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The two-particle two-slit experiment

Pedro Sancho

Published Aug 17, 2016• 2 citations
OpenAlex

Abstract

Identical two-particle interferometry provides a scenario where interference and exchange effects manifest at once. We present a detailed calculation of the detection patterns in the two-particle two-slit experiment by extending Feynman's Gaussian slit approach to multi-mode states. We show the existence of two regimes depending on the mode distributions. In one of them we find a novel behavior for bosons, with detection patterns almost equal to those of distinguishable particles although the overlapping is large. As a byproduct of our analysis we conclude that the interaction at the diffraction grating is an efficient method to increase the initial overlapping. We propose a scheme, within the reach of present day technology, to experimentally verify our results.

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Quantum theory of interference phenomena does not take the diameter of the particle into account, since particles were much smaller than the width of the slits before the rise of molecular interferometry. In the experiments with large molecules, the diameter of the particle has approached the width of the slits. Therefore, an analytical description of these cases should include a finite particle size. An asymmetric double-slit grating seems to be very suitable for the study of the influence of a particle's size on the interference pattern. We identify three characteristic cases for the ratio of slit widths ${\ensuremath{\delta}}_{1}$ and ${\ensuremath{\delta}}_{2}$ and the particle diameter $D$: $D⪡{\ensuremath{\delta}}_{1}$ and $D⪡{\ensuremath{\delta}}_{2}$, ${\ensuremath{\delta}}_{1}>D>{\ensuremath{\delta}}_{2}$, and $D>{\ensuremath{\delta}}_{1}>{\ensuremath{\delta}}_{2}$. Taking into account the influence of both slits on the particle wave function, regardless of through which slit the particle passed, we treat the particle-wall interaction in a simple fashion, such that if the particle size is greater than the slit opening there is no transmission. The transverse momentum distribution is independent of the distance from the slits and the particle size, while the space distribution strongly depends on this distance and the particle size. We found that the interference is absent only when the particle's diameter is larger than both slit widths, $D>{\ensuremath{\delta}}_{1}>{\ensuremath{\delta}}_{2}$.

Physical Review A•May 18, 2004•14 citations
Identical two-particle interferometry provides a scenario where interference and exchange effects manifest at once. We present a detailed calculation of the detection patterns in the two-particle two-slit experiment by extending Feynman's Gaussian slit approach to multi-mode states. We show the existence of two regimes depending on the mode distributions. In one of them we find a novel behavior for bosons, with detection patterns almost equal to those of distinguishable particles although the overlapping is large. As a byproduct of our analysis we conclude that the interaction at the diffraction grating is an efficient method to increase the initial overlapping. We propose a scheme, within the reach of present day technology, to experimentally verify our results.
We study diffraction and interference of indistinguishable particles. We consider some examples where the wavefunctions and detection probabilities can be evaluated in an analytical way. The diffraction pattern of a two-particle system shows notorious differences for the cases of bosons, fermions and distinguishable particles. In the example of near-field interferometry, the exchange effects for two-fermion systems lead to the existence of planes at which the probability of double detection is null. We also discuss the relation with the approach to systems of identical particles based on correlation functions. In particular, we shall see that these functions reflect, as in noise interferometry, the underlying periodic structure of the diffraction grating.
An extension of Feynman's rule, relating probability amplitudes and probabilities in two-photon interferometry, has been proposed recently [G. Jaeger et al., Phys. Rev. A 48, 1023 (1993)]. It would be interesting to analyze the validity of this rule in other physical situations not considered by these authors. In particular, we show in this paper that the extended rule cannot be applied to the gedanken two-slit experiment. This result suggests the existence of two quantum regimes, differentiated by the validity of the generalized rule. The distinguishability of one particle and the visibilities of one-particle and two-particle interferences are calculated. \textcopyright{} 1996 The American Physical Society.
We analyse the Bragg regime of the two-particle Kapitza–Dirac arrangement, completing the basic theory of this effect. We provide a detailed evaluation of the detection probabilities for multi-mode states, showing that a complete description must include the interaction time in addition to the usual dimensionless parameter w . The arrangement can be used as a massive two-particle beam splitter. In this respect, we present a comparison with Hong–Ou–Mandel-type experiments in quantum optics. The analysis reveals the presence of dips for massive bosons and a differentiated behaviour of distinguishable and identical particles in an unexplored scenario. We suggest that the arrangement can provide the basis for symmetrization verification schemes.
Abstract Chapter 11 introduces the essential mystery of quantum mechanics, shows how it is resolved, and then goes on to examine related phenomena. The mystery is how individual photons, not electromagnetic waves, can give rise to the interference pattern seen in the two-slit experiment. They are shown to do so because the relevant quantum amplitude is a linear combination of two terms, leading to the pattern when neither slit is identified as the one the photon went through, but collapsing to one term and no pattern if the slit is identified. Similar results are shown to occur when individual electrons are incident on the two slits, and when large molecules, which have de Broglie wavelengths, are scattered by diffraction gratings. Many other interference experiments are described, including those where a photon was shown to be in two places simultaneously and one where a photon displayed both wave and particle features.
Matter-wave interferometry has been largely studied in the last few years. Usually, the main problem in the analysis of the diffraction experiments is to establish the causes for the loss of coherence observed in the interference pattern. In this work, we use different type of environmental couplings to model a two slit diffraction experiment with massive particles. For each model, we study the effects of decoherence on the interference pattern and define a visibility function that measures the loss of contrast of the interference fringes on a distant screen. Finally, we apply our results to the experimental reported data on massive particles C 70 .
Quantum theory of interference phenomena does not take the diameter of the particle into account, since particles were much smaller than the width of the slits before the rise of molecular interferometry. In the experiments with large molecules, the diameter of the particle has approached the width of the slits. Therefore, an analytical description of these cases should include a finite particle size. An asymmetric double-slit grating seems to be very suitable for the study of the influence of a particle's size on the interference pattern. We identify three characteristic cases for the ratio of slit widths ${\ensuremath{\delta}}_{1}$ and ${\ensuremath{\delta}}_{2}$ and the particle diameter DDD: $D⪡{\ensuremath{\delta}}_{1}$ and $D⪡{\ensuremath{\delta}}_{2}$, ${\ensuremath{\delta}}_{1}>D>{\ensuremath{\delta}}_{2}$, and $D>{\ensuremath{\delta}}_{1}>{\ensuremath{\delta}}_{2}$. Taking into account the influence of both slits on the particle wave function, regardless of through which slit the particle passed, we treat the particle-wall interaction in a simple fashion, such that if the particle size is greater than the slit opening there is no transmission. The transverse momentum distribution is independent of the distance from the slits and the particle size, while the space distribution strongly depends on this distance and the particle size. We found that the interference is absent only when the particle's diameter is larger than both slit widths, $D>{\ensuremath{\delta}}_{1}>{\ensuremath{\delta}}_{2}$.