very high resolution atomic beam microwave spectroscopy. Large cesium beam clocks incorporating Ramsey-type cavities dominated the field of accurate atomic frequency standards for metrology laboratories until the mid-1990s, and compact versions of those clocks are still the devices of choice as accurate time and frequency standards for industrial, military, and space applications.

The performance achieved by these clocks reflects many evolutionary design and construction improvements, and they are very close to optimal for that type of clock technology. However, laser-based optical techniques can be used to further improve the performance of cesium beam clocks in two different ways. Laser optical pumping allows interrogation of essentially all the atoms in the beam, instead of a few percent as is the case in conventional cesium beam clocks; this results in a much improved signal-to-noise ratio. Laser cooling allows increasing the length of time the atoms interact with the microwave field, thereby reducing the frequency uncertainty of the clock signal.

Zacharias proposed the use of slow atomic beams for an atomic clock in 1953. He proposed directing a thermal atomic beam vertically to form a "fountain," using the slowest atoms in the beam as they turn around and fall under the influence of gravity. In such an atomic fountain, interaction times of up to 1 second would be possible.

Nobel Prizes awarded for work later applied to atomic clocks

1902—Lorentz and Zeeman: for Zeeman effect
1907—Michelson: for speed of light measurements
1922—Bohr: for "old" quantum mechanics
1932—Heisenberg: for matrix quantum mechanics
1933—Dirac and Schroedinger: for quantum mechanics
1943—Stern: for atomic beam method
1944—Rabi: for resonance method
1952—Bloch and Purcell: for magnetic resonance
1964—Townes, Basov, and Prokhorov: for lasers and masers
1966—Kastler: for optical pumping
1981—Bloembergen and Schawlow: for laser spectroscopy
1989—Ramsey: for Ramsey method; Dehmelt and Paul: for ion traps
1997—Phillips, Cohen-Tannoudji, and Chu: for laser cooling and trapping

Zacharias's vision was not realized at the time, however, because the fraction of sufficiently slow atoms in the beam was too small. The atomic fountain had to wait more than 3 decades for the techniques of laser cooling to be developed, but today atomic fountain clocks are the most stable and accurate in the world.

Laser cooling is the process of slowing atoms by means of optical forces. For a simple picture of how light can slow atoms, consider an atom moving with velocity v and a laser beam directed at the atom in the opposite direction. If the laser is tuned near the resonance frequency of the atom, the atom will absorb a photon from the laser beam and experience a momentum kick, since photons carry momentum, slowing it down a bit (about 3.5 millimeters per second for a cesium atom). Before the atom can absorb another photon, it must spontaneously radiate the photon it has already absorbed, and it may do this in any random direction. After many such absorption-emission events (about 90,000 for cesium atoms from an oven), the atoms slow to a crawl.

This technique of laser slowing of atomic beams is very useful for many applications, but is not so well suited to atomic clocks, especially those compact ones intended for use in space. The reason lies in the small atom velocity loss from each photon-scattering event. Well over a meter is required to slow a beam of atoms from a cesium oven, making for an unacceptably long beam tube. Worse still, during the slowing process the atoms actually gain momentum in the transverse direction because of the emission of roughly 90,000 spontaneous photons in random directions. This means that a great many atoms are lost before reaching the end of the atomic clock, degrading clock performance.

The solution is to cool the atoms in three dimensions simultaneously, using a technique known as "optical molasses," in which counter-propagating laser beams provide a force opposing the motion of the atoms and proportional to the atomic velocity. With three counter-propagating pairs of laser beams oriented along three orthogonal directions, an atom at their intersection experiences a slowing force regardless of its direction of motion, as if it were "swimming through molasses." Using this technique, atoms can be cooled to within a few millionths of a degree above absolute zero.

An atomic fountain. Laser-cooled atoms in optical molasses are launched vertically by off-setting the frequency of the molasses laser beams. The atoms are decelerated under the influence of gravity, turn around, and fall back through the system.

By offsetting in opposite ways the frequencies of one pair of counter-propagating laser beams, the atoms see the molasses in a frame of reference moving along that direction (because of the Doppler shift), and are carried along with it. In this way, atoms slowed in optical molasses can be launched in any desired direction. This is how modern atomic fountains work.

The first atomic fountain was built by Steve Chu at Stanford University. Today the world's most stable and accurate clock is a cesium atomic fountain at the Laboratoire Primaire du Temps et des Fréquences in Paris, with a stability of 2 X 10^-13/, where is time in seconds. Similar metrology fountain clocks are under development at the National Institute of Standards and Technology (NIST) and the U.S. Naval Observatory.

In fountain-type clocks, a "ball" of atoms is cooled in three-dimensional molasses and launched upward. The ball of cold atoms passes through a microwave cavity twice, on its way up and on its way down. As the ball of atoms falls below the microwave cavity, the number of atoms that changed state is measured by optical means to generate the equivalent of the beam signal in conventional cesium beam clocks. Then the next ball of atoms is cooled and trapped, and the process starts anew.

Alas, the fountain idea as such cannot be used for space applications, since the whole clock is in free fall and gravitational forces are too small to turn the atoms around to pass through the microwave cavity a second time. Nevertheless, a French consortium of academic and government laboratories is building a metrology space atomic clock (known as PHARAO, after its French acronym) using the techniques developed for the fountain clock in a Ramsey-type configuration. This clock is expected to fly in the International Space Station to perform fundamental physics experiments in a microgravity environment. A similar device is under construction at NIST and JPL (NASA Jet Propulsion Laboratory).

The Aerospace Cold Atom Clock

One drawback to these proposals for laser-cooled atomic clocks for space applications is the pulsed nature of their atomic beam, and hence of the frequency measurement process. During the interval between measurements the frequency of the local oscillator of the clock may wander slightly. This slight error on a short time scale can be converted by the clock's frequency-lock feedback loop to degraded clock performance over medium and long time scales.

This degradation is known as the Dick effect, and places very stringent requirements on the local oscillator's frequency stability. Because of that, fountain clocks and proposed metrology space clocks such as PHARAO use hydrogen masers as local oscillators. However, that is not a practical solution for clocks needed for systems such as GPS.

The Aerospace design for an optically pumped space clock using laser-cooled cesium atoms. A continuous cold atomic beam is extracted from a magneto-optic trap (MOT) through a hole in a hollow conical mirror. The cold beam is then optically collimated (to improve the signal-to-noise ratio) and deflected (to reduce light shifts from MOT light) before passing through a Ramsey cavity.

At Aerospace we have designed a laser-cooled atomic clock well-suited to operation in space. Our design is compact, robust, and employs a continuous cold atomic beam, thus avoiding the problems associated with the Dick effect.

The Aerospace design is based upon a simple, robust cold atom source employing trapped, laser-cooled atoms. The heart of the source is a magneto-optic trap, or MOT, which combines three-dimensional molasses with a set of coils producing an inhomogeneous magnetic field that traps the cold atoms at its center.

A large-diameter, circularly polarized laser beam is incident upon a hollow conical mirror. The conical mirror is placed at the center of a pair of oppositely oriented current-carrying coils. These coils produce the inhomogeneous magnetic field needed to trap the cold atoms. In this way, the combination of incident laser, its reflection and polarization by the conical mirror, and the inhomogeneous magnetic field provide just the right configuration to produce a MOT with simultaneous cooling and confinement of the atoms.

At the apex of the cone is a small hole. Since in the "shadow" of this hole the retroflected laser beam is missing, the atoms are pushed by the incident laser, which ejects them from the MOT through the hole. This low velocity, intense source produces a cold continuous atomic beam, which is then used in a Ramsey-type atomic beam clock.

Light from the MOT laser beam entering the Ramsey cavity would perturb the interaction between atoms and microwaves, and thus impair the clock accuracy. In order to minimize this problem, the atomic beam is deflected in one-dimensional optical molasses, allowing the Ramsey cavity to be offset away from the offending light.

This design is significantly simpler than others because the cold atom beam is produced by a single laser. It is compact, mechanically robust, and requires relatively low power, making it well suited for space applications. Based on our calculations of achievable atomic beam velocity and flux, we estimate that our clock will provide a one-hundred-fold improvement over the frequency stability of current space-qualified atomic beam clocks.