User:Jabeles/sandbox

To discuss Chip-Scale Atomic Clocks it is first useful to establish the context for clocks, and atomic clocks, in general.

Every autonomous clock must contain a single-frequency oscillator combined with a means of counting the oscillator cycles so as to mark time. Traditionally clocks employed mechanical oscillators. Classical mechanical oscillators are, firstly, the pendulum and, secondly, a mass combined with a spring. To make an accurate clock, one desires an oscillator which approximates ideality in that its oscillation occurs at a single frequency (does not drift with time). One also desires a practical means of interrogating the oscillator without disturbing the oscillation frequency.

Clock accuracy is quantified in terms of the relative accuracy of the clock as a function of the time interval being considered. Thus, the time interval over which the clock is relied upon to provide accurate time must be understood (either explicitly specified or implicitly understood from the context) when discussing clock stability. A given relative accuracy represents considerably different absolute accuracy depending on the time interval considered (e.g., 10^-12 relative accuracy represents 86 nsec in one day, 0.6 µsec in one week, or 31.4 µsec in a year since there are 0.86×10^5 seconds in one day, 0.60×10^6 seconds in a week, or 3.14×10^7 seconds in a year).

However, in general relative clock accuracy is not constant with the interval being measured as follows:

For shorter time intervals, in general, the relative accuracy of a clock improves proportionately to the square root of the time interval. This means that the time inaccuracy worsens not proportionately with the time interval (which would be the case if the relative clock accuracy were constant with time interval), but rather proportionately to the square root of the time interval. The cause of this behavior is understood in terms of random variations in the frequency of the clock which tend to average over time and cancel out.

For long time intervals, those over which random variations (having been averaged out) no longer affect the stability of the clock from a practical standpoint, the physics of the underlying oscillator determines the clock stability. In general, any oscillator mechanism is subject to variation in oscillation frequency imposed by alteration of the mechanism itself. For mechanical oscillators, the accumulation of dirt or grime in the pivot point of a pendulum will affect the oscillation frequency as would the accumulation of dirt or grime on a sprung mass. These alterations affect the long term stability of a clock.

With the advent of modern physics and quantum mechanics in the early 20th century it was discovered that individual atoms are complex oscillators with numerous atomic vibrations. This understanding sprung from the theoretical speculation that the electron orbit around a nucleus is quantized according to the number of wavelengths that equal the orbital circumference is attributed to Arnold Sommerfeld (see Bohr model).

Thus, the atom itself represented a new type of previously unknown oscillator. As came to be understood, atomic vapors could provide a large ensemble of truly identical particles which (being in a gaseous phase) were each isolated from other particles save for infrequent collision processes either with one another, with another gaseous species (potentially to be included purposefully), or with walls. This arbitrarily large ensemble of oscillators would, for the first time in the history of clock design, facilitate the essential interrogation function (to determine the atomic oscillator's frequency and count oscillations) with minimal effect on any one atom.

In the 1950s physicists at Harvard University, Princeton University, and collaborators such as ITT Corporation identified alkali atoms, which are hydrogen-like in that a single valence electron is bound to a complete inner shell structure, as having particularly convenient properties for atomic clock applications. The atomic species include lithium, sodium, potassium, rubidium, and cesium. (Francium, the last element in the Periodic Table Column I, which is radioactive, is difficult to work with.) All these atoms exhibit similar spectroscopy with a hyperfine structure split ground state. The hyperfine structure, essentially, is a splitting of the ground state in the magnetic field of the nucleus. What is more important, however, is the frequency of the splitting. Many atomic transitions are optical in nature with frequencies in the THz range. Such frequencies could not (prior to the recent invention of the frequency comb technique) easily be measured accurately until the recent invention. For rubidium and cesium, the splitting is a particular frequency in the microwave range. Thus, conventional radio frequency signal processing techniques can be used to measure this frequency.

A traditional atomic clock is an opto-electronic-atomic system which