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arXiv:2408.16205 · American Journal of Physics

Demonstrating two-particle interference with a one-dimensional delta potential well

Zhi Jiao Deng, Xin Zhang, Yong Shen, Wei-Tao Liu, Ping-Xing Chen

Published Sep 20, 2024• 1 citation
arXivHTMLPDF

Abstract

In quantum mechanics, the exchange symmetry of wave functions for identical particles has observable effects, including the widely studied Hong–Ou–Mandel (HOM) effect. A theoretical description using second quantization is elegant but abstract. In contrast, this paper describes a simple model of two-particle interference using a one-dimensional delta potential well as a beam splitter. The conditions for the HOM effect are derived from the perspective of wave packet evolution. Furthermore, the interference processes of bosons, fermions, and distinguishable particles are demonstrated and compared in detail. The method presented here is concrete, easy to visualize, and can help students to better understand the effects arising from the exchange symmetry of wave functions. The main results can be animated for classroom teaching or developed into an undergraduate seminar topic.

DOI
10.1119/5.0176364

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In quantum mechanics, the exchange symmetry of wave functions for identical particles has observable effects, including the widely studied Hong–Ou–Mandel (HOM) effect. A theoretical description using second quantization is elegant but abstract. In contrast, this paper describes a simple model of two-particle interference using a one-dimensional delta potential well as a beam splitter. The conditions for the HOM effect are derived from the perspective of wave packet evolution. Furthermore, the interference processes of bosons, fermions, and distinguishable particles are demonstrated and compared in detail. The method presented here is concrete, easy to visualize, and can help students to better understand the effects arising from the exchange symmetry of wave functions. The main results can be animated for classroom teaching or developed into an undergraduate seminar topic.
Hong-Ou-Mandel (HOM) effect is known to be one of the main phenomena in quantum optics. The effect occurs when two identical single-photon waves enter a 1:1 beam splitter, one in each input port. When the photons are identical, they will extinguish each other. One of the main elements of the HOM interferometer is the beam splitter, which has its own coefficients of reflection R=1/2R = 1/2R=1/2 and transmission $ T = 1/2 $. In this work, the general mechanism of the interaction of two photons in a beam splitter is considered using an analytical solution, which shows that in the HOM theory of the effect it is necessary to know (including when planning the experiment) not only $ R = 1/2 $ and $ T = 1/2 $, but also their root-mean-square fluctuations $ ΔR ^ 2, ΔT ^ 2 $, which arise due to the dependence of $R = R(ω_1, ω_2) $ and $ T = T (ω_1, ω_2) $ on the frequencies where ω1,ω2ω_1, ω_2ω1​,ω2​ are the frequencies of the first and second photons, respectively. Under certain conditions, specifically when the dependence of the fluctuations $ ΔR^2 $ and $ ΔT^2 $ can be neglected and $ R=T=1/2 $ is chosen, the developed theory coincides with previously known results.
Abstract The Hong‐Ou‐Mandel interference of two identical particles evolving on a 1D tight‐binding lattice where a potential barrier plays the role of a beam splitter is described. Careful consideration of the symmetries underlying the two‐particle interference effect allows to reformulate the problem in terms of ordinary wave interference in a Michelson interferometer. This approach is easily generalized to the case where the particles interact, and we compare the resulting analytical predictions for the bunching probability to numerical simulations of the two‐particle dynamics.
Hong-Ou-Mandel (HOM) effect is known to be one of the main phenomena in quantum optics. It is believed that the effect occurs when two identical single-photon waves enter a 1:1 beam splitter, one in each input port. When the photons are identical, they will extinguish each other. In this work, it is shown that these fundamental provisions of the HOM interference may not always be fulfilled. One of the main elements of the HOM interferometer is the beam splitter, which has its own coefficients of reflection [Formula: see text] and transmission [Formula: see text]. Here we consider the general mechanism of the interaction of two photons in a beam splitter, which shows that in the HOM theory of the effect it is necessary to know (including when planning the experiment) not only [Formula: see text] and [Formula: see text], but also their root-mean-square fluctuations [Formula: see text], which arise due to the dependence of [Formula: see text] and [Formula: see text] on the frequencies where [Formula: see text] are the frequencies of the first and second photons, respectively. Under certain conditions, specifically when the dependence of the fluctuations [Formula: see text] and [Formula: see text] can be neglected and [Formula: see text] is chosen, the developed theory coincides with previously known results.
The celebrated Hong-Ou-Mandel effect is the paradigm of two-particle quantum interference. It has its roots in the symmetry of identical quantum particles, as dictated by the Pauli principle. Two identical bosons impinging on a beam splitter (of transmittance 1/2) cannot be detected in coincidence at both output ports, as confirmed in numerous experiments with light or even matter. Here, we establish that partial time reversal transforms the beam splitter linear coupling into amplification. We infer from this duality the existence of an unsuspected two-boson interferometric effect in a quantum amplifier (of gain 2) and identify the underlying mechanism as time-like indistinguishability. This fundamental mechanism is generic to any bosonic Bogoliubov transformation, so we anticipate wide implications in quantum physics.
Classical Hong-Ou-Mandel (HOM) effect – two-particle interference on a lossless beamsplitter, reveals the fundamental difference between bosonic and fermionic particles. As a result of such interference, pairs of bosons coalesce while pairs of fermions anti-coalesce. Here we report an observation of the anti-HOM effect where bosons anti-coalesce and fermions show coalescent-like behavior when interfere on a lossy beamsplitter. By exploiting two-photon entangled states, we provide an experimental demonstration of the anti-HOM effect for both bosonic and fermionic spatial wavefunctions of the photons. This fundamental phenomenon may enrich quantum information and metrology protocols where states of entangled photons are dynamically converted.