Mercury Trapped Ion Frequency Standards

How Trapped Ions Can Be Used to Make a Clock

Ions can be used to set the frequency of a microwave signal, and frequencies can be converted to time by simple addition. To see how this works, you must realize that if you have a periodic signal of known frequency "f", all you need to do is find a way to count anything that occurs once per period, and one second will be of "f" of them. This is why the most precise clocks are more accurately referred to as frequency standards. For example, if you had a voltage that went up and down past zero once each period, you could measure a second by counting the passage of "f" maxima, minima, upward-going zero crossings, or downward-going zero crossings. A specific example could be a pendulum clock. If you know that it goes back and forth every 4 seconds, then all you have to do is count the number of times it goes all the way to the right and multiply by 4 to get the number of seconds that have gone by. Of course, in practice such counting is not always so simple. Also, if the frequency is large it is usually necessary to subtract the frequency of interest from a second frequency, which yields a measurement of only the difference betweentwo frequencies.

Ions (ionized atoms) can absorb and re-emit radiation at certain very specific frequencies. By trapping the ions, they can interact for several seconds with microwaves whose frequency can be varied so as to be "exactly" equal to, or offset by a known amount from, that frequency which the ion scan absorb and re- emit. The longer the ions can interact with the microwave frequency without being disturbed, the more precisely they can distinguish between microwaves at the resonant frequency which they most strongly absorb and those at slightly different frequencies. In the case of mercury, this resonant microwave frequency is 40,507.348 MHz, which is subtracted from a similar frequency generated from the Master Clock. As described above, this frequency difference can be summed to convert into a time difference between the mercury clock and the Master Clock.

The Technique of Trapping Ions

It is well known that ions can be trapped in an oscillating quadrupole field, which is dramatized in the graphic above. As the ions move back and forth in response to the changing electrical force, it can be shown that they experience a net inward force, called the pondermotive force. Because about one million ions are trapped, this attractive force is balanced by the mutual repulsion of like charges, so that the resulting density of mercury ions is largely confined to and approximately uniform within a radius of 2.5 millimeters.

By using such a force field to trap mercury ions and the technique known as optical pumping to prepare the state of the mercury ions, it is possible to tune an input 40.5 GHz microwave field so that its frequency matches the natural frequency of the trapped mercury. Measurements of this tuned frequency forms the basis of a clock. It can be shown that the intrinsic accuracy of such a clock is chiefly affected by the second-order Doppler effect of the ionic motions(also known as time dilation).

Trapped Ions At the U.S. Naval Observatory(USNO)

In the 1980's, the Time Service Department of the USNO purchased three prototype trapped ion standards from Hewlett-Packard, which trap about two million ions in a spherical quadrupole potential. Details of their theory, design, and performance are provided or referenced in "Eight Years of Experience with Mercury Stored-Ion Devices," by D. Matsakis, A. Kubik, J. De Young, R. Giffard, and L. Cutler, Proceedings of IEEE Frequency Control Symposium, 86 (1995). These units were phased out because of hardware problems and the superiority of the improved models described below. In 1995, the vacuum system of unit 1 was refurbished for test purposes. Unit 2 was dismantled for parts in 1992. Unit 3 went off-line due to a problem with its electron filament. All units were turned off in June, 1998.

In 1995, the USNO installed a new kind of trapped ion clock, developed by the Time and Frequency Standards Division of the Jet Propulsion Laboratory (JPL).This design differs from the earlier models in many ways, but the most critical is that the ions are trapped along a line, and the quadrupole force is applied in two dimensions only. This permits the ions to be trapped closer to the center of symmetry where they experience less net motion, and their second-order Doppler effect is therefore an order of magnitude smaller. This unit is being evaluated by the Clock Development Division for both its short-term and long-term performance. Since 1995, JPL has brought about a significant improvement in accuracy and stability by implementing a means to shuttle ions between regions optimized for state preparation and others for state sampling.

Trapped Ions Around the World

Impressive results have been achieved by the Ion Storage Groupat the National Institute of Standards and Technology( NIST), in Boulder, Colorado. There, a few (between one and twenty) individual mercury ions are trapped. In addition, these ions are also cooled by lasers and stored in a cryogenic vacuum chamber.

Using similar methods to the JPL group, a group headed by Peter Fisk at Australia's National Measurement Laboratory has achieved excellent stabilities with trapped ytterbium. The lower microwave frequency of 12.6 GHz is compensated by the high signal to noise achievable with optical pumping, and the strong magnetic field dependence of the relevant transitions can be calibrated by the magnitude of the line splittings it induces (Zeeman effect).

The rapid progress being achieved in these areas can be followed in the annual Proceedings of the IEEE Frequency Control Symposium and the Proceedings of the Precise Time and Time Interval(PTTI) Systems and Applications Meetings, as well as the refereed literature.

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