Randomness in quantum mechanics—nature's ultimate cryptogram?. T. Erber and S. Putterman in Nature 318:41 (1985). What the paper says!?
This is an interesting discussion of randomness in resonance fluorescence.
One of their most important observation is that the generation of genuine random numbers with such a simple system is, intrinsically, mysterious:
They discuss how this could compare a fundamental theory to deterministic mechanisms which appear to be random, e.g.,
and they argue that such functions appear random, but can be detected to have some structure. In fact this is quite trivial even to the eye:
frand = NestList[-Log[Abs[2 Exp[-#] - 1]] &, 315/100, 100];
ListPlot[N[frand, 200]]
Note the precision: the 53th iteration evaluates to $\approx\ln(1/2)$ so that the 54th is indeterminate to machine precision. This is because this map shifts one bit of the seed by iteration and the mantissa is . Their claims come from deeper maths than straight numerical treatments, e.g., they computed the excess as $\langle|\Delta|\rangle=\int_0^\infty |f(x)-x|\,e^{-x}\,dx = 1.0986\ldots$. I find $\langle|f^{i+1}(3.15)-f^{i}(3.15)|\rangle\approx1.11$ to $1.15$ depending on truncation for small sampling.
This discussion is fascinating:
Regarding more conventional physics aspects, they credit the pioneering input of Dehmelt (not his 1975 paper[1] though and neither his not yet published Ref. [2] although they mention the coming Bergquist et al.[3] experiment) and also credit the follow-up theory by Cook and Kimble[4].
They describe how this scheme leads to the famous telegraph signal
The authors also argue that the simplicity of the two-level system removes some unwanted quantum complications, such as bunching or correlations from the emission, and also the macroscopicity removes "watched-pot" (Zeno) effects, Turing paradox, retrodiction, etc. In particular, this statement, is probably demonstrably false (with our multiphoton virtual processes):
They refer to Narozhny et al.[5] for this last statement (their Ref. 19). Interesting. Should be pursued.
They link the mechanism to SQUID analogue-to-digital converters (their Ref. 9)
References
- ↑ Proposed ${10}^{14}\Delta\nu < \nu$ Laser Fluorescence Spectroscopy on $\text{Tl}^+$ Mono-Ion Oscillator II (spontaneous quantum jumps). H. G. Dehmelt in Bull. Amer. Phys. Soc. 20:60 (1975).
- ↑ Shelved optical electron amplifier: Observation of quantum jumps. W. Nagourney, J. Sandberg and H. Dehmelt in Phys. Rev. Lett. 56:2797 (1986).
- ↑ Observation of Quantum Jumps in a Single Atom. J. C. Bergquist, R. G. Hulet, W. M. Itano and D. J. Wineland in Phys. Rev. Lett. 57:1699 (1986).
- ↑ Possibility of Direct Observation of Quantum Jumps. R. Cook and H. Kimble in Phys. Rev. Lett. 54:1023 (1985).
- ↑ Coherence versus incoherence: Collapse and revival in a simple quantum model. N. Narozhny, J. Sanchez-Mondragon and J. Eberly in Phys. Rev. A 23:236 (1981).