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arXiv:1103.2270 · Physical Review A

Visibility bound caused by a distinguishable noise particle

Miroslav Gavenda, Lucie Čelechovská, Jan Soubusta, Miloslav Dušek, Radim Filip

Published Apr 15, 2011• 7 citations

Abstract

We investigate how the distinguishability of a ``noise'' particle degrades interference of the ``signal'' particle. The signal, represented by an equatorial state of a photonic qubit, is mixed with noise, represented by another photonic qubit, via linear coupling on a beam splitter. We report on the degradation of the signal photon interference depending on the degree of indistinguishability between the signal and noise photons. When the photons are completely distinguishable in principle but technically indistinguishable, the visibility drops to the value $1/\sqrt{2}$. As the photons become more indistinguishable, the maximal visibility increases and reaches the unit value for completely indistinguishable photons. We have examined this effect experimentally using a setup with a fiber-optics two-photon Mach-Zehnder interferometer.

DOI: 10.1103/physreva.83.042320

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We investigate how the distinguishability of a noise'' particle degrades interference of the signal'' particle. The signal, represented by an equatorial state of a photonic qubit, is mixed with noise, represented by another photonic qubit, via linear coupling on a beam splitter. We report on the degradation of the signal photon interference depending on the degree of indistinguishability between the signal and noise photons. When the photons are completely distinguishable in principle but technically indistinguishable, the visibility drops to the value

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We study the fringe visibility and the distinguishability of a general Mach–Zehnder interferometer with an asymmetric beam splitter. Both the fringe visibility V and the distinguishability D are affected by the input state of the particle characterized by the Bloch vector S = ( S x , S y , S z ) and the second asymmetric beam splitter characterized by the paramter β . For the total system is initially in a pure state, it is found that the fringe visibility reaches the upper bound and the distinguishability reaches the lower bound when cos β = − S x . The fringe visibility obtain the maximum only if S x = 0 and β = π /2 when the input particle is initially in a mixed state. The complementary relationship V 2 + D 2 ≤ 1 is proved in a general Mach–Zehnder interferometer with an asymmetric beam splitter, and the conditions for the equality are also presented.

We present a multimode model to describe an arbitrary

N

-photon state with a wide spectral range and some arbitrary temporal distribution. In general, some of the

N

photons are spread out in time while others may overlap and become indistinguishable. From this model, we find that the temporal (in)distinguishability of photons is related to the exchange symmetry of the multiphoton wave function. We find that simple multiphoton detection scheme gives rise to a more general photon bunching effect with the famous two-photon effect as a special case. We then send this

N

-photon state into a recently discovered multiphoton interference scheme. We calculate the visibility of the multiphoton interference scheme and find that it is related to the temporal distinguishability of the

N

photons. Maximum visibility of one is achieved for the indistinguishable

N

-photon state whereas the visibility degrades when some of the photons are separated and become distinguishable. Thus we can identify an experimentally measurable quantity that may quantitatively define the degree of indistinguishability of an

N

-photon state. This presents a quantitative demonstration of the complementary principle of quantum interference.

We present a multi-mode model to describe an arbitrary N-photon state with a wide spectral range and some arbitrary temporal distribution. In general, some of the

N

photons are spread out in time while other may overlap and become indistinguishable. From this model, we find that the temporal (in)distinguishability of photons is related to the exchange symmetry of the multi-photon wave function. We find that simple multi-photon detection scheme gives rise to a more general photon bunching effect with the famous two-photon effect as a special case. We then send this N-photon state into a recently discovered multi-photon interference scheme. We calculate the visibility of the multi-photon interference scheme and find that it is related to the temporal distinguishability of the

N

photons. Maximum visibility of one is achieved for the indistinguishable N-photon state whereas the visibility degrades when some of the photons are separated and become distinguishable. Thus we can identify an experimentally measurable quantity that may quantitatively define the degree of indistinguishability of an N-photon state. This presents a quantitative demonstration of the complementary principle of quantum interference.