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Acta Physica Sinica

General theory of quantum holography based on two-photon Interference

Yao-Kun Xu, Shi‐Hai Sun, Yaoyuan Zeng, Jungang Yang, Wei-Dong Sheng, Wei-Tao Liu

Published Jan 1, 2023• 2 citations
Publisher

Abstract

As a kind of quantum phenomenon, Hong-Ou-Mandel (HOM) interference is more robust against phase noise. Because of this feature, robust quantum holography emerges, through which wave function of interested photon can be retrieved according to HOM interference pattern. For better understanding and developing this method, we derive a theoretical framework of robust HOM holography. In the quantum holography scheme, test state and reference state interfere at beam splitter (BS). Then, degree of freedom (DOF) resolved detections (such as spatial resolved detection, temporal resolved detection or spectrum resolved detection) are used at the BS output ports, respectively. Based on the single photon detection results, the DOF resolved coincidence counts are postselected, producing interference patterns. The information of the test states is retrieved from the patterns. According to different test states and reference states, four combinations are analysed, including measuring the wave function of single photon state by using standard single photon state or coherent state and measuring the wave function of coherent state through using standard single photon state or coherent state. In all cases, information of the test states is reflected in normalized second-order correlation function or interference patterns in similar forms. Specially, the wave function of test states can be directly retrieved from the interference patterns, with no complex algorithm required. Besides, phase noise from environment has no influence on this kind quantum holography. Comparison between traditional holography and quantum holography is made and analysed.

DOI
10.7498/aps.72.20231242

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As a kind of quantum phenomenon, Hong-Ou-Mandel (HOM) interference is more robust against phase noise. Because of this feature, robust quantum holography emerges, through which wave function of interested photon can be retrieved according to HOM interference pattern. For better understanding and developing this method, we derive a theoretical framework of robust HOM holography. In the quantum holography scheme, test state and reference state interfere at beam splitter (BS). Then, degree of freedom (DOF) resolved detections (such as spatial resolved detection, temporal resolved detection or spectrum resolved detection) are used at the BS output ports, respectively. Based on the single photon detection results, the DOF resolved coincidence counts are postselected, producing interference patterns. The information of the test states is retrieved from the patterns. According to different test states and reference states, four combinations are analysed, including measuring the wave function of single photon state by using standard single photon state or coherent state and measuring the wave function of coherent state through using standard single photon state or coherent state. In all cases, information of the test states is reflected in normalized second-order correlation function or interference patterns in similar forms. Specially, the wave function of test states can be directly retrieved from the interference patterns, with no complex algorithm required. Besides, phase noise from environment has no influence on this kind quantum holography. Comparison between traditional holography and quantum holography is made and analysed.
As a kind of quantum phenomenon, Hong-Ou-Mandel (HOM) interference is more robust against phase noise. Due to this feature, robust quantum holography emerges, through which wave function of interested photon can be retrieved according to HOM interference pattern. For better understanding and developing this method, we derive a theoretical framework of robust HOM holography. In quantum holography scheme, test state and reference state interfere at beam splitter (BS). Then, degree of freedom (DOF) resolved detections (such as spatial resolved detection, temporal resolved detection or spectrum resolved detection) are applied at the BS output ports, respectively. Based on the single photon detection results, the DOF resolved coincidence counts are postselected, producing interference patterns. The information of the test states is retrieved from the patterns. According to different test states and reference states, four combinations are analysed, including measuring the wave function of single photon state using standard single photon state or coherent state and measuring the wave function of coherent state using standard single photon state or coherent state. In all cases, information of the test states is reflected in normalized second-order correlation function or interference patterns in similar forms. Specially, the wave function of test states can be directly retrieved from the interference patterns, with no complex algorithm required. Besides, phase noise from environment has no influence on this kind quantum holography. Comparison between traditional holography and quantum holography is analysed.
Containing the capacity to record both amplitude and phase information of the light field, holography is of great importance in science and technology. Here, we present robust holography via second-order interference, considering both single-photon states and coherent states. Temporal amplitude and phase distribution carried by a weak coherent state are reconstructed experimentally. By comparison between holography using first-order interference and second-order interference, the robustness against phase noise of our method is verified. Besides, information about the state can be directly retrieved, with no complex algorithm required.
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.
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.
In the context of Fock states, demonstrating multiphoton quantum interference, e.g., the generalized Hong-Ou-Mandel (HOM) interference, is at the core of many applications of quantum technologies. However, it is difficult to demonstrate high-visibility quantum interference for a large number of photons. Here, we introduce an experimentally feasible proposal to achieve this goal using phase-randomized weak coherent states and practical photon-number-resolving detectors. Our method can be used to obtain analytically tight bounds of the generalized HOM dip in a beam splitter, and it is robust against practical errors. The simulation shows that for an ideal detector that can resolve any number of photons without an upper bound, the proposed method can bound the generalize HOM interference for a large number of photons, e.g., 100 photons; for a practical detector that can resolve up to 29 photons, the proposed method can bound the generalized HOM interference for 56 photons with visibility 99.499.4%99.4. Our proposal is a general approach for multiphoton quantum interference in optical networks with multiple inputs and outputs.
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.