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Currently, the System International (SI) second is defined as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom". Cesium atomic clocks have been in existence since the late 1950's and have been gradually improved to the point where modern cesium-fountain clocks (Fountain Project) realize the definition of the second with a relative uncertainty of about 1x10-15. These clocks use millions of atoms at any one time and it is expected that their accuracy ultimately may be limited by collisions between the atoms.
For approximately twenty years, it has been possible to hold a single charged atom (ion) in a small electromagnetic trap under a high vacuum. One can then slow down the motion of this ion to the point where it is confined to a region of space smaller than one cubic micron (10-6 m)3. It was quickly realized that such an ion was almost completely isolated from the surrounding environment and could serve as the ultimate frequency or time standard with a reproducibility and stability several orders of magnitude superior to the best cesium time standards. At NRC, the Optical Frequency Standards (OFS) Project has developed an optical frequency standard, based on a single, trapped and laser cooled strontium-88 ( 88Sr) ion.
The 88Sr ion was chosen because of the availability of the lasers necessary for laser cooling and probing of the "clock" transition. The ion is levitated inside a high-vacuum chamber by a small Paul trap. The distance between the two end electrodes is approximately 1 mm. A radio-frequency voltage applied between the ring and endcap electrodes results in an electromagnetic force on the ion which keeps it near the centre of the trap. When it is first captured, the ion moves around inside the electromagnetic trap typically at speeds of about 300 m/s. A blue laser is focused onto the ion and used to slow it down through a process called laser cooling. Here, the laser frequency is tuned to the low frequency (red) side of a strong electronic transition at 422 nm. Whenever the ion moves towards the laser, it sees the laser frequency Doppler shifted to a higher frequency, closer to the linecentre of the 422-nm transition. This process is similar to how the pitch of the whistle changes as a train goes by. The ion can therefore preferentially absorb a photon of light from the laser beam when its motion opposes the direction of the light beam. For each photon absorbed, the ion receives a small kick in the direction opposite to its motion. Since the re-emitted photon goes off in a random direction, the ion's velocity toward the laser is reduced. After absorbing and re-emitting several thousand photons, the ion's speed can be reduced to only a fraction of a metre per second. The electromagnetic trap then confines the ion to a much smaller volume of space than it would without laser cooling.
The figure on the right shows an energy level diagram for the 88Sr ion. Three lasers are required for the frequency standard: the 422 nm blue laser, required for laser cooling; an auxiliary infrared laser at 1092 nm, required to repump the ion back to the P1/2 state when it occasionally decays to the long-lived D3/2 state; and a red laser at 674 nm, whose optical frequency is locked to the S1/2 - D5/2 "clock" or reference transition. This latter transition is an electric quadrupole transition and is so weak that an ion excited to the D5/2 state takes, on the average, about 0.3 s to decay back to the S1/2 ground state - a very long time on an atomic scale. This results in an extremely sharp spectral line at 674 nm and a correspondingly narrow tuning range for the 674-nm laser over which it is capable of exciting the ion to the D5/2 state. In fact, the natural linewidth of the S1/2 - D5/2 transition is less than 1 Hz, compared to its centre frequency of 445 THz (445x1012 Hz)!
In order to use this narrow transition and the 674-nm laser in an optical frequency standard, the 674-nm laser must be extremely stable and locked in frequency to the centre of the S1/2 - D5/2 transition. Our laser is based on a red diode laser, similar to those used in bar-code scanners, with its optical frequency carefully controlled so that an integer multiple of its wavelength is exactly equal to twice the length of a stabilized optical cavity. A photograph of this cavity is shown above. It is approximately 25 cm in length and made from a special glass that expands or contracts very little with changes in temperature. The cavity is temperature-stabilized and placed in a vacuum chamber in order to isolate it from acoustic noise.
The vacuum chamber is mounted on a vibration-isolating table located in a concrete bunker. Part of the light from this laser is shifted in frequency to the centre of the S1/2 - D5/2 transition by a device called an acousto-optic modulator (AOM). Our current laser has achieved a drift rate of a fraction of one hertz per second and a linewidth of less than 5 Hz - approaching the natural linewidth of the S1/2 - D5/2 transition.
The absorption of single photons from the 674-nm laser beam by the strontium ion at a rate of only a few per second would be undetectable by normal means. Any slight decrease in the beam power would be completely masked by the normal power fluctuations present in the laser. A special technique is therefore required to tell when the laser frequency is tuned onto the narrow S1/2 - D5/2 transition. This technique is called the method of quantum jumps.
When the ion is excited by the 422-nm laser, it makes millions of transitions every second back and forth between the S1/2 and P1/2 levels, so many in fact that the fluorescence photons at 422 nm from one solitary ion can be detected by a sensitive photomultiplier. However, when the strontium ion absorbs a single photon at 674 nm, it jumps to the long-lived D5/2 state and no longer interacts with the 422-nm laser beam. The fluorescence at 422 nm suddenly stops. Only after the ion decays back to the S1/2 state does the florescence at 422 nm reappear. These jumps in the fluorescence signal are known as quantum jumps.
The figure above shows a 15-s plot of the measured fluorescence signal. Several quantum jumps can be seen. In our experiment, a computer is used along with the AOM to scan the optical frequency of the 674-nm laser across the S1/2 - D5/2 transition. The computer counts the number of quantum jumps in a certain time interval and uses this information to lock the shifted laser frequency to the centre of the transition.
The frequency of the S1/2 - D5/2 transition at 674 nm was measured in the late 1990's at NRC using a complicated device known as an optical frequency chain. A value of 444 779 044 095 400 Hz with an uncertainty of only 200 Hz was measured. This corresponds to a relative uncertainty of just 5 parts in 1013. Although this uncertainty is very small, it is several orders of magnitude larger than any suspected systematic offsets or errors in the S1/2 - D5/2 transition frequency due to perturbations of the ion. Errors in the locking of the 674-nm laser to the centre of the transition and errors in the frequency chain limited the accuracy achieved in our measurements.
Recent measurements at NRC and the National Physical Laboratory (NPL) in Britain using a new device called an Optical Frequency Comb (The Optical Frequency Comb) have confirmed earlier frequency chain measurements and reduced the uncertainty to the order of only a few hertz.
Soon after the frequency of the S1/2 - D5/2 transition was measured; the single ion standard was used in measurements of other important optical frequency standards. These included a standard near 1500 nm, with applications in the field of fibre optic telecommunications, and an iodine-stabilized helium-neon laser standard at 633 nm, which is used worldwide as a practical realization of the SI metre (Maintaining the SI Metre).
The recent development of optical frequency combs (The Optical Frequency Comb) has made it possible to measure the frequency of almost any stable optical laser source to unprecedented accuracy. An optical frequency comb can be used to compare quickly and accurately the frequency of other optical standards to the single 88Sr ion standard or to the Cs atomic clock SI realization of the second. It should also be possible to use the 88Sr ion as the source of regularly timed "ticks" in a new kind of atomic clock - the optical clock. The optical frequency comb is capable of counting every cycle of the laser locked to the 88Sr S1/2 - D5/2 transition, no mean feat since there are 445 trillion of these cycles every second. Such an optical clock, with the 88Sr ion as the source of ticks and the optical frequency comb serving as the clockwork, is expected to be far superior to the best cesium atomic clocks in terms of reproducibility and stability.
If the single trapped strontium ion standard is to be used as an optical clock, it must engineered to be accurate and reliable and capable of being operated unattended for long periods of time. Currently, we are working towards those objectives. Several new laser systems have recently been developed in our laboratory that provide better control of the ion and can be operated reliably for days. A new ion trap of the end-cap design has been constructed. This new trap, which is shown in the photograph below, will provide improved control on the position and motion of the ion and result in reduced sytematic uncertainties in the “clock” transition frequency. In parallel with this work, we have developed a fibre-based optical frequency comb that can operate unattended for days and will serve as the clockwork for the optical clock.