Quantum Decay Tail: How the Memory of Birth Depends on Color ✛
A quantum system, once born, does not forget it. Even after dozens of lifetimes, a trace of the initial state remains in its decay: a slowly decreasing power-law tail. For two fluorescent dyes, erythrosine B and eosin Y, this tail has been observed for the first time in two spectral channels simultaneously. It turns out that different colors fade differently, but the overall rhythm is set by a single conductor: a common lifetime.
The experiment used an inverted confocal microscope Nikon Eclipse Ti-E with a picosecond laser (438 nm), collecting fluorescence through two hybrid detectors PicoQuant PMA Hybrid 40. Bandpass filters 520/35 nm and 600/50 nm split the light into two channels. For erythrosine B, the lifetime was 0.448 ns in both channels, while the power-law exponents β diverged: 1.559±0.014 and 2.019±0.017. Eosin Y showed a similar pattern: τ = 1.054 ns, β = 1.512±0.019 and 1.845±0.051. The power-law tail appeared after about 10 lifetimes. A two-exponential model could not describe the data, while an exponential plus a power law fit significantly better.
Theoretical model with a threshold spectral density of the form ρ(E) ∝ (E−Eth)^γ with γ<0 reproduces the observed β in the range 1<β<3. Multichannel analysis shows that late channel intensities behave as $t^{-(2γ_{i+3})}$ for one channel and $t^{-(γ_1+γ_{2+3})}$ for the other, explaining the difference in exponents. Previously, such deviations were seen only in a single channel, but now it is clear: the memory of birth is distributed unevenly across channels.
This result changes our understanding of late decay stages in molecular physics, nuclear physics, and particle physics. Now one can test predicted oscillations in the spectral density at high temporal resolution, study the influence of state preparation conditions on the tail shape, and extend the approach to quantum tunneling. For practice, this means more accurate calibration of fluorescence measurements in biology and chemistry, where late times matter.
The late power-law tail means that the quantum system remembers the moment of its birth even after dozens of lifetimes. In the experiment, photon counting continued up to 95 nanoseconds, which corresponds to about 200 lifetimes for erythrosine B.
In Stanislaw Lem's novel "Solaris," the ocean manifests memory of the past in unexpected forms. Here, the quantum system also stores memory of the moment of birth, but manifests it in a channel-dependent power-law decay tail.