研究目的
To propose and experimentally demonstrate a method to directly measure a nonlocal wave function of a bipartite system, using modular values, for a photon pair in a hyperentangled state.
研究成果
The study successfully demonstrates the direct measurement of nonlocal wave functions using modular values for the first time. The method extends the applicability of direct measurement techniques to scenarios involving nonlocal entanglement, offering new possibilities for studying quantum mechanics and its applications.
研究不足
The method is limited to pure states and requires high interference visibility. For mixed states, the method would be more resource intensive.
1：Experimental Design and Method Selection:
The experiment involves using modular values to measure the wave function of a bipartite system. The theoretical model employs weak values and modular values to obtain the complex amplitudes of the wave function.
2：Sample Selection and Data Sources:
Hyperentangled photon pairs, entangled both in polarization and momentum degrees of freedom, are used as the sample.
3：List of Experimental Equipment and Materials:
The setup includes a β-BaB2O4 crystal pumped by a vertically polarized ultraviolet laser, spherical mirror, QWP, neutral optical attenuators, half- and quarter-wave plates, glass compensators, unpolarized beam splitter, glass plates, PBS, spectrum filters, and avalanche single-photon detectors.
4：Experimental Procedures and Operational Workflow:
Photon pairs are prepared in a hyperentangled state. The modular values are measured using the path of a photon as a meter and its polarization as the system. The probabilities are obtained by Franson interference.
5：Data Analysis Methods:
The complex amplitudes of the wave function are reconstructed from the measured modular values using Eq. (1).
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β-BaB2O4 crystal
Used to generate photon pairs via spontaneous parametric down-conversion.
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ultraviolet laser
Pumps the β-BaB2O4 crystal to generate photon pairs.
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spherical mirror
Reflects the photon pairs and the pump beam for a second pass through the crystal.
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QWP
Manipulates the polarization of the photon pairs.
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neutral optical attenuators
ATTs
Reduces the relative intensity of relevant modes to prepare the initial meter state.
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half- and quarter-wave plates
HWP, QWP
Manipulates the polarization of each path independently.
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glass compensators
COs
Offsets the phase difference between paths.
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unpolarized beam splitter
BS
Combines the two paths of each photon.
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glass plates
GPs
Introduces a controllable phase for measuring different path states.
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PBS
Postselects the final polarization state.
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spectrum filters
Filters the photons before detection.
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avalanche single-photon detectors
D-1,2,3,4
Detects the photons after being guided by single-mode fibers.
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