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Europhysics Letters (EPL)

Beam Splitting Experiments with Classical and with Quantum Particles

Robert Lange, Jurgen Brendel, Ernst Mohler, W. Martienssen

Published Apr 1, 1988• 22 citations
Publisher

Abstract

The probability of separating k particles from a beam of n classical distinguishable particles by a beam splitter is given by the Bernoulli distribution. When turning to indistinguishable Bose quantum particles, this distribution is preserved by a refined interplay between interference and stimulation effects. This behaviour is demonstrated in an experiment where pairs of photons interact with an optical beam splitter. The distinguishability of the photons within a pair is changed by varying the degree of coherence.

DOI
10.1209/0295-5075/5/7/008

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The probability of separating k particles from a beam of n classical distinguishable particles by a beam splitter is given by the Bernoulli distribution. When turning to indistinguishable Bose quantum particles, this distribution is preserved by a refined interplay between interference and stimulation effects. This behaviour is demonstrated in an experiment where pairs of photons interact with an optical beam splitter. The distinguishability of the photons within a pair is changed by varying the degree of coherence.
Quantum interference constitutes one of the sharpest divides between our classical intuition and the weirdness of the quantum world. Whenever there are multiple paths leading to the same outcome, it is the interplay of associated probability amplitudes that determines measurement results. In the double slit experiment, wave-like interference governs the distribution of particles on a detection screen. Extending to multiple particles allows behaviour that cannot be described by a classical wave, such as the bunching of photon pairs in Hong-Ou-Mandel interference. In both these examples, the ability to distinguish the interfering paths leads to degradation of interference and a return to behaviour described by probabilities. Understanding how this transition evolves for larger multiparticle quantum systems is of fundamental interest and also vital for developing photonic quantum technologies that rely on many-photon interference. In this thesis we investigate the role of distinguishability in the interference of three and four independent photons by using polarisation and time delays. For three photons, a new type of collective distinguishing phase appears that goes beyond a pairwise description of the similarity of quantum states. We use nonlinear photon sources and a fibre interferometer to experimentally demonstrate the ability to tune and isolate this phase in interference statistics. Extending to four photons we show that, contrary to intuition from two-photon experiments, the interference of photons prepared in distinguishable states is possible due to a four-particle phase. This is confirmed experimentally using a bulk four-mode interferometer. We then extend our study to include the effects of state impurity in the interference of three photons. New properties of this interference enable diagnosis of realistic experimental imperfections and characterisation tasks impossible using only two photons. Finally, we link discussions of state distinguishability to the group representations underpinning the exchange symmetry of multiparticle wavefunctions.
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 1/21/\sqrt{2}1/2​. 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.
The familiar input-output relations for an optical beam splitter are generalized to allow for linear absorption by the medium forming the mirror. Beam-splitter losses generally affect the noise levels detectable in experiments involving nonclassical light. When employed to investigate two-photon interference effects, a lossy beam splitter can lead to apparent nonlinear absorption, which, in the most extreme case, leads to either both or neither of the photons being absorbed. The degree of second-order coherence of antibunched light can be maintained on transmission through the beam splitter but any amplitude squeezing in the incident light is degraded.