A cavity cat loses coherence before it loses its energy

Two phases of stored light

In 1996 Brune and colleagues stored a field of a few microwave photons in a cavity and coupled it to Rydberg atoms. These atoms have an electron excited far from the core, making them sensitive probes of the weak field. The interaction tied two possible internal atomic states to two different phases of the light, creating a small version of a Schrödinger cat state.

Phase describes where an oscillation is in its cycle. A coherent microwave field can have a definite phase even though its photon number fluctuates. The cat preparation combined two distinguishable phase alternatives in a quantum superposition. The experimenters wanted to follow what happened to the relationship between those alternatives as they waited.

Read the evidence: M. Brune et al. (1996), Observing the Progressive Decoherence of the “Meter” in a Quantum Measurement, Phys. Rev. Lett. 77, 4887–4890

Interference reveals the relationship

Imagine preparing one of two possible light fields by tossing a coin. Half the runs contain the first field and half the second. That ordinary mixture can give the same relative counts as a coherent superposition when the measurement only asks which field is present.

The difference appears when the alternatives are brought together. A coherent superposition can produce interference, a signal that depends on their relative phase. The mixture has lost that relationship. Measuring only the energy or identifying two separate components leaves this difference hidden.

Brune’s team used a second atom to make that relationship observable after a delay. They counted the joint outcomes of the two atoms. A particular difference between conditional detection probabilities served as the interference-sensitive signal. This was a two-atom correlation measurement; full reconstruction of the stored field came in later experiments.

Read the evidence: M. Brune et al. (1996), Observing the Progressive Decoherence of the “Meter” in a Quantum Measurement, Phys. Rev. Lett. 77, 4887–4890 S. Haroche (2013), Nobel Lecture: Controlling Photons in a Box and Exploring the Quantum to Classical Boundary, Rev. Mod. Phys. 85, 1083–1102 — published version of the 2012 lecture

The environment can carry away the difference between branches

As light leaks out, the outgoing field becomes correlated with what remains inside. If the escaped light differs for the two branches, the environment carries information about which alternative occurred. Ignoring that environment weakens the interference accessible in the cavity, even when nobody detects the escaped light. This reduction in accessible interference is decoherence.

The formula gives a general two-branch model. Psi is the normalized state of system and environment together; the labels one and two denote orthonormal system alternatives, and the two e states describe normalized environment states. The c coefficients are complex probability amplitudes. The density-matrix element rho with subscripts one and two measures the coherence; it is multiplied by the overlap between the environment states. A small overlap means the environment can distinguish the alternatives well.

This simple formula uses orthogonal system branches. The coherent-field components of an actual cavity cat need not be exactly orthogonal. The physical point is the same: entanglement with an unobserved environment can make the accessible field behave like a mixture.

\begin{aligned}|\Psi\rangle&=c_1|1\rangle|e_1\rangle+c_2|2\rangle|e_2\rangle\\ \rho_{12}&=c_1c_2^*\langle e_2|e_1\rangle\end{aligned}

Read the evidence: S. Haroche (2013), Nobel Lecture: Controlling Photons in a Box and Exploring the Quantum to Classical Boundary, Rev. Mod. Phys. 85, 1083–1102 — published version of the 2012 lecture

Energy lifetime and coherence time are different clocks

The cavity can still hold much of its mean energy after the interference has faded. Losing energy and losing coherence are different processes to measure: the first tracks how much excitation remains, and the second tracks the relationship between the alternatives. Leakage connects the two because the escaped field can carry branch information.

A small amount of leaked light is more informative when the alternatives are already easy to distinguish.

In the 1996 study, coherence decayed faster when the two field components were more widely separated in phase space, a way to describe their amplitudes and phases together. The comparison included the prepared field, known cavity loss and finite experimental contrast. Its result concerned those preparations and that damping model; different cat states can have different decay scales.

Fading fringes need control experiments

Random technical phase drift can also wash out an averaged fringe. The experiment therefore had to control the delay and separation of the components, know the cavity damping and characterize the detector response independently. Holding preparation and analysis fixed while changing the wait made the fading coherence a testable trend.

The measured correlation points, the theory curve and a phase-space sketch have different roles. Changing the calibration or estimator at every delay could manufacture a trend, so the comparison depends on a stable measurement procedure. Under those controls, the experiment followed the loss of coherence in a deliberately prepared quantum state.

Entanglement with the environment explains how accessible interference can fade. It leaves the question of why a particular measurement yields one outcome open, along with the wider debate over interpretations of quantum mechanics. Here a concrete part of the quantum-to-classical transition became something experimenters could prepare, delay and measure.