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arXiv:2203.13187 · Physical review. D/Physical review. D.

Effect of relativity and vacuum fluctuations on quantum measurement

Adam Bednorz, Wolfgang Belzig

Published May 31, 2022• 1 citation
arXivHTMLPDF

Abstract

Vacuum fluctuations can obscure the detection signal of the measurement of the smallest quantum objects like single particles seemingly implying a fundamental limit to measurement accuracy. However, as we show relativistic invariance implies the disappearance of fluctuations for the spacelike spectrum of an observable at zero temperature. This complete absence of noise can be harnessed to perform noiseless measurement of single particles, as we illustrate for electrons or photons. We outline a general scheme to illustrate the noiseless measurement involving the spacelike spectrum of observables based on the self-interference of counterpropagating paths of a single particle in a triangular Sagnac interferometer.

DOI
10.1103/physrevd.105.105027

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Vacuum fluctuations can obscure the detection signal of the measurement of the smallest quantum objects like single particles seemingly implying a fundamental limit to measurement accuracy. However, as we show relativistic invariance implies the disappearance of fluctuations for the spacelike spectrum of an observable at zero temperature. This complete absence of noise can be harnessed to perform noiseless measurement of single particles, as we illustrate for electrons or photons. We outline a general scheme to illustrate the noiseless measurement involving the spacelike spectrum of observables based on the self-interference of counterpropagating paths of a single particle in a triangular Sagnac interferometer.
The interaction of a particle with vacuum fluctuations-which theoretically exist even in the complete absence of matter-can lead to observable irreversible decoherence if it were possible to switch on and off the particle charge suddenly. We compute the leading order decoherence effect for such a scenario and propose an experimental setup for its detection. Such a measurement might provide further insights into the nature of vacuum fluctuations and a novel precision test for the decoherence theory.
Experimental tests for assessing the physical reality of the hypothetical wave modes of quantum vacuum with zero-point energy are of fundamental importance for quantum field theories and cosmology. Physical effects like the Casimir effect have alternate description in terms of retarded interaction between charged matter, due to quantum fluctuations of material dipoles. However, there are simple quantum optical configurations where the hypothetical quantum vacuum modes seem to assume an essential real role in the observable quantum noise of optical signals. I present the logical and theoretical basis of a decisive test that relies on the comparisons of balanced homodyne detection with a novel differential scheme of balanced wave-front division detection, when the two real optical beams at the detectors are derived from one coherent beam as input. Both ideal and practical configurations of my experimental test are discussed. Results from the experiments on balanced detection, beam localization of optical beams, and atomic Bose-Einstein condensates are used to reach definite conclusions against the reality of the wave modes of quantum vacuum. It is shown that the entire quantum noise follows consistently from the state reduction of quantum superpositions of particle-number states at the point of detection, where the quantum measurement is completed. This is consistent with the demonstrated applications of squeezed light in interferometry and quantum metrology. This result achieves consistency between quantum noise in quantum optics and observational cosmology based on general relativity, by avoiding the wave modes of quantum vacuum with divergent zero-point energy density. Generalization from the limited sphere of quantum optics to general quantum field theories promises the complete solution to the problem of a divergent cosmological constant.
I assume that everywhere in space there is a real random electromagnetic radiation, or zeropoint field (ZPF), which looks similar for all inertial observers, so that the stochastic properties of the field should be Lorentz invariant. This fixes the spectrum except for a single adjustable parameter measuring the scale, which is identified with Planck's constant, so making the ZPF identical to the quantum electromagnetic vacuum. Photons are just fluctuations of the random field or, equivalently, wavepackets in the form of needles of radiation superimposed to the ZPF. Two photons are "classically correlated" if the correlation involves just the intensity above the average energy of the ZPF, but they are "entangled" if the ZP fields in the neighbourhood of the photons are also correlated. These assumptions may explain all quantum optical phenomena involving radiation and macroscopic bodies, provided the latter may be treated as classical. That is, we have an interpretation of quantization for light but not for matter. Detection of photons involves subtracting the ZPF, which cannot be made without a fundamental uncertainty. This explains why photon counters cannot be manufactured with 100% efficiency and no noise (dark rate), which prevents the violation of a genuine Bell inequality (this is the so-called detection loophole). The theory thus obtained agrees very closely with standard quantum optics if this is formulated in the Wigner representation.
The interference pattern of coherent electrons is effected by coupling to the quantized electromagnetic field. The amplitudes of the interference maxima are changed by a factor which depends upon a double line integral of the photon two-point function around the closed path of the electrons. The interference pattern is sensitive to shifts in the vacuum fluctuations in regions from which the electrons are excluded. Thus this effect combines aspects of both the Casimir and the Aharonov-Bohm effects. The coupling to the quantized electromagnetic field tends to decrease the amplitude of the interference oscillations, and hence is a form of decoherence. The contributions due to photon emission and to vacuum fluctuations may be separately identified. It is to be expected that photon emission leads to decoherence, as it can reveal which path an electron takes. It is less obvious that vacuum fluctuations also can cause decoherence. What is directly observable is a shift in the fluctuations due, for example, to the presence of a conducting plate. In the case of electrons moving parallel to conducting boundaries, the dominant decohering influence is that of the vacuum fluctuations. The shift in the interference amplitudes can be of the order of a few percent, so experimental verification of this effect may be possible. The possibility of using this effect to probe the interior of matter, e.g., to determine the electrical conductivity of a rod by means of electrons encircling it is discussed. (Presented at the Conference on Fundamental Problems in Quantum Theory, University of Maryland, Baltimore County, June 18-22, 1994.)
Quantum contextuality can be observed in three path interferometers, suggesting a fundamental contradiction between wave propagation and particle propagation inherent in the wave-particle dualism. Here, we investigate this contradiction in a three path interferometer specifically designed to illustrate the paradoxical aspects of single particle interference. A particularly clear violation of non-contextual assumptions is obtained when interference effects suppress detection probabilities to zero in paths that seem to be necessary to explain the observation of photons in the output. This contradiction between detection probabilities in the paths and detection probabilities in the output cannot be explained by any assignment of photon paths through the interferometer, demonstrating a fundamental incompatibility of wave propagation and particle propagation.
Quantum physics rules the dynamics of small objects as they interact over microscopic length scales. Nevertheless, quantum correlations involving macroscopic distances can be observed between entangled photons as well as in atomic gases and matter waves at low temperatures. The long-range nature of the electromagnetic coupling between charged particles and extended objects could also trigger quantum phenomena over large distances. Here, we reveal a manifestation of quantum mechanics that involves macroscopic distances and results in a nearly complete depletion of coherence associated with which-way free-electron interference produced by electron-radiation coupling in the presence of distant extended objects. This is a ubiquitous effect that we illustrate through a rigorous theoretical analysis of a two-path electron beam interacting with a semi-infinite metallic plate and find the inter-path coherence to vanish proportionally to the path separation at zero temperature and exponentially at finite temperature. The investigated regime of large distances originates in the coupling of the electron to radiative modes assisted by diffraction at material structures but without any involvement of material excitations. Besides the fundamental interest of this macroscopic quantum phenomenon, our results suggest an approach to measuring the vacuum temperature and nondestructively sensing the presence of distant objects.