Interference fringes test only first-order coherence
Split a beam, delay one copy and bring them together again. Bright and dark fringes reveal how consistently the field oscillations keep their relation across that delay. This is a first-order test of coherence. Two sources can have similar spectra, the distribution of light among frequencies, and similar fringe contrast, yet different patterns of photon detections.
Glauber’s 1963 paper introduced a hierarchy of field correlations to describe those differences. The 2005 prize recognized this theoretical framework, which ties coherence to what detectors actually count. Photon-correlation experiments have their own experimental history; an ideal coherent-state description of a narrow laser beam still requires a test of its photon statistics.
A phase lock answers a first-order question
A weak reference field can stop another oscillator’s phase from continually running ahead. Its frequency follows the reference, with a fixed phase offset that need not be zero. Outside the locking range, the phase keeps slipping and the receiver sees a beat. This is injection locking, a way to control the relative field phase.
That control still leaves the photon-counting question open. A stable relative phase and a narrow beat spectrum describe the field relation to the reference. Coincidences ask how detection events occur together. Glauber’s hierarchy keeps both questions in the same theory.
The same distinction appears when several amplifiers feed one focus. Adjusting each beam's overall phase can brighten the center by redirecting light that previously interfered elsewhere. It does not straighten tilted beams or equalize their powers. A 2017 seven-channel experiment by Dong Zhi and colleagues compared phase control with separate pointing control and found that both affected the power concentrated in the focus. This is still a measurement of interfering fields; coincidences answer the additional photon-counting question.
Coincidences are counted at a chosen delay
Split a stationary beam, one whose statistics do not drift over time, into two channels. Count all detector pairs whose time difference falls in a chosen delay bin. Independent arrivals would give the product of the two single-channel count rates, the acquisition time and the bin width. Divide the observed pair count by that expected count to obtain a dimensionless correlation averaged over the bin. This continuous-beam estimate assumes a delay much shorter than the acquisition time and negligible dead-time losses; pulsed measurements need a normalization matched to their repetition and detection gates.
In the first line, the numerator is the pair count in the delay bin; the denominator uses the two singles rates in counts per second, the acquisition time in seconds and the bin width in seconds. If the correlation changes across a wide bin, the average need not equal its value at the bin center.
For ideal single-mode light, the zero-delay value can be written in terms of photon number. Subtracting one counts only pairs of distinct photons in the same mode. The mean photon number must be nonzero; with no light at all there is nothing to normalize.
One, two and zero are ideal limits
In an ideal coherent state, detections have no extra tendency to arrive together, giving one. A single thermal mode, one independently fluctuating field pattern, gives two because the counts cluster. An ideal single-photon state gives zero: its mode contains only one photon, so it cannot supply a pair. These are model limits. A detector that mixes many independent thermal modes measures weaker bunching.
Detector timing resolution, dead time, background counts and afterpulsing also change a measured histogram. Compare any dip or peak with the instrument response and the acquisition window. Assess a photon source using its count statistics together with a calibrated detector response.
Coherent light need not be monochromatic
Glauber’s abstract states that coherent fields need not be monochromatic. A pulse whose frequency components keep fixed phases relative to each other contains a whole spectrum. Conversely, filtering thermal light to a narrow band does not give it the photon statistics of a coherent state.
A laser can also acquire a complicated spectrum when a mirror returns an earlier copy of its field. The returning oscillation interferes with the field already present. The altered light intensity changes how quickly the material gives up its stored excitation energy. The delay and the return phase can then sustain oscillations or irregular fluctuations. Such dynamics already occur in classical equations for the light field and stored excitation, with no photon noise added. A broadened spectrum describes those changing fields; a counting experiment is needed to determine the detection statistics.
This links the visibility measurements in the Michelson article to photon counting. First-order and higher-order experiments ask different but compatible questions about the same light.
Counting time changes how clearly the difference appears
Counting for longer reduces the scatter from a finite number of detections. Choosing a wider delay bin collects more pairs, but also averages over more of the correlation curve. Source statistics and detector timing must be considered together when interpreting a measured peak or dip.