# NIST Cesium Fountains Set Standard for Precision Timekeeping

by Microwave Product Digest

Cesium fountain clocks are currently the most accurate frequency standards in the world, with uncertainties reaching as low as 1 part in 10^{16}. This means that if a cesium fountain clock were to run for 100 million years, it would lose or gain only about one second. This exceptional accuracy makes cesium fountain clocks essential tools for maintaining international time standards, conducting precision scientific experiments, and enabling technologies like global navigation satellite systems.

The primary frequency standard in the U.S. is a cesium fountain atomic clock developed at the National Institute of Standards and Technology (NIST) laboratories in Boulder, CO where it contributes to the calibration of the official international time scale Coordinated Universal Time (UTC), and to its local realization UTC(NIST) which is synthesized and distributed from NIST’s Boulder laboratories.

**The Cesium Fountain Explained**

A cesium fountain is a device used to create a controlled, fountain-like motion of cesium atoms, and is a key component of cesium fountain atomic clocks (**Figure 1**). In a cesium fountain, a gas of cesium atoms is first cooled to temperatures near absolute zero using laser cooling techniques. This process involves using lasers tuned to specific frequencies to slow down the motion of the atoms, effectively reducing their temperature to just a few millionths of a degree above absolute zero.

Once the atoms are cooled, they are launched upwards through a vacuum chamber using carefully controlled laser pulses. The atoms follow a parabolic trajectory, moving upwards and then falling back down under the influence of gravity, much like a fountain. As the atoms move through the vacuum chamber, they pass through a microwave cavity twice—once on the way up and once on the way down. The microwave cavity is tuned to a specific frequency that corresponds to the energy difference between two hyperfine states of the cesium atom.

By measuring the transition probability between these two states as the atoms pass through the microwave cavity, the frequency of the microwave radiation can be precisely determined. This frequency serves as the basis for the atomic clock’s timekeeping. The atoms’ fountain-like motion is crucial because it allows for a longer interaction time with the microwave radiation. This longer interaction time, combined with the atoms’ low temperatures, greatly enhances the precision of the frequency measurement.

The term “fountain” in this context refers to the upward and downward motion of the atoms, which resembles the flow of water in a traditional fountain. This innovative design has led to significant advancements in the field of atomic timekeeping and has enabled the development of ultra-precise atomic clocks.

**Cesium Fountains at NIST**

The resonance frequency of the hyperfine splitting in cesium has defined the second since 1967. The history of the uncertainty in the measurement of this frequency at NIST is illustrated in **Figure 2**. For many years, the primary frequency standard was a cesium fountain known as NIST-F1, which operated from 2000 to 2015. During this time, a cryogenic cesium fountain known as NIST-F2 was also developed. The first new generation of these clocks is the NIST-F3 (**Figure 3**), which provides input for the NIST timescale and assists with the evaluation of NIST’s primary and secondary frequency standards.

It has achieved short-term frequency stability of 2.2 x10^{-13}/√t for averaging times as long as 5×10^{4} s (where t is the averaging time in seconds). Unlike other NIST fountains, NIST-F3 is not intended to realize the definition of the second of the International System of Units (SI) with state-of-the-art accuracy. Instead, NIST-F3 is intended to be a stable system that operates with high up-time.

NIST-F4 (**Figure 4**) is an advanced atomic clock currently under development by NIST that is designed to be a next-generation cesium fountain clock that will push the boundaries of timekeeping precision even further. The goal of the NIST-F4 project is to create a cesium fountain clock with an uncertainty of just 1 part in 10^{-19}, which would represent a significant improvement over the best current cesium fountain clocks, such as NIST-F1 and NIST-F2, which have uncertainties of about 1 part in 10^{16}. To achieve this unprecedented level of accuracy, the NIST-F4 design incorporates several innovative features including:

- Advanced laser cooling: The clock will use a novel laser cooling technique to bring the cesium atoms to even lower temperatures than current fountain clocks, reducing uncertainties related to atomic motion
- Improved magnetic shielding: The clock will employ advanced magnetic shielding to minimize the effects of external magnetic fields on the cesium atoms, which can cause errors in the frequency measurement
- Enhanced microwave cavity design: The microwave cavity will be designed to optimize the interaction between the cesium atoms and the microwave radiation, further improving the precision of the frequency measurement
- Increased atom numbers: By using a larger number of cesium atoms in the fountain, the statistical uncertainty of the frequency measurement can be reduced

NIST-F4 will represent a major milestone in the field of atomic timekeeping and could have significant implications for a wide range of applications, from precision navigation and communication systems to fundamental physics research. As of this year, the clock is still in development and will likely be several years before it becomes fully operational and takes over as the primary frequency standard at NIST.

**The NIST-F3 Evaluation**

This article described the details of the NIST-F3 apparatus to demonstrate short-term frequency stability of 2.2 x10^{-13}√t for averaging times as long as 5 × 10^{4} s. The article also presents an initial evaluation of the main frequency biases. Due to the particulars of the microwave cavity design employed in NIST-F3, the fountain exhibits a relatively large tilt sensitivity. Although fractional frequency shifts of 10^{-14}/mrad have been observed when tilting the fountain, the tilt sensitivity can be managed with standard techniques developed for cold-atom fountains. This investigation suggests it will be possible to achieve the goal of fractional frequency stability better than 0.5 x 10^{-15} for up to a few months of averaging time.

Since the first evaluation of NIST-F1, cesium fountain clocks have improved by an order of magnitude and the definition of the second can now be realized with an uncertainty approaching 1 x 10^{-16} at metrological institutes around the world. This exquisite accuracy is possible because of the long interrogation times and detailed control of the atomic motion that is enabled by laser cooling. The next generation of atomic frequency reference utilizes laser cooling and ultra-stable lasers to measure frequencies with a fractional uncertainty approaching 1 x10^{18}.

Frequency references based on cold atoms can provide excellent long-term stability. Several timing laboratories have shown that this long-term frequency stability can be used to improve the stability of a local realization of Coordinated Universal Time (UTC) by incorporating signals from cold-atom fountains based on microwave transitions or an optical lattice clock. The local realization of UTC maintained by NIST does not currently receive input from a cold-atom frequency reference. NIST-F3 may ultimately achieve a fractional frequency stability better than 0.5 x10^{-15} up to a few months of averaging time. To realize this goal, it’s necessary to understand, control, and monitor the largest frequency biases of NIST-F3.

**The Ramsey Cavity**

Ramsey cavities are essential components in atomic clocks, which are used in GPS, telecommunications, and other applications requiring high-precision timing. They are also used in other precision frequency standards, such as hydrogen masers and trapped ion clocks. A Ramsey cavity, also known as a Ramsey cell (**Figure 5**), is used to interrogate atoms or molecules and determine their resonance frequency with high precision. It consists of two separated interaction zones (cavities) through which atoms or molecules pass. The cavities are connected by a drift region, allowing the atoms to interact with the microwave field at two different points in time.

The atoms are exposed to a microwave field in the first cavity, then allowed to drift freely before interacting with the field again in the second cavity. This creates an interference pattern that is highly sensitive to the frequency of the microwave field relative to the atomic resonance frequency.

By measuring the interference pattern, the atomic resonance frequency can be determined with much higher precision than with a single cavity. This is because the Ramsey method is less sensitive to certain systematic effects, such as Doppler shifts and cavity phase shifts.

**Discussion**

In most respects, NIST-F3 is a typical cesium fountain in which cesium atoms are cooled in an optical molasses at the bottom of the fountain with two pairs of horizontal laser beams and one pair of vertical laser beams. The atoms are launched upward to a height of about 0.78 m above the molasses zone (0.17 m above the Ramsey cavity) by introducing frequency shifts into the vertical molasses beams. After the launch, atoms in the |F = 3, m = 0⟩ hyperfine state are isolated by use of a microwave pulse in the state selection cavity followed by a resonant laser pulse which removes the atoms in the |F = 4⟩ state.

The selected atoms then pass through a second microwave cavity that realizes Ramsey interrogation during the atoms’ parabolic flight. The atomic state is detected at the end of the fountain sequence by collecting fluorescence from the atoms as they cross several resonant laser beams. In a typical experiment, we load the optical molasses for 0.5 s and allow 0.9 s for the fountain sequence. The Ramsey time is approximately 0.38 s, and we obtain Ramsey fringes with a width of 1.3 Hz (full width at half maximum). A photograph of the vacuum system is shown in **Figure 6**.

There are a few features of the apparatus that are worthy of note. The laser system uses two commercial distributed Bragg reflector (DBR) laser diodes with one driving the cooling transition while the other drives the repump transition. A tapered amplifier is used to ensure there is sufficient power available on the cooling transition, and acousto-optic modulators are used to prepare and control the beams required for the fountain sequence. The use of DBR laser diodes allows the laser system to be relatively simple, but this comes at the cost of increased laser frequency noise that can limit the achievable signal-to-noise ratio.

In addition, the microwave cavity uses a relatively simple feed structure compared to other microwave cavities developed for NIST fountains. NIST-F3 includes two cylindrical TE011 microwave cavities, one for state selection and one for the Ramsey interrogation of the clock transition. Both cavities have the same geometry. The radius is R = 3 cm, and the height is h ≈ 2.17 cm. The cavity assembly is made of aluminum that has conductivity s = 2.5 × 107 S/m, about a factor of 2.3 smaller than the conductivity of copper.

Microwave energy can be fed into each cavity by use of handmade loop antennas that are inserted into the upper endcap. For the Ramsey cavity, we measure a loaded quality factor, Q, of about 5 x 10^{3} compared to a theoretical Q of approximately 14 x 10^{3} for a weakly coupled cavity with this geometry and conductivity. The two feeds to the Ramsey cavity are asymmetric; one feed requires nearly 16 dB more microwave energy to drive the atomic resonance. This is illustrated in **Figure 1c** with measurements of the Rabi oscillations as a function of microwave amplitude for the two feeds.

The asymmetry in the feeds is not an inherent feature of the cavity design; a possible source of the asymmetry is a small, unintended movement of one feed during the final cavity assembly and bakeout. These features enhance NIST-F3’s sensitivity to DCP errors. The lower conductivity of aluminum increases the DCP biases by a factor of about 1.5 compared to a copper cavity with the same geometry.

A typical measurement of the short-term frequency stability of NIST-F3 is shown in **Figure 1d**. To measure the collisional shift, we modulate the atom number by varying the loading time of the optical molasses. The detected atom number varies by about a factor of four between high-density and low-density mode. With the fountain operating in high-density mode, fractional frequency stability is 2.2 x 10^{-13}/√t, and in low-density mode, stability is 4 x10^{-13}√t. The limitations of the short-term frequency stability in NIST-F3 are currently under investigation.

In most cesium fountains, the four largest frequency biases are the quadratic Zeeman shift caused by the magnetic field used to lift the degeneracy between the atom’s magnetic sublevels, the BBR shift caused by the atoms interacting with the thermal radiation field, the collisional shift caused by the cold atoms interacting with each other, and the gravitational redshift that depends on where the fountain is located. Alongside these biases, there is a significant number of other shifts that must be considered, but they typically have a magnitude less than 1 x 10^{-15} in fractional frequency assuming the fountain is healthy.

Although we are not aiming to achieve state-of-the-art accuracy with NIST-F3, it is still important to monitor frequency biases that can vary in time, such as the quadratic Zeeman shift, the BBR shift, and the collisional shift, to realize our frequency stability goals. It is also useful to correct the fountain for large but relatively stable biases like the gravitational redshift. The quadratic Zeeman shift is determined by the magnetic field seen by the atoms inside the vacuum chamber. This magnetic field can be measured experimentally by driving a magnetically sensitive atomic transition, and the measured field can be used to calculate the bias on the clock transition.

The BBR shift can be accurately calculated if the apparatus’s temperature is known. The collisional shift can be measured by varying the launched atom number. The gravitational redshift is known from geodetic surveys of the clock labs at NIST Boulder. **Table 1** summarizes typical values for these four biases along with conservative estimates of the uncertainty.

Once the known shifts have been corrected, we can estimate the size of the remaining frequency biases by comparing NIST-F3’s frequency offset to one of NIST’s local timescales or to the ensemble of primary and secondary frequency standards (PSFS) via Circular T. During our initial characterization, we discovered a large frequency bias of order 10^{-14} after correcting for the four biases summarized in **Table 1**.

Subsequent investigations revealed that this bias was a first-order Doppler shift caused by a tilt in the atom’s launch velocity with respect to gravity combined with an incorrect balance of the two feeds for the Ramsey cavity. When the two feeds are incorrectly balanced, there is a transverse phase gradient in the cavity. In this case, the cold-atom cloud will experience a different average phase each time the atoms cross the cavity if the atom’s launch velocity is tilted with respect to gravity. This phase shift produces a frequency bias in the Ramsey interrogation.

To quantify this bias, it is useful to measure the fountain’s frequency offset as a function of both the launch angle and the feed configuration. The results are shown in **Figure 7** by the strong coupling of the cavity feeds. We observed single-feed tilt sensitivities that are asymmetric and of order 10^{-14} mrad. The cavity’s relatively low conductivity enhances NIST-F3’s tilt sensitivity.

The asymmetric tilt sensitivity is consistent with two feeds that have asymmetric coupling to the cavity. Even in the case of asymmetric coupling to the cavity, it would be expected that it is still possible to find a configuration with both feeds active where the transverse phase gradient is canceled, and the fountain has minimal tilt sensitivity. As **Figure 6** shows, we have achieved a configuration where the tilt sensitivity of the fountain with both feeds active is less than 1 × 10^{-15} /mrad. Empirically, we found that this required the weakly coupled feed to supply about 0.3 of the pulse area used to drive the atoms while the rest of the pulse area is supplied by the opposite feed.

The small, measured tilt sensitivity is encouraging, but one must be concerned that the apparatus might drift away from this configuration and develop a frequency bias. We routinely check that the fountain is well aligned vertically by comparing measurements with the fountain driven from the individual feeds and with both feeds. We also check for tilt sensitivity with both feeds operational. As the NIST-F3 has been in operation consistently for five months, it appears possible to keep this shift suppressed at a level sufficient for our frequency stability goals.

To evaluate the long-term stability of NIST-F3, we compare the fountain to the PSFS ensemble via Circular T. Measurements of NIST-F3’s offset relative to PSFS over five months are shown in **Figure 7** with corrections applied for the shifts in **Table 1**. The weighted average of these measurements gives an offset F3 − PSFS ≈ (0.9 ± 0.4) × 10^{-15}. The quadratic sum of the uncertainties given in **Table 1** is 1 x 10^{-15}. A linear fit to the data gives a drift rate of −1 ± 6 × 10^{-18}/day.

NIST-F3 is now operating reliably, and we have completed an initial evaluation of the largest systematic biases. We are currently working to upgrade the apparatus and to investigate the residual frequency bias found in this first measurement campaign. Looking further out, we believe NIST-F3 will achieve its stability goals and begin contributing to the NIST time scale and the evaluation of NIST’s frequency standards.

**Editor’s note:**

One of the primary sources for this article is the publication “NIST-F3, a Cesium Fountain Frequency Reference”, authored by Gregory W. Hoth, Jeff A. Sherman, National Institute of Standards and Technology, Alexander G. Radnaev, Peter Mitchell, Infleqtion, and Vladislav Gerginov, National Institute of Standards and Technology and the University of Colorado Boulder. That publication can be found here.

https://tf.nist.gov/general/pdf/3232.pdf

(47)