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Superlattices and Microstructures

The number-phase uncertainty principle and fundamental limits of quantum interference devices

Akira Shimizu, H. Sakaki

Published Jan 1, 1992• 4 citations
Publisher
DOI
10.1016/0749-6036(92)90394-k

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Most sensors traduce various environmental, industrial, or laboratory parameters into electrical signals. Quantum sensing pushes this to the ultimate limit of achievable sensitivity, detectivity, resolution, and stability. Quantum mechanics sets these limits through the uncertainty principle. It causes the ubiquitous 1/f noise, as we show here for LiNbO3. Quantum 1/f theory, known as the quantum theory of the fundamental 1/f noise phenomenon, is a new aspect of quantum mechanics, that governs the nonlinear interaction of particle and field, introducing the new notions of "physical cross sections" (PCS) and "physical process rates" (PPR). These contain the fundamental macroscopic quantum 1/f fluctuations. They yield the usually defined PCS and PPR with infrared radiative corrections, when the expectation value is taken over the low-frequency photon states of negative entropy. The physical charged particle, such as an electron, contains both the bare particle and its electromagnetic field. The latter is in a coherent state, where the phase of the electromagnetic field oscillators is determined. Heisenberg’s uncertainty principle then requires that the energy must be uncertain, leading to nonstationary states describing the particle. The particle’s resulting fractional current fluctuations in large devices always have the spectrum 2α/πf, where α=1/137 is the fine structure constant.
Heisenberg’s uncertainty principle states that there is a fundamental limit to the precision with which certain pairs of physical properties of a particle (complementary variables) can be measured simultaneously. Heisenberg’s uncertainty principle has indubitable support, but the origin behind this principle is unexplained. If complementary variables of particles are considered as complex numbers—for example, in calculating particle position, a complex vector coordinate space is necessary instead of the Cartesian space—then the origin of lower limit of Heisenberg’s uncertainty principle emerges.