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From

Analyzing the Decoherence on Biphoton and Schrödinger Cat States through Wigner Function

Simanshu Kumar, Nandan S Bisht

International Journal of Physics. 2025, 13(3), 73-79 doi:10.12691/ijp-13-3-5
  • Figure 1. A patterned HOM interferometer is placed in contact with an external environment. |𝑝1⟩ and |𝑝2⟩ representing the quantum state of photon-1 and photon-2 before entering the HOM interferometer, 𝜇 and 𝛿 representing the position and momentum translation in the quadratures of respective photons. BS is a 50:50 beam splitter, environmental interaction is represented by the state vector |𝜖⟩, and A and B are the photon coincidence detectors
  • Figure 2. The figure illustrates the correlation detection rate in for the HOM interferometry of biphoton, depicting the extraction of position marginals from the Wigner distribution function of the biphoton state across varying values of decoherence time (𝜏)
  • Figure 3. The figure illustrates the correlation between the coincidence detection rate for the HOM interferometry. It showcases the extraction of posi-tion marginals from the Schrödinger cat state Wigner distribution function, with a focus on varying decoherence time (𝜏) values
  • Figure 4. The figure presents a visual portrayal capturing the intricate process of decoherence in the biphoton state, meticulously illustrated from left to right. Through the utilization of the Wigner probability density function, this figure provides a profound glimpse into the dynamic behaviour of quantum entanglement and its susceptibility to environmental influences
  • Figure 5. The figure illustrates the phenomenon of decoherence in the Schrödinger cat state, depicted statically from left to right. The visual representation showcases the evolution of the Wigner probability density function, providing insights into the intricate interplay between quantum superposition and environmental interactions
  • Figure 6. The figure depicts the Wigner distribution of decoherence that occurred in a biphoton state when the photons impinge with a slight change in position 𝛿 and the momentum variable 𝜇 of the photons before interacting with the external environment including the beam splitter with variable decoherence time (a) 𝜏 = 0 ps, (b) 𝜏 = 1.2 ps, (c) 𝜏 = 1.4 ps, and (a) 𝜏 = 1.6 ps. It is straightforward to see from the contours that the interference vanishes with the decoherence time
  • Figure 7. The figure depicts the Wigner distribution of decoherence that occurred in a Schrödinger cat state of two photons when the photons impinge with a slight change in position 𝛿 and the momentum variables 𝜇 of the photons before interacting with the external environment including the beam splitter in HOM interferometer with variable decoherence time (a) 𝜏 = 0 ps, (b) 𝜏 = 0.2 ps, (c) 𝜏 = 0.4 ps, and (d) 𝜏 = 0.6 ps. It is straightforward to see the contours of the interference vanish with the decoherence time