---
title: "Reading the sidebands in the first ion ground-state cooling experiment"
description: "How do you read the 1989 mercury-ion spectra without confusing a weak red sideband with a complete temperature measurement?"
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[Quantum physics: reading the evidence](https://sandboxphysics.com/stories/quantum-evidence/)

Nobel A · Evidence and control

# Reading the sidebands in the first ion ground-state cooling experiment

Sandbox Physics · 2026-10-15

How do you read the 1989 mercury-ion spectra without confusing a weak red sideband with a complete temperature measurement?

## Open the four-page paper beside the spectrum

Open Diedrich, Bergquist, Itano and Wineland, “Laser Cooling to the Zero-Point Energy of Motion,” Physical Review Letters 62, 403–406 (1989), in the NIST scan. Figure 1 gives the optical transitions and beam geometry; Figure 2 compares the motional sidebands; Figure 3 tests how the ion heats during a delay. Reading them in that order explains what the paper’s approximately ninety-five-percent ground-state statement covers.

The system is one mercury ion in a Paul trap. The trap keeps it nearby, but the ion can still occupy many vibrational energy levels. Ground-state cooling means bringing it to the lowest of those levels with high probability. Position and momentum still fluctuate there. The probability of occupying the ground state is the quantity to recover from the spectrum.

Read the evidence: F. Diedrich et al. (1989), Laser Cooling to the Zero-Point Energy of Motion, Phys. Rev. Lett. 62, 403–406 — NIST scan

## Figure 1 separates cooling from reading the result

Start with the level diagram in Figure 1(a). Strong ultraviolet light at 194 nanometres provides the first cooling stage and fluorescence detection. A narrow transition near 282 nanometres addresses the motion more selectively. The 398-nanometre light helps empty the long-lived upper level, allowing the cooling sequence to proceed faster.

A narrow transition can be driven below its carrier frequency, the frequency of the internal transition without changing vibrational energy. Absorbing on this first red sideband removes one quantum of motion as it excites the internal state. Subsequent relaxation resets the internal state, so the cycle can repeat and drain vibrational energy.

Keep the preparation interval and the spectroscopy interval separate as you follow the timing description. The experiment repeats cooling and probing, then uses the bright transition to read whether the narrow transition was excited. The plotted absorption percentages summarize those repeated preparations.

Read the evidence: F. Diedrich et al. (1989), Laser Cooling to the Zero-Point Energy of Motion, Phys. Rev. Lett. 62, 403–406 — NIST scan D. J. Wineland (2013), Nobel Lecture: Superposition, Entanglement, and Raising Schrödinger’s Cat, Rev. Mod. Phys. 85, 1103–1114 — published version of the 2012 lecture

## Figure 2 shows what changed after cooling

Figure 2 is on page 404. Its inset shows the spectrum before sideband cooling: a carrier near zero detuning and peaks on either side. In the enlarged main plot, the horizontal axis is detuning in megahertz, with an axis break between the negative and positive sides. The vertical axis is absorption in percent. The points are averages over repeated sweeps; the smooth profiles are fits.

The lower-frequency peak is the red sideband; it excites the ion while removing motion. The upper-frequency peak is the blue sideband; it excites the ion while adding motion. A ground-state oscillator has no quantum available to remove, but it can accept one. Suppression of the red response beside a surviving blue response is the useful comparison.

Read the caption before turning a peak-height ratio into an occupation. The inset used lower power to avoid saturation. The main measurement used saturating interrogation, and the authors treated that response with the analysis described in the paper. These are two probing conditions in one figure.

Read the evidence: F. Diedrich et al. (1989), Laser Cooling to the Zero-Point Energy of Motion, Phys. Rev. Lett. 62, 403–406 — NIST scan

## Keep the weak-probe calculation in its own box

For a separate textbook limit, suppose the ion moves much less than the optical wavelength, the first sidebands are resolved, and a weak unsaturated probe has the same response on the two sides. The red strength weights each vibrational level by the number of quanta it can lose; the blue strength has one extra quantum available. Their summed strengths then have the ratio below.

Here the two A symbols are matched sideband strengths, r is their dimensionless ratio, and the barred n is mean motional occupation, also dimensionless. The second line adds a thermal-distribution assumption. For a thermal mode, knowing the mean fixes the entire level distribution and therefore its ground-state probability. A nonthermal distribution needs more information.

As an illustrative calculation, a weak-probe ratio of five percent gives a mean occupation of about 0.0526 and a thermal ground-state probability of ninety-five percent. Those numbers demonstrate the relation. The 1989 saturated measurement used its own absorption analysis, so this exercise cannot be substituted for the historical fit.

$$
\begin{aligned}r&=\frac{A_{\mathrm{red}}}{A_{\mathrm{blue}}}=\frac{\bar n}{\bar n+1}\\P_0^{\mathrm{thermal}}&=\frac{1}{1+\bar n}\end{aligned}
$$

Read the evidence: Leibfried et al. (2003), Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 F. Diedrich et al. (1989), Laser Cooling to the Zero-Point Energy of Motion, Phys. Rev. Lett. 62, 403–406 — NIST scan

## Return to the beam direction before quoting ninety-five percent

Figure 1(b) supplies a geometrical limitation on Figure 2. The probe is almost perpendicular to one direction of motion, so the spectrum has very little sensitivity to energy in that direction. The authors explicitly withheld a meaningful energy estimate for it.

For the other two directions, the analysis assumes a division of energy between them. Under temperature equilibrium between those directions, the paper infers about ninety-five percent ground-state occupation for each of those modes. That qualification belongs beside the number. A laser measures motion projected onto its direction; the trap can hold the ion in all three directions without the probe measuring all three equally well.

Read the evidence: F. Diedrich et al. (1989), Laser Cooling to the Zero-Point Energy of Motion, Phys. Rev. Lett. 62, 403–406 — NIST scan

## Figure 3 asks how long the cold preparation lasts

On page 405, Figure 3 uses a changed trap setting that separates the axial sideband. Read its horizontal axis as the delay between the end of cooling and the probe, in milliseconds. The vertical axis is the inferred mean vibrational quantum number for that axial mode.

The rise with delay reveals heating while the ion waits. The extrapolation toward zero delay estimates the occupation at the end of cooling. This is why the waiting period is part of the measurement: a cold preparation and a later probe need not describe the same distribution. The plotted fit and its uncertainty carry information that would disappear in a single phrase such as “the ion stopped moving.”

Read the evidence: F. Diedrich et al. (1989), Laser Cooling to the Zero-Point Energy of Motion, Phys. Rev. Lett. 62, 403–406 — NIST scan

## What to write down for the next spectrum

Keep the preparation, probe power, mode frequency, beam direction, analysis model and delay with the result. Check that the red and blue measurements have matched coupling and detection conditions. Near a vanishing red signal, retain the uncertainty bound; noise or background subtraction can produce a negative numerical estimate even though occupation is nonnegative.

Resolved Raman sideband cooling in three dimensions was demonstrated later by Monroe and colleagues in 1995. The 1989 spectrum should be read with its own directional coverage. RF micromotion, the forced motion at the trap’s drive frequency, also needs a separate diagnostic from the slower mode used for the sideband thermometer. These distinctions tell you which physical motion a quoted cooling fraction describes.

Read the evidence: Leibfried et al. (2003), Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 C. Monroe et al. (1995), Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy — NIST author abstract D. J. Berkeland et al. (1998), Minimization of Ion Micromotion in a Paul Trap, J. Appl. Phys. 83, 5025–5033

## Continue with the models

These teaching Labs produce simulated data, which are separate from the historical observations discussed above.

- [Probe the sidebands of the ion’s oscillation](https://sandboxphysics.com/labs/trapped-ion-sideband-spectroscopy/)
- [Read the internal state through fluorescence](https://sandboxphysics.com/labs/fluorescence-quantum-jumps/)

## Sources and reading notes

The 1989 NIST scan was reread visually on pages 403–405 for this revision, including Figures 1–3 and their captions. The weak-probe arithmetic is a separate illustrative limit, not a refit of the saturated historical measurement. The review supplies thermal-distribution relations, and the 1995 NIST author abstract supplies the later three-dimensional comparison. The sideband Lab computes an effective oscillator and synthetic binary counts; RF motion is a separate SI protocol.

1. [Leibfried et al. (2003), Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281](https://www.nist.gov/document/rmp1pdf)
2. [D. J. Berkeland et al. (1998), Minimization of Ion Micromotion in a Paul Trap, J. Appl. Phys. 83, 5025–5033](https://tf.nist.gov/general/pdf/1226.pdf)
3. [D. J. Wineland (2013), Nobel Lecture: Superposition, Entanglement, and Raising Schrödinger’s Cat, Rev. Mod. Phys. 85, 1103–1114 — published version of the 2012 lecture](https://www.nist.gov/system/files/documents/2017/05/09/2677.pdf)
4. [F. Diedrich et al. (1989), Laser Cooling to the Zero-Point Energy of Motion, Phys. Rev. Lett. 62, 403–406 — NIST scan](https://tf.nist.gov/general/pdf/877.pdf)
5. [C. Monroe et al. (1995), Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy — NIST author abstract](https://www.nist.gov/publications/resolved-sideband-raman-cooling-bound-atom-3d-zero-point-energy)

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