Atomic Clock Simulator
Free atomic clock simulator: see how a caesium clock locks a quartz oscillator to atoms, tune Ramsey fringes in a fountain clock, race quartz against rubidium, caesium and optical clocks, compare their stability, and work out how far any clock drifts.
An atomic clock is a quartz oscillator that is kept honest by atoms. Switch the lock on and off, then warm the room, and watch what the atoms do.
The longer the atoms are probed, the sharper the resonance. A fountain tosses laser-cooled atoms up so they spend about half a second between two microwave pulses.
Each atom's two energy levels are one arrow on a sphere: south pole = ground state, north pole = excited. Watch the arrow through the two microwave pulses and see why the fringes appear. Drag the sphere to turn it.
A caesium fountain clock in 3D: six laser beams cool a ball of atoms, one more push tosses it up through the microwave cavity, and gravity brings it back. Drag to look around it.
Drawn to scale in height; the cloud and the cavity opening are exaggerated sideways (cloud 6×). Atoms that drift outside the 1 cm opening on the way back (red) are lost to the wall. The microwave offset is the probe set on the “Fringes” tab, so atoms that flipped turn gold after the second pulse.
Seven clocks start together, perfectly set. Speed up time and see how far each one wanders from the true second.
Bars use a log scale: each step to the right is ten times more error. The last column is how long the clock would typically take to be off by a full second.
Stability chart (Allan deviation): how steady is each clock when you average its frequency for a given time? Lower is better.
Each curve falls with a slope of −½ while the noise of the measurement averages away (twice as long averaging, a 1.4× steadier clock), then flattens at a floor that no averaging can beat. The dashed line is the fountain you built on the “Fountain & fringes” tab.
How far off will a clock be? Enter its frequency error, or how many seconds it gains or loses, and see the drift over any period.
| After | Clock is off by | Light travels in that time | Caesium cycles counted |
|---|
The distance column is why timing matters: GPS works by timing radio signals, which travel 30 cm in one nanosecond. A satellite clock that is wrong by 100 ns puts you about 30 m off.
How an atomic clock works
Every clock counts something that repeats: a pendulum swing, the vibration of a quartz crystal, a wave. The trouble is that no pendulum or crystal is perfect: heat, age and shocks change how fast they run. Atoms are all identical, and an atom of caesium-133 will absorb microwaves of one exact frequency and no other. So an atomic clock does not count atoms. It uses them as a reference to correct an ordinary oscillator that does the counting.
The loop, step by step
- Quartz oscillator: a crystal rings at, say, 10 MHz. It is cheap, quiet in the short term and wanders in the long term.
- Synthesiser: multiplies that signal up to about 9.19 GHz, the caesium microwave frequency.
- Atoms: a puff of caesium atoms, all prepared in one of the two ground-state levels, passes through the microwaves. If the frequency is exactly right, every atom flips to the other level. A little off, and only some do.
- Detector: counts how many atoms flipped. That number is a signal that peaks on resonance.
- Servo: nudges the microwaves up on one cycle and down on the next, compares the two counts, and steers the quartz so the signal stays at the peak. The quartz now inherits the atoms' frequency; the clock's output is the quartz signal, divided down to one pulse per second.
Why a fountain beats a tube
The resonance gets narrower the longer the atoms are probed (the time–frequency trade-off: width ≈ 1/(2T)). In a beam clock the atoms zip through a metre-long tube in about 10 ms, giving a line roughly 50 Hz wide. In a fountain clock, lasers cool the atoms to a few microkelvin and toss them up about a metre; they fall back through the same cavity half a second later. Two short pulses with a long wait between them make Ramsey fringes: a central fringe about 1 Hz wide, on a line at 9.19 GHz, a quality factor near 10¹⁰. NIST-F2 and its cousins in about a dozen countries realise the SI second to about 1 part in 10¹⁶.
The fountain: why it is tossed up, and why not higher
Six laser beams meeting at one point cool a ball of about a million caesium atoms to a couple of microkelvin, a few millimetres across. Slightly detuning the upward and downward beams then launches the ball (“moving molasses”) at a few metres per second, so it rises through the microwave cavity, slows, turns around under gravity a metre or less higher, and falls back through the same cavity: two microwave pulses, T apart, with the atoms in free flight and undisturbed in between. A longer flight narrows the fringe, but the cloud spreads sideways as it flies, and atoms that miss the cavity opening on the way back are lost. At some height the signal falls as fast as the fringe narrows, so a taller fountain stops helping unless the atoms are colder; that is why labs chase lower temperatures and why the best clocks of this kind fly their atoms about a second.
The Bloch sphere: why fringes appear
A two-level atom can be drawn as an arrow on a sphere (the Bloch sphere): the south pole is the lower level, the north pole the upper level, and the equator an equal mix of both. The first microwave pulse is exactly long enough to tip the arrow from the south pole to the equator (a "π/2 pulse"). During the wait the atom's own oscillation turns the arrow around the equator at the rate by which the microwaves are off resonance; if they are exactly on resonance it does not turn at all relative to them. The second pulse then tips it further. If the arrow has not turned, the second pulse continues the same motion and all atoms arrive at the north pole. If it has turned half a circle, the second pulse undoes the first and the atoms return to the south pole. Turning by one full circle brings back the maximum: that repeating pattern is the Ramsey fringes, and the longer the wait, the less detuning it takes to turn the arrow half a circle, so the fringes get narrower.
Why the next clocks use light
Frequency counts cycles, so a clock that ticks 50,000 times faster has more to divide with. Optical lattice clocks probe atoms such as strontium or ytterbium with a laser at about 430 THz, and they are accurate to a few parts in 10¹⁸: they would lose less than a second in the age of the universe. The General Conference on Weights and Measures is preparing to redefine the second on an optical transition. They are so precise that they notice the effect of gravity on time when one clock is raised by a centimetre (general relativity, tested in the lab).
What the page simulates, and what it does not
The line shapes (Rabi and Ramsey) are the exact two-level formulas. The locked clock follows the standard stability law above, with the signal-to-noise and linewidth you choose, and the quartz oscillator is modelled as a random walk in frequency plus temperature kicks. The clock ladder (quartz, TCXO, rubidium, caesium beam, hydrogen maser, caesium fountain, strontium optical) uses ballpark accuracy and stability figures from data sheets and national-laboratory papers; real instruments vary. Not modelled: the many small systematic shifts that metrologists correct for (Zeeman, blackbody, collisions, gravity), the exact servo electronics, and the dead time between cycles. It is a teaching model, not a metrology tool.
Things people ask
- Is there radioactivity in an atomic clock? No. Caesium-133 is the one stable isotope of caesium, and the clock only looks at how its electrons' energy levels respond to microwaves.
- Why caesium? It has a convenient microwave transition, atoms that are easy to cool and handle, and it was chosen in 1967 after decades of comparison. Rubidium and hydrogen are used too.
- Is an atomic clock in my phone? No: the phone has a quartz oscillator and gets the time from the network or GPS, which are tied to atomic clocks in satellites and national labs.
- What is UTC? A time scale built from about 450 atomic clocks in 80 labs, steered to the best fountains, with leap seconds added so it stays within a second of Earth's rotation.
Everything runs on your device; nothing is uploaded. Clock · Time zone converter · Timers · Photoelectric effect simulator · More MES tools