Measurement at the Microscopic Level

Zhu Ruogo, Zhou Keining, Yu Huang +1 more

With the deep research of measurement for microscopic or nanometer level scale at present the concept of Critical Dimension(CD) is pointed out in many papers[1,4,], they always include some analyses of measuring uncertainty for current technology of measurement, but our new idea or definition for geometrical action scale (GAS) is the limited scale or uncertainty of measurement in microscope that we can approach to for the most advanced method, technology, set-up or instrument, for example: The modern interferometer, SPM[5] and other various scattering experiments using the beam of microscopic particles. It would be found that the research included fundamentals for microscopic particle geometric scale is not easy to explore, some reasons perhaps are affected by which the classical quantum mechanics study of matter usually start from energy or energy level not from geometrical scale and by the Heisenberg relation of measuring uncertainty. Our work just wants to research on these fundamentals in physics for microscopic particles geometric scale. At first, a new physical quantity relative to microscopic particle geometric scale is directly suggested in this paper, it also may be deduced from the completeness of units system or dimension system refer to optics principles or quantum optics principles. We find that the wavelength of Louis de Broglie matter wave is either the length dimension or relative to the geometric scale of microscopic particles, and we define it as the geometrical action scale (GAS) of microscopic particles. The significance of the geometrical scale of microscopic particles or GAS in physics is discussed.

Julian Schwinger

Nobuyuki Imoto, Masahito Ueda, Tetsuo Ogawa

This paper proposes a microscopic model for the continuous measurement of photon numbers where the continuous measurement is simulated by a sequence of infinitesimal processes. Each process is composed of a unitary evolution for the coupled system, which consists of the field and the measuring apparatus, followed by a projection according to the readout of the measuring apparatus. The proposed model consists of two-level atoms that are coupled one by one with an optical cavity field via the electric-dipole interaction. Each atomic level is then read out after the interaction, causing a nonunitary state reduction of the field. In particular, it is shown that this microscopic model leads to the Srinivas-Davies model that has been postulated for the photodetection process.

Henryk Gzyl

In this work we reexamine the EPR paradox for composite systems with a finite number of levels. The analysis emphasizes the connection between measurements and conditional probabilities. This connection implies that when a measurement is performed, the microscopic states compatible with the measurement is different from the class of all possible microscopic states, therefore the new quantum state and the probability distribution change and become a function of the observable being measured. Therefore, the predictions that one can make given the knowledge of the result of a measurement change. Systems with finitely many levels are simpler to describe because the analysis is not encumbered by the mathematical technicalities of the continuous case, the underlying physical interpretations are the same and the experimental setups used to test quantum mechanics with the paradox in mind finitely many levels.e same.

Pierre Meystre

Pedro S. Correia, Adalberto D. Varizi, Gabriel Dias Carvalho

Quantum systems governed by unitary and reversible microscopic dynamics may nevertheless exhibit equilibration, in the sense that some effective description becomes time-independent. Standard equilibration results usually consider two separate situations: system-environment structures, in which the composite system evolves unitarily while the system of interest equilibrates, and restricted measurements, such as coarse-grained POVMs and observables, in which the measurement statistics equilibrate. Here, we bring these descriptions into a common state-level framework using the concept of generalized subsystems, where the accessible effective state appears as the output of a quantum channel acting on the microscopic state. We derive bounds showing that generalized subsystems equilibrate when their dimension is small compared with the effective dimension of the discarded microscopic information. We further show that this condition is met for typical initial states in large subspaces and that the resulting equilibrium description is largely insensitive to microscopic initial details. The framework recovers the usual equilibration bounds for ordinary subsystems and finite families of POVMs. As an example, we also introduce a finite-resolution energy channel that maps unresolved microscopic energy levels into effective energy levels, thereby making residual effective coherences explicit and showing how spectral multiplicities constrain those coherences while strengthening equilibration. Our results provide a unified state-level formulation of quantum equilibration under general forms of limited accessible information.