A trapped ion can still carry motional energy
Confinement prevents escape; cooling changes the motional-state distribution. A narrow optical transition can connect internal excitation with changes in one oscillator mode. Spectral peaks displaced from the carrier then encode exchanges of motional quanta, rather than additional electronic species.
Diedrich and colleagues reported near-ground-state motion of a single trapped mercury ion in 1989. Their approximate ninety-five percent population for the two optically visible directions used an assumption about energy sharing between them. The evidence was unequal lower and upper sideband absorption after cooling, not simply an ion remaining near the trap center.
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
Red removes a quantum; blue can add one
For absorption from the lower internal state, the first red sideband excites the internal transition while removing one motional quantum. The first blue sideband adds one. A ground-state oscillator cannot supply a quantum for red-sideband absorption, although blue-sideband absorption remains possible.
This explanation presumes a resolved mode and a specified internal-state preparation. Higher sidebands, other modes and off-resonant excitation complicate the spectrum. A weak peak by itself could also reflect poor coupling or an unsuitable probe, so the comparison needs matched conditions.
Read the evidence: F. Diedrich et al. (1989), Laser Cooling to the Zero-Point Energy of Motion, Phys. Rev. Lett. 62, 403–406 — NIST scanD. J. Wineland (2013), Nobel Lecture: Superposition, Entanglement, and Raising Schrödinger’s Cat, Rev. Mod. Phys. 85, 1103–1114 — published version of the 2012 lecture
A ratio becomes a thermometer only with a model
In the Lamb–Dicke regime and weak, unsaturated probing with matched red and blue response, summed first-sideband strengths have the ratio below. The numerator weights each occupation by the number of removable quanta; the denominator has one extra available quantum. The mean occupation is dimensionless.
For a thermal distribution of this one mode, the second relation converts the inferred mean to ground-state population. That last conversion is an additional assumption: a mean alone does not determine the ground-state population of an arbitrary nonthermal distribution. Nor should saturated peak heights be inserted without checking the probing model.
Read the evidence: Leibfried et al. (2003), Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281
Five percent is a useful arithmetic check
If the ideal weak-probe ratio were five percent, the mean occupation would be about 0.0526 and the thermal ground-state probability ninety-five percent. This is an arithmetic example. The 1989 probe was not in the unsaturated regime and used its own absorption analysis; the displayed weak-probe relation must not be substituted for that historical analysis.
A measured ratio close to zero still needs an upper uncertainty bound; a noisy or background-subtracted negative estimate is not a physical negative occupation. Collection drift, state-preparation errors, carrier leakage and finite excitation can all change the inference.
Read the evidence: F. Diedrich et al. (1989), Laser Cooling to the Zero-Point Energy of Motion, Phys. Rev. Lett. 62, 403–406 — NIST scanLeibfried et al. (2003), Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281
One cold mode is not three cold directions
A laser probes motion through its wave-vector projection. In the 1989 geometry, one direction was nearly perpendicular to the probe, preventing a meaningful energy estimate for that direction. The two visible directions required an energy-partition assumption. A later resolved axial-mode measurement in the same paper supplied a distinct check.
Monroe and colleagues’ 1995 work used resolved Raman sidebands to address three-dimensional zero-point cooling. Read it as a later experiment with its own method and coverage. Cooling one secular mode also does not certify removal of driven RF micromotion or the absence of later heating.
Read the evidence: F. Diedrich et al. (1989), Laser Cooling to the Zero-Point Energy of Motion, Phys. Rev. Lett. 62, 403–406 — NIST scanC. Monroe et al. (1995), Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy — NIST author abstractD. J. Berkeland et al. (1998), Minimization of Ion Micromotion in a Paul Trap, J. Appl. Phys. 83, 5025–5033
The ground state has fluctuations
A harmonic oscillator in its ground state retains zero-point position and momentum fluctuations. Ground-state cooling concerns occupation, not a particle frozen at a perfectly definite position with zero momentum. Temperature language is useful only insofar as the distribution supports it.
The sideband Lab uses an effective oscillator and declared sampling assumptions. It can help compare spectra and finite records; it does not establish the historical cooling fraction, full electrode motion or a three-dimensional thermometry calibration. Those claims require the experiment’s own controls.
Read the evidence: D. J. Wineland (2013), Nobel Lecture: Superposition, Entanglement, and Raising Schrödinger’s Cat, Rev. Mod. Phys. 85, 1103–1114 — published version of the 2012 lectureLeibfried et al. (2003), Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281