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arXiv:2002.00443

Hong-Ou-Mandel interference on a real beam splitter

Dmitry N. Makarov

Published Feb 2, 2020• 0 citations
arXivHTMLPDF

Abstract

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 $R = 1/2$ 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 $ω_1, ω_2$ 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.

DOI
10.48550/arxiv.2002.00443

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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=1/2T = 1/2T=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=1/2R = 1/2R=1/2 and T=1/2T = 1/2T=1/2, but also their root-mean-square fluctuations ΔR2,ΔT2ΔR ^ 2, ΔT ^ 2ΔR2,ΔT2, which arise due to the dependence of R=R(ω1,ω2)R = R(ω_1, ω_2) R=R(ω1​,ω2​) and T=T(ω1,ω2)T = T (ω_1, ω_2)T=T(ω1​,ω2​) 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 ΔR2ΔR^2ΔR2 and ΔT2ΔT^2ΔT2 can be neglected and R=T=1/2R=T=1/2R=T=1/2 is chosen, the developed theory coincides with previously known results.
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.
Two-photon interference effects arise because photons are indistinguishable particles. In the wellknown Hong-Ou-Mandel (HOM) effect, the transmission of two photons at a beam splitter interferes destructively with the reflection of both photons, requiring both photons to "bunch up" by leaving the beam splitter on the same side. Here, we show that the interference between locally propagating photons and photons exchanged by a mode swap can be implemented by post-selecting spatially separated photon outputs of a four-path interferometer. Even though the photons detected at spatially separated locations must have travelled along paths that never met up at the same beam splitter, the Hong-Ou-Mandel effect can be observed in correlations between the output ports that originate from the association of detection events with non-local output modes defined by the two single photon inputs. Local phase shifts can be used to map out non-classical correlations between the photons detected at different output locations, clarifying the role of linear optics in generating entanglement between spatially separated photons. Our work thus establishes a fundamental relation between multiphoton interference and entanglement, opening the door to new possibilities in optical quantum technologies.
The Hong-Ou-Mandel (HOM) interference is one of the most fundamental quantum-mechanical effects that reveal a nonclassical behavior of single photons. Two identical photons that are incident on the input ports of an unbiased beam splitter always exit the beam splitter together from the same output port, an effect referred to as photon bunching. In this Letter, we utilize a single electro-optic phase modulator as a probabilistic frequency beam splitter, which we exploit to observe HOM interference between two photons that are in different spectral modes, yet are identical in other characteristics. Our approach enables linear optical quantum information processing protocols using the frequency degree of freedom in photons such as quantum computing techniques with linear optics.
It is well known that the Hong–Ou–Mandel (HOM) effect can be realized on beam splitters (BSs) in the form of coupled waveguides. It is believed that in this case, the theory is similar to HOM interference on conventional BSs. In this work, it is shown that if a BS is used in the form of a coupled waveguide, the theory of HOM interference can differ significantly from the known one. It is shown that even in the case of completely identical photons, the visibility of V can essentially differ from unity. The developed theory must be taken into account in quantum optical schemes, where BSs are represented mainly as coupled waveguides.
The Hong-Ou-Mandel effect (HOH) is used in many fields of quantum optics and quantum technologies. It is well known that this effect occurs when two identical photons in different modes hit a beam splitter (BS) with a reflection coefficient of R=1/2. The classical effect consists in the interaction of two photons and was first experimentally demonstrated by Hong and co-authors in 1987. In this paper, it was shown that this effect can be realized using free charged particles. It was determined when this effect would manifest itself. The results obtained for HOME diving have an analytical form, which simplifies its analysis. The Hong-Ou-Mandel effect is of fundamental importance in quantum physics and quantum computer science, as it demonstrates quantum entanglement and interference. The results of the research can be used in problems of quantum physics and quantum computer science.
We examine multiphoton interference with a symmetric SU(N)SU(N)SU(N) beam splitter SNS_NSN​, an extension of features of the SU(2)SU(2)SU(2) 50/50 beam splitter extended Hong-Ou-Mandel (eHOM) effect, whereby one obtains a zero amplitude (probability) for the output coincidence state (defined by equal number of photons n/Nn/Nn/N in each output port), when a total number nnn of photons impinges on the NNN-port device. These are transitions of the form ∣n1,n2,…,nN⟩→SN∣n/N⟩⊗N|n_1,n_2,\ldots,n_N\rangle\overset{S_N}{\to}|n/N\rangle^{\otimes N}∣n1​,n2​,…,nN​⟩→SN​∣n/N⟩⊗N, where n=∑i=1Nnin=\sum_{i=1}^N n_in=∑i=1N​ni​, which generalize the Hong-Ou-Mandel (HOM) effect $|1,1\rangle \overset{S_2}{\to}|1,1\rangle $, the eHOM effect $|n_1,n_2\rangle \overset{S_2}{\to}|\tfrac{n_1+n_2}{2},\tfrac{n_1+n_2}{2}\rangle $, and the generalized HOM effect (gHOM) ∣1⟩⊗N→SN∣1⟩⊗N|1\rangle^{\otimes N}\overset{S_N}{\to}|1\rangle^{\otimes N}∣1⟩⊗N→SN​∣1⟩⊗N, which have previously been studied in the literature. The emphasis of this work is on illuminating how the overall destructive interference occurs in separate groups of destructive interferences of sub-amplitudes of the total zero amplitude. We develop symmetry properties for the generalized eHOM effect (geHOM) ∣n1,n2,…,nN⟩→SN∣n/N⟩⊗N|n_1,n_2,\ldots,n_N\rangle\overset{S_N}{\to}|n/N\rangle^{\otimes N}∣n1​,n2​,…,nN​⟩→SN​∣n/N⟩⊗N involving a zero amplitude governed by Perm(ΛΛΛ)=0, for an appropriately constructed matrix Λ(SN)Λ(S_N)Λ(SN​) built from the matrix elements of SNS_NSN​. We develop an analytical constraint equation for Perm(Λ)(Λ)(Λ) for arbitrary NNN that allows us to determine when it is zero. We generalize the SU(2) beam splitter feature of central nodal line (CNL), which has a zero diagonal along the output probability distribution when one of the input states is of odd parity (containing only odd number of photons), to the general case of N=2∗N′N = 2 * N'N=2∗N′ where N′∈oddN'\in oddN′∈odd.