NRC's Cesium Fountain Clock - FCs1

Currently, a cesium fountain clock is under construction at the National Research Council of Canada. Recent results obtained from the prototype show a stability of 1.5 x 10-12-1/2, limited by the uniformity and stability of the C-field.

The definition of the second

"The second is equal to the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom." This definition for the second was adopted in 1967. The definitions used prior to 1967 were discarded because the techniques used to measure the second did not provide results stable or accurate enough for modern use.

Several cesium thermal beam clocks currently provide Canada with a primary time standard and contribute to the TAI (International Atomic Time). The performance of atomic clocks is expressed in terms of accuracy and stability. Traditional cesium thermal beam clocks have attained a stability and accuracy in the range of 10-13 to 10-14. Fountain clocks should be able to produce a signal ten to one hundred times better.

How does the cesium fountain work?

Trapping: Cesium atoms are trapped and cooled in a magneto-optical trap.

Cesium atoms are present in gaseous form inside the vacuum chamber. When a cesium atom intersects the cooling laser beams, it experiences laser cooling which reduces its velocity considerably and cools it to a few micro Kelvin.
At the same time, a magnetic field gradient is applied using anti-Helmholtz coils. The magnetic field gradient and the cooling laser beams give rise to a trapping force. All these forces and effects are applied simultaneously to hold the 109 atoms in a 2 mm diameter ball at the center of the trap.

Launch: The atoms are launched upwards.

The magnetic field is switched off and the cloud of atoms is launched upwards by two pairs of laser beams. The atoms are launched with a velocity of 2 to 5 metres per second. During the lift in the laser beams, the atoms are further cooled to approximately 2μK.

Preparation: The atoms are pumped into the upper level of the clock transition.

Atoms can change energy levels by absorbing or emitting a photon of light with a frequency that is close to their resonant frequency. On their flight upwards, the atoms pass through a laser beam with a frequency close to one of cesium's resonant frequencies. Some atoms undergo a transition between energy levels so that all atoms are at the same energy level F=4,mF=0 before entering the microwave cavity.

Interrogation: The atoms follow a fountain-like course, passing through the microwave cavity twice.

The atoms continue and pass through the microwave cavity, are in free flight above it for approximately 0.5 s, and are then pulled back down under the force of gravity. During each of the two passages through the microwave cavity, the atoms interact with microwaves of frequency is 9192631770 Hz After passing through the cavity a second time (on the way down), almost all of the atoms have made the transition into the F=3, mF=0 state.

Detection: The atoms are detected.

Below the microwave cavity, the descending atoms are probed with several laser beams. The lasers cause the atoms to change atomic states and fluoresce (emit light). The fluorescence photons are detected by a photodiode and are used to build up the clock signal. When all the atoms have undergone the transition into the desired state, the signal is at a maximum. The intensity of the signal is used to correct the frequency of the microwaves in the cavity.

The fountain cycle is repeated.

What is a clock?

A clock is a device used for keeping track of time and for measuring the second. It includes an oscillator, a counter of periods, and a registering device. A frequency standard is a device that provides a calibrated frequency signal and measures time intervals. Thus, a clock is a frequency standard with which one counts and registers periods of oscillations. An atomic clock uses atoms as a frequency reference by measuring their natural frequency of radiation. Clocks producing the definition of the second (using cesium) with the highest accuracy are termed primary clocks and are mostly found in national laboratories.

Where does the time signal come from?

The time signal comes from an ultra-stable oscillator, in our case a quartz crystal (with a frequency of 5 MHz), that is part of the loop shown in the diagram on the top left. This signal is multiplied using a frequency multiplier to generate hyper frequencies, or microwaves. The microwaves irradiate the atoms as they pass through the microwave cavity. The atoms' response depends on the microwave frequency as is shown on the diagram on the lower right. When the frequency of the microwave radiation is perfectly tuned to cesium's transition frequency (o), the atoms' response is maximized. By slightly modulating the microwave frequency, the atoms' response to a range of known frequencies can be determined. Each time the atoms respond to the microwave radiation, an error signal can be constructed and sent via a feedback loop to stabilize the local oscillator at the right frequency. Thus, the fountain and quartz crystal work in conjunction to provide the frequency standard for the second and the number of seconds are counted by a registering device.

Why do we need accurate time?

The operation of modern-day technology requires an accurate knowledge of time. Telecommunications rely heavily on timing to operate switches routing signals through networks. The Global Positioning System (GPS) which is used for navigation of ships, airplanes, etc. relies on the accuracy of the time signals broadcast from atomic clocks on satellites orbiting the earth. In metrology, most units are exactly defined in terms of the second, such as the Josephson volt and the metre. Accurate time is required for many areas of fundamental physics such as astrophysics, geophysics, and relativistic physics.

How is the fountain different from a beam clock?

Until recently, cesium beam clocks were the most precise way to measure time. However, after many years of development, cesium beam clocks reached their performance limit. The advancement in laser technology permitted some improvement in the traditional beam clocks but also made a new clock configuration possible. Laser cooling was developed and put to use in the new generation of atomic clocks: cesium fountain clocks. A brief comparison of the beam and fountain clocks is given in the table.

The differences between the two clocks result in improvements in the accuracy and stability of the signal:

• The interrogation time of atoms in the fountain is longer than it is for atoms in the beam clock. This is because of differences in clock configurations and atomic velocities. The longer interrogation time means better accuracy.
• The single microwave cavity of the fountain clock presents an advantage over the U shaped cavity of the beam clock because it eliminates the possible phase difference between the two arms of the U cavity in the beam clock.
• In the fountain clock, the preparation of all atoms in one state (using laser cooling) means that no atom must be discarded as was necessary in beam clocks. The result is a bigger signal to noise (S/N) ratio which translates into better stability.
• The continuous flow of atoms in the beam clock presents an advantage over the pulsed operation of the fountain clock since the local oscillator for the fountain does not receive continuous feedback. To compensate for this disadvantage, NRC's fountain will have multi-pulsed rather than single-pulsed operation. When one ball of atoms is in free flight above the microwave cavity, another is being prepared. With one ball of atoms almost always above the microwave cavity, the local oscillator will receive nearly continuous feedback.

The differences between the two clock types are significant enough to mean that fountain clocks may eventually be 100 times better than beam clocks.

Canada's Most Stable Cesium Clock: The Cesium Fountain FCs1

In July 2001, the stability of the Cs fountain reached a level at which it is more stable than NRC's cesium beam atomic clocks. Work is in progress to complete the magnetic shield that will allow a complete evaluation of the accuracy of the clock.

Ramsey Spectrum

Frequency - 9 192 631 770 Hz

Energy levels of a 133Cs Atom

According to the atomic theory, an atom can only occupy discrete quantized energy levels. Atomic transitions between energy levels occur through emission or absorption of electromagnetic radiation (photons).

The diagram below displays the energy levels of the cesium 133 atom. The energy of the Zeeman (m_F) sublevels is proportional to the local magnetic field and is given below in kHz/G. In the absence of a magnetic field, the m_Fsublevels are degenerate. To ensure that the sublevels are distinct in the fountain, a weak magnetic field, the "C-field", is applied.

The definition of the second (adopted in 1967) is based on the transition between the two hyperfine levels of the ground state of the cesium 133 atom. This is the "clock transition" shown in the energy level diagram below.

Click to enlarge.

Cesium

Natural cesium is a non radioactive element with atomic number 55 and atomic weight 133. It is the most electropositive natural element and reacts violently with water and oxygen.

Cesium is part of the Alkali metals group (group I of the periodic table). This group of elements, along with ions from other elements, is the most used for frequency standards. Elements of this group have only one valence electron. Consequently, their fundamental state is 2S1/2 which breaks down into only two hyperfine levels because of the interaction with the nucleus' magnetic spin.

The definition of the second is based on the transition between cesium's two hyperfine states which corresponds to a frequency of 9192631770 Hz. When determining the definition of the second in 1967, cesium was a good choice for the following reasons:

• Like all alcali atoms, cesium's fundamental state splits into only two hyperfine levels.
• At room temperature, all cesium atoms are in the fundamental state (62S1/2) and are equally distributed between the two hyperfine levels.
• The transition chosen (F =3 to F =4) is a dipolar magnetic transition. The probability that the atom will undergo a spontaneous dipolar magnetic transition is low, meaning that atoms in the F=4 state will stay in that state for a very long time (have a long lifetime) compared to the observation time. The transition chosen has also a significant energy difference compared to the energy between the ground state and the first excited state.
• The transition frequency between the two hyperfine states is a hyperfrequency which is detectable using available electrical systems. (Microwave systems that detect hyperfrequencies were developed during the second world war.) For certain element choices, transition frequencies might not have been detectable using easily available electrical systems.
• Cesium is relatively insensitive to electric fields. Small electric fields created by the environment will have a negligible effect on the cesium atoms in the clock.
• Cesium is less expensive than other elements in group I such as Rubidium.

It must be noted that the selection of the cesium atom was made in 1967. The progress in the area of frequency standards could make it possible for another atom or ion to eventually present more advantages.

Laser Cooling

Radiation Pressure Force

Since photons have momentum, the flux of photons making up a beam of light can transfer momentum to atoms. As an atom absorbs and emits photons, the atom's momentum changes over time, giving rise to a force called radiation pressure. This force can cause an atom to accelerate at very high rates (as much as thousands of times the acceleration due to gravity) or slow it down considerably.

• An atom absorbs a photon from a laser beam and the photon's energy and momentum are transferred to the atom. The atom will only absorb photons whose frequency equals its own resonance frequency. The atom is then in an excited state and its momentum is altered.
• The atom decays back to its ground state via spontaneous emission of a photon in a random direction. The atom loses energy and its momentum changes when the photon is released.

Each time a photon is absorbed and released, the atom's velocity changes by a very small amount. But the change in atomic velocity becomes significant after many cycles since the time for the absorption and emission process is short.

Doppler Cooling

Using the Doppler effect and the principle of radiation pressure, a radiation pressure force can be applied to oppose the atoms' motion, thus slowing and cooling them.

The Doppler effect is the apparent difference between the frequency of a wave leaving a source and the frequency of the wave reaching a moving observer. This effect results from the relative movement of the source with respect to the observer. The Doppler effect means that an observer moving towards (or away from) a wave source experiences a higher (or lower) frequency than an observer at the source. A familiar example is the sound of a car as it passes a stationary person. The person hears a higher sound when the car is approaching but the sound gradually lowers as the car moves away. This same effect is also present with electromagnetic radiation.

In the laboratory frame, the frequencies L of two contrapropagating laser beams are tuned slightly lower than the frequency o of the atomic transition (with a detuning δ) .

In the atomic frame, since the atoms are moving relative to the laser beams, the laser frequency is Doppler-shifted from the lasers' frequency L. The frequency of photons in the contrapropagating laser beam is observed as higher, and therefore closer to the atoms' resonant frequency o while the frequency of photons in the copropagating laser beam is lower. Consequently, the atoms interact preferentially with photons of the contrapropagating beam. This creates a radiation pressure force which acts in a direction opposite that of the velocity of the atom, like a friction force slowing down the atoms and thus cooling them.

Doppler cooling can cool atoms down to 125 μK. This limit is explained by the theory of radiation pressure force.

NRC's cesium fountain uses three pairs of contrapropagating laser beams (one pair aligned on the horizontal and the other two at 45° to the vertical, perpendicular to each other) to cool the cesium atoms.

Sub-Doppler Cooling (or Sisyphus cooling)

The key of sub-Doppler cooling is the Zeeman structure of ground state Alkali atoms and the fact that an atom can return to another ground state sublevel after an absorption-emission cycle.

Greek mythology has it that Sisyphus must endlessly roll a stone up a hill in the Underworld. As soon as he reaches the top the stone rolls down again.

Two distinct mechanisms are encompassed in sub-Doppler cooling: linlin requires two contrapropagating linearly polarized laser beams and σ+σ- requires two contrapropagating circularly polarized laser beams. The precise mechanisms of the two types of cooling are different but lead to very similar results. Linlin cooling will be discussed in the following paragraphs.

When an atom is placed in a laser beam, its energy level depends on the intensity, polarization, and frequency of the beam. An atom is essentially an electric dipole that can interact with the electromagnetic field of a light beam. The atom's interaction with an electric or magnetic field causes changes in the atom's fundamental energy levels. An atom can change energy levels by absorption or emission of a photon having a frequency close to resonance.

Suppose an atom is traveling along the z axis. If two contrapropagating laser beams with equal amplitudes but perpendicular linear polarizations are aligned with the axis, they will interfere to create a standing wave with a polarization gradient. The polarization of the standing wave will vary with position (and will repeat itself every λ/2). Since the polarization of the incident laser beams affects the atom's energy levels, the energy of the atom's sublevels will vary sinusoidally with the position of the atom along the axis. The atom will see a succession of hills and wells of potential energy as it travels along the axis. The specific sequence and size of the hills and valleys depend on the atom's energy level and sublevel.

Suppose an atom has just reached the top of a "potential hill" and has low kinetic energy. (By the law of conservation of energy, in order for the potential energy to increase, the kinetic energy must decrease.) There, the atom emits a photon which takes with it the kinetic energy lost by the atom. The atom's energy sublevel changes and the pattern of hills and valleys seen by the atom is inverted. The already slowed atom is at the bottom of an energy well (or valley). If it has sufficient kinetic energy left, it will go up another potential energy hill and lose more kinetic energy. After many such cycles, the atom's kinetic energy has lowered considerably and the atom will not have enough kinetic energy to climb another potential energy hill. The atom will be trapped in an energy well with low kinetic energy.

This mechanism can cause cooling down to temperatures of a few μK. The limit is due to the recoil velocity of the atom when it emits or absorbs a photon.

Trapping Force for the Magneto-Optical Trap (MOT)

To trap atoms in space, the radiation pressure force can be made position dependent by using an non-homogeneous magnetic field and polarized laser beams. A particular combination of the magnetic field gradient (produced by anti-Helmholtz coils) and polarized laser beams can push the atoms into a region of space and hold them there until the laser beams and magnetic field gradient are turned off.

Suppose that the direction of the magnetic field (produced by the anti-Helmholtz coils) is along the z axis and that the magnetic field is non-homogeneous. Then the magnetic field at positions z along the axis will be: B(z) = bz where b is the magnetic field gradient.

When cesium atoms are in a magnetic field, their energy levels are subdivided into sublevels (Zeeman sublevels) proportional to the local magnetic field. Since the magnetic
field varies along the z axis, the energy sublevels (mF) of the Cesium atom will depend on the atom's position along the axis. This means that the frequency difference between the laser light and the atomic sublevel depends on the atom's position along the axis. Thus, the probability of photon absorption also depends on the atom's position along the axis.

Selection rules depend on the polarization of an incident laser beam because of conservation of magnetic moment. The σ+ photons will only interact with the mF =+1 level while the σ- photons only with the mF =-1 level (see diagram). For an atom in negative z (respectively positive z), σ+ photons (respectively σ-) are closer to resonance. The atom is more likely to interact with photons whose frequency is closer to resonance. Therefore, the atom experiences a radiation pressure force pushing it back towards z = 0, the centre of the trap. At z = 0, an equal number of photons coming from positive and negative z are absorbed and so the net force traps the atom in this particular region of space.

Microwave Cavity

The microwave cavity is of utmost importance in any atomic clock because it's where the cesium atoms interact with photons of frequency 9192631770Hz. The following are some characteristics of the fountain's microwave cavity:

• Cavity is strongly coupled in the TE012 Mode
• Transverse BRF parallel to the C-field (transverse C-Field generated by two pairs of parallel rods)
• Single Feed (no ground loop, but possible linear transverse phase shift)
• High quality factor
  

Phase modulation Operation

In single-pulse fountain operation, there is only one ball of atoms moving through the fountain at a time. Since the fountain cycle takes approximately one second to complete, but the atoms are being interrogated for half a second, the local oscillator receives feedback for only half the cycle time. During the time that the local oscillator is not receiving feedback, a phase error may occur on the signal. The degradation of the clock's performance during the period of time when the local oscillator is not being stabilized by the atomic frequency is known as the Dick effect.

To minimize the Dick effect, the local oscillator must receive feedback corresponding to a signal representing the phase measurement over the entire cycle time. If one ball of atoms could be trapped and launched while another is in free flight above the microwave cavity, then the local oscillator would receive feedback twice as frequently. However, light from one ball of atoms must not reach the other because stray light could affect the atoms' state and thus change their response to the detection lasers.

Scientists at NRC have developed shutters to prevent the passage of light from one ball of atoms to the other. One shutter will be placed just above the magneto-optical trap and the other just below the microwave cavity. The shutters will open to allow the passage of atoms but will remain closed at all other times.