Visibility of Interference Fringes and the Double Slit

E. L. Cleveland

Akira Matsumura, Taishi Ikeda, Shingo Kukita

When individual particles pass through a double slit, a fringe pattern appears on a screen. If an observer detects the path of the particle, the interference fringes disappear. This is called the quantum decoherence. In this paper, we discuss a parameter estimation problem using the quantum decohenrece in the double-slit experiment. As a simple model, we consider a massive scalar field interacting with the particle which have passed through the double slit. The scalar field, as well as the observer, can induce the loss of the fringe pattern of the particle. Because the interference fringes of the particle depend on the field mass and coupling, we can estimate the field parameters from the fringes. For qualitative analysis, we introduce the interferometric visibility of the fringe pattern and the Fisher information (FI) matrix of the field mass and coupling. Using the fringe pattern observed on the distant screen, we derive a simple relation between the visibility and the FI matrix. Also if we focus on FI of the mass, then we find that FI characterizes the wave-particle duality in the double-slit experiment.

Natalie G. Ferris

HE Long-qing

Young's double slits experiment was simulated by means of field superposition and numerical calculations.The effects on the interference fringes by the width of source,the width of slits,and the distance from the source to the double slits were discussed.The results showed that the visibility of the fringes decreased when the width of source and the distance between the two slits decreased.

Daqing Daching Piao

Lay Summary Whether and how consciousness could affect a physical system is a fundamental question. Radin et al (Radin et al 2012, 2013) reported that consciousness could perturb the fringe pattern of the classical experiment of double-slit illuminated by a laser beam. In understanding the possible physical cause to the observed change of the fringe, Radin et al modeled that the light intensity passing a slit subjected to consciousness intention could have changed. By using computer simulation based on standard wave approaches to light, we demonstrate that the extent of the change to the double-slit fringe as reported by Radin et al can be caused by a spectral perturbation to the light, which would take only approximately times of the energy change pertinent to the intensity change as was modeled by Radin et al. This indicates that the intensity change as modeled was unlikely the physical precursor to the observed effect. Scientific Abstract Significance: Recent reports [Radin 2012, Radin 2013] on variations to the fringe visibility of the interference patterns of laser-engaged double-slit experiments that seemed inexplicable at the absence of psychophysical influences have elicited notable debates within the scientific community and substantial interest in the lay population. In accounting for the observed changes of fringe pattern, Radin et al. modeled that the electrical field of the light passing the two slits might have reached an asymmetry of 3:1 in comparison to the generally symmetric baseline. However, a change to the double-slit interference fringe could have multiple causes. Identifying the most plausible cause to the fringe-pattern changes as were reported is fundamental to the understanding of the nature of psychophysical effect should it exist. Aim: To theorize an alternative interpretation to the fringe pattern changes of the double-slit interference that could be substantially more plausible than the one conjectured by Radin et al. Approach: We implement computer simulations of double-slit fringe pattern based on the Huygens-Fresnel principle using the primary experimental geometrical parameters of Radin et al. to assess how an asymmetry of the double-slit configuration could affect the fringe visibility. Specifically, we assess how an asymmetry in the physical size properties (slit-width and the lateral offset of the slit-center) and the photonic/spectral properties (intensity, wavelength, and spectral bandwidth) between the two slits would affect the fringe pattern. Fourier transformation of the double-slit interference fringe is also conducted when prompted to infer differences between fringe patterns that may be grossly equivocal in terms of the fringe visibility. Results: The main result is that the normalized interference fringe corresponding to the asymmetry of the electrical field of 3/1 or 1/3:1 is grossly indifferent from that caused by an asymmetry of the spectral bandwidth of 0.00205nm between the two slits at 6328nm center wavelength. A spectral broadening of 0.00205nm centered at 632.8nm would take approximately times of the energy of reducing the electrical field of light of that slit to 1/3 to reach a 3:1 inter-slit ratio of the electrical field. This 0.00205nm spectral broadening of the light could be associated with an energy change of no more than 10 picowatts for the experimental setting utilized by Radin et al. Conclusions: A change to the fringe pattern in the double-slit of Radin et al that was fitted with a 3:1 asymmetry of the electrical field between the two slits could be modeled alternatively by an asymmetry of ~0.00205nm in the spectral bandwidth between the two slits. The latter one, which would take approximately times of the energy-change of the former one to happen, could be substantially more plausible than the former one in acting as the physical precursor to the deviation of the double-slit fringe from the baseline pattern as reported by Radin et al.

Ralph F. Baierlein, Vacek Miglus