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Simultaneous observation of particle and wave behaviors of entangled photons

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ABSTRACT

We theoretically study wave-particle duality of two entangled photons in the spirit of quantum version of delayed-choice experiments using Hadamard gate controlled by the quantum state of an ancilla and show that the two photons may globally exhibit particle-like, wave-like or simultaneously both particle-like and wave-like behavior. We prove that the obtained results cannot be satisfactorily explained by any hidden-variable theory. We also propose an efficient and experimentally feasible scheme without using any ancilla and controlled-gates to directly (i.e., without postselection) observe the two-photon wave-particle superposed state as well as the continuous transition of their behavior between wave-like one and particle-like one.

No MeSH data available.


The collective detection probabilities P00′ = P11′ of the two photons as functions of α and φ for the Werner-like input state (27) for q = 1/2 and for (a) θ = π/8 and (b) θ = 3π/8. The morphing between the particle-like (α = 0) and the wave-like (α = π/2) behavior of the two photons can still be seen by changing α from 0 to π/2 or vice versa.
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f4: The collective detection probabilities P00′ = P11′ of the two photons as functions of α and φ for the Werner-like input state (27) for q = 1/2 and for (a) θ = π/8 and (b) θ = 3π/8. The morphing between the particle-like (α = 0) and the wave-like (α = π/2) behavior of the two photons can still be seen by changing α from 0 to π/2 or vice versa.

Mentions: Clearly, the above state (28) is reduced to Eq. (22) when q = 1 and θ = π/4 corresponding to the maximally entangled input state /Ψ0〉AA′. Note that for q = 0 the input state of the two photons is separable (here each photon is in a maximally mixed state) and no interference patterns appear at all (ρA and ρA′ are both independent of φ), indicating the necessity of entanglement in the input state for observing the photons’ wave-like feature. The dependences of P00′ = P11′ on α and φ for 0 < q < 1 and θ ≠ π/4, are displayed in Fig. 4(a) and (b) for q = 1/2, while θ  = π/8 and θ  = 3π/8, respectively. Apart from the quantitative differences with respect to the imperfection-free situation (i.e., q = 1 and θ = π/4), the figures still qualitatively demonstrate the particle-like (wave-like) behavior at α = 0 (α = π/2) and a continuous transition between these two extreme cases as α gradually varies from 0 to π/2 or vice versa.


Simultaneous observation of particle and wave behaviors of entangled photons
The collective detection probabilities P00′ = P11′ of the two photons as functions of α and φ for the Werner-like input state (27) for q = 1/2 and for (a) θ = π/8 and (b) θ = 3π/8. The morphing between the particle-like (α = 0) and the wave-like (α = π/2) behavior of the two photons can still be seen by changing α from 0 to π/2 or vice versa.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5304183&req=5

f4: The collective detection probabilities P00′ = P11′ of the two photons as functions of α and φ for the Werner-like input state (27) for q = 1/2 and for (a) θ = π/8 and (b) θ = 3π/8. The morphing between the particle-like (α = 0) and the wave-like (α = π/2) behavior of the two photons can still be seen by changing α from 0 to π/2 or vice versa.
Mentions: Clearly, the above state (28) is reduced to Eq. (22) when q = 1 and θ = π/4 corresponding to the maximally entangled input state /Ψ0〉AA′. Note that for q = 0 the input state of the two photons is separable (here each photon is in a maximally mixed state) and no interference patterns appear at all (ρA and ρA′ are both independent of φ), indicating the necessity of entanglement in the input state for observing the photons’ wave-like feature. The dependences of P00′ = P11′ on α and φ for 0 < q < 1 and θ ≠ π/4, are displayed in Fig. 4(a) and (b) for q = 1/2, while θ  = π/8 and θ  = 3π/8, respectively. Apart from the quantitative differences with respect to the imperfection-free situation (i.e., q = 1 and θ = π/4), the figures still qualitatively demonstrate the particle-like (wave-like) behavior at α = 0 (α = π/2) and a continuous transition between these two extreme cases as α gradually varies from 0 to π/2 or vice versa.

View Article: PubMed Central - PubMed

ABSTRACT

We theoretically study wave-particle duality of two entangled photons in the spirit of quantum version of delayed-choice experiments using Hadamard gate controlled by the quantum state of an ancilla and show that the two photons may globally exhibit particle-like, wave-like or simultaneously both particle-like and wave-like behavior. We prove that the obtained results cannot be satisfactorily explained by any hidden-variable theory. We also propose an efficient and experimentally feasible scheme without using any ancilla and controlled-gates to directly (i.e., without postselection) observe the two-photon wave-particle superposed state as well as the continuous transition of their behavior between wave-like one and particle-like one.

No MeSH data available.