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arXiv:1612.05470 · Journal of Optics

Holographic quantum imaging: reconstructing spatial properties via two-particle interference

Nils Trautmann, Gergely Ferenczi, Sarah Croke, Stephen Mark Barnett

Published Mar 20, 2017• 5 citations
arXivHTMLPDF

Abstract

Two particle interference phenomena, such as the Hong–Ou–Mandel (HOM) effect, are a direct manifestation of the nature of the symmetry properties of indistinguishable particles as described by quantum mechanics. The HOM effect has recently been applied as a tool for pure state tomography of a single photon. In this article, we generalize the method to extract additional information for a pure state and extend this to the full tomography of mixed states as well. The formalism is kept general enough to apply to both boson and fermion based interferometry. Our theoretical discussion is accompanied by two proposals of interferometric setups that allow the measurement of a tomographically complete set of observables for single photon quantum states.

DOI
10.1088/2040-8986/aa67b6

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Two particle interference phenomena, such as the Hong–Ou–Mandel (HOM) effect, are a direct manifestation of the nature of the symmetry properties of indistinguishable particles as described by quantum mechanics. The HOM effect has recently been applied as a tool for pure state tomography of a single photon. In this article, we generalize the method to extract additional information for a pure state and extend this to the full tomography of mixed states as well. The formalism is kept general enough to apply to both boson and fermion based interferometry. Our theoretical discussion is accompanied by two proposals of interferometric setups that allow the measurement of a tomographically complete set of observables for single photon quantum states.
Hong-Ou-Mandel (HOM) interference [1] is a bunching phenomenon based on the bosonic nature of photons. When two photons that are perfectly indistinguishable from each other are mixed using a half beam splitter (HBS), they always bunch and exhibit the absence of coincidence resulting in a specific interferogram called HOM dip. The important property of the HOM interference is that the decrease in coincidence reflects the degree of indistinguishability of the input photons, i.e., it provides information regarding the probability of overlap of the input photons. Thus, this property should enable the estimation of a target photon in an unknown quantum state using a probe photon in a known state. In this work, we realize the above concept as the quantum state tomography (QST) applicable to d-dimensional photonic qudits, which we call HOM-QST [2]. Interestingly, we observe that HOM-QST is robust against various imperfections and that the probe photon can be replaced by classical light. Furthermore, we confirm this by demonstrating a proof-of-principle experiment using two-dimensional polarization qubits.
Hong-Ou-Mandel (HOM) interference [1] is a bunching phenomenon based on the bosonic nature of photons. When two photons that are perfectly indistinguishable from each other are mixed using a half beam splitter (HBS), they always bunch and exhibit the absence of coincidence resulting in a specific interferogram called HOM dip. The important property of the HOM interference is that the decrease in coincidence reflects the degree of indistinguishability of the input photons, i.e., it provides information regarding the probability of overlap of the input photons. Thus, this property should enable the estimation of a target photon in an unknown quantum state using a probe photon in a known state. In this work, we realize the above concept as the quantum state tomography (QST) applicable tod-dimensionald\text{-dimensional}d-dimensionalphotonic qudits, which we call HOM-QST [2]. Interestingly, we observe that HOM-QST is robust against various imperfections and that the probe photon can be replaced by classical light. Furthermore, we confirm this by demonstrating a proof-of-principle experiment using two-dimensional polarization qubits.
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.
The second-order intensity correlation of entangled photons has been intensively studied for decades, particularly for the Hong-Ou-Mandel (HOM) effect and nonlocal correlation -- key quantum phenomena that have no classical counterparts. Recently, a path-entangled two-photon state has been experimentally demonstrated for both bosonic (symmetric) and fermionic (anti-symmetric) HOM effects by manipulating the photon phase at one input port. Entanglement represents a quantum superposition of path- or energy-correlated two-photon states with a relative phase. According to the conventional quantum mechanics, this phase is not an individual property but collective attribute of interacting photons. Here, the wave nature of photons is employed to coherently analyze the phase-controlled HOM effects recently observed in npj Quantum Info. 5, 43 (2019). A pure coherence approach is applied to derive a general solution for these phase-controlled HOM effects. Consequently, the quantum mystery of HOM effects, traditionally interpreted through the particle nature of quantum mechanics, is revealed as a coherent phenomenon between entangled photons via a selective choice of correlated photons.
Hong-Ou-Mandel (HOM) interference, i.e. the bunching of indistinguishable photons at a beam splitter is a staple of quantum optics and lies at the heart of many quantum sensing approaches and recent optical quantum computers. Although originally proposed as a method for sensing micron-scale variations in photon propagation path lengths and despite the detection of photon bunching using camera technologies, the technique is still to be extended to the imaging domain. We report a full-field, scan-free, quantum imaging technique that exploits HOM interference to reconstruct the surface depth profile of transparent samples. We measure both the bunched and anti-bunched photon-pair distributions at the HOM interferometer output which are combined to provide a lower-noise image of the sample. This approach demonstrates the possibility of HOM microscopy as a tool for label-free imaging of transparent samples in the very low photon regime.