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Optica Quantum

Complementarity of which-path information in induced and stimulated coherences via four-wave mixing process from warm Rb atomic ensemble

Danbi Kim, Jiho Park, Changhoon Baek, Sun Kyung Lee, Han Seb Moon

Published Jul 17, 2024• 4 citations
Publisher

Abstract

Complementarity, a fundamental tenet of quantum optics, is indispensable for elucidating the fundamental principles of quantum physics and advancing quantum information processing applications. In the context of wave–particle duality, induced-coherence experiments were understood through the lens of which-path information. Conversely, the stimulated-coherence experiments were explained by using the indistinguishability of the photon statistics of conjugate photons as a means of realizing complementarity. Here, we report a systematic approach for establishing a complementary relationship between the interference visibility, concurrence, and predictability in the crossing of induced and stimulated coherences of two-mode squeezed coherent states. This is achieved using a double-path interferometer involving two independent four-wave mixing (FWM) atomic samples generated via spontaneous and stimulated FWM processes from a warm atomic ensemble of 87 Rb. We demonstrate that the transition from quantum to classical behavior can be characterized by the induced coherence effect, distinguishing between the two-mode squeezed vacuum and coherent states. Moreover, our experimental scheme, employing two FWM atomic ensembles with long-coherent photons, provides valuable insights into the complementarity of which-path information in induced and stimulated coherences.

DOI
10.1364/opticaq.528135

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Complementarity of which-path information in induced and stimulated coherences via four-wave mixing process from warm Rb atomic ensemble

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Complementarity of which-path information in induced and stimulated coherences via four-wave mixing process from warm Rb atomic ensemble: publisher’s note

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This publisher’s note reports a correction made to Optica Quantum 2 , 288 ( 2024 ) 10.1364/OPTICAQ.528135 .

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Abstract Induced coherence was first demonstrated three decades ago in a proof‐of‐principle experiment using entangled photons from spontaneous parametric down‐conversion in nonlinear crystals. This phenomenon is considered an interesting instance of complementarity, which lies at the heart of quantum optics. Here, the first demonstration of induced coherence across two coupled interferometers based on spontaneous four‐wave mixing (SFWM) in two independent hot‐atomic‐vapor‐based entangled photon sources is reported. When both the pump and coupling lasers are split and interact with two warm 87 Rb atomic ensembles, single‐photon interference is observed between the two idler photons of the narrowband photon pairs, generated via SFWM from the two cascade‐type atomic systems. Furthermore, it is found that the phase memory effect arises from the phase of the bidirectional counter‐propagating pump and coupling lasers, respectively. This work takes an important step toward the transition to the era of quantum optics being driven by atomic ensembles from solid‐state systems.

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A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality characterized by an interference visibility and a which-path information has trade-off relation known as complementarity. These quantities are related to the first-order coherence, and the interference is based on the phase correlation between lights coming from two arms. However according to quantum optics theory, such a simple wave-particle picture is not enough to understand the nature because the theory showed an importance of higher-order coherence in the sense of both interference and statistical distribution of photons. Second-order intensity correlation is especially crucial to reveal distinctive quantum features of photons with no classical analogue. Here, in an intensity interferometric scenario as represented by the Hong-Ou-Mandel interferometer, we discuss a wave-particle duality of light based on a which-path information and a quantity characterizing a magnitude of the intensity interferometric effect. We show, for classical light, the two quantities obey the complementary principle similar to the case of the double-slit experiment, but do not for nonclassical light. The nonclassical light such as photons at two arms is allowed to show larger which-path information and intensity interference simultaneously beyond the complementary relation. Moreover, the violation reveals a new nonclassical nature of light although both of the above two quantities seem to be understandable classically, which is never found from a consideration of only one side of wave-particle duality.

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Coherence and path information

Xin Lü

Complementarity, or more specifically, the wave-particle duality, and quantum coherence are two fundamental concepts in quantum mechanics. Recently, motivated by the progress of the quantification of quantum coherence, the complementary relation between coherence and path information is investigated by many authors, and various duality relations between them are established. Such relations not only provide insights into fundamental problems of quantum mechanics, such as the understanding of quantum coherence and wave-particle duality; but also are important in applications of quantum technologies. In this paper, based on the Bures distance and unambiguous quantum state discrimination, systematic analysis of the complementarity between the quantum coherence and path information in two path interferometers is carried out. Similarly as other related works, the wave aspect, or the visibility of the interferometer, is quantified by the l1-norm measure of quantum coherence, and the path information is considered via unambiguous quantum state discrimination. In this way, a novel duality relation in two path interferometers is obtained. Compared with known results, our work considers mixed states as well as pure states; considers the path predictability resulting from the intrinsic path asymmetry of the quantum state, as well as the path distinguishability resulting from the use of a which-path detector. Therefore, our work systematically generalizes known results in two path interferometers by removing all the unnecessary restrictions. Specifically, the most general form of quantum states in two path interferometers is considered and the duality relation between quantum coherence and path information is proved based on the positivity property of density matrices. The cases of path predictability and path distinguishability are considered separately. For path predictability, the proof is straightforward; whereas some advanced mathematical techniques, such as the Schur-Weyl inequality, properties of the fidelity and properties of positive matrices, are required in order to give a rigorous proof of the duality relation between coherence and path distinguishability. Concrete examples are provided to illustrate the abstract method and results. Our work concerns about two path interferometers exclusively and depends heavily that the dimensionality is two, therefore it would be an interesting task to generalize the results in this paper to n-path interferometers.

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Complementarity in biphoton generation with stimulated or induced coherence

Axel Heuer, R. W. Menzel, Peter W. Milonni

Coherence can be induced or stimulated in parametric down-conversion using two or three crystals when, for example, the idler modes of the crystals are aligned. Previous experiments with induced coherence [Phys. Rev. Lett. 114, 053601 (2015)] focused on which-path information and the role of vacuum fields in realizing complementarity via reduced visibility in single-photon interference. Here we describe experiments comparing induced and stimulated coherence. Different single-photon interference experiments were performed by blocking one of the pump beams in a three-crystal setup. Each counted photon is emitted from one of two crystals and which-way information may or not be available, depending on the setup. Distinctly different results are obtained in the induced and stimulated cases, especially when a variable transmission filter is inserted between the crystals. A simplified theoretical model accounts for all the experimental results and is also used to address the question of whether the phases of the signal and idler fields in parametric down-conversion are correlated.

arXiv:1506.00457•Physical Review A•Sep 18, 2015•40 citations
Complementarity, a fundamental tenet of quantum optics, is indispensable for elucidating the fundamental principles of quantum physics and advancing quantum information processing applications. In the context of wave–particle duality, induced-coherence experiments were understood through the lens of which-path information. Conversely, the stimulated-coherence experiments were explained by using the indistinguishability of the photon statistics of conjugate photons as a means of realizing complementarity. Here, we report a systematic approach for establishing a complementary relationship between the interference visibility, concurrence, and predictability in the crossing of induced and stimulated coherences of two-mode squeezed coherent states. This is achieved using a double-path interferometer involving two independent four-wave mixing (FWM) atomic samples generated via spontaneous and stimulated FWM processes from a warm atomic ensemble of 87 Rb. We demonstrate that the transition from quantum to classical behavior can be characterized by the induced coherence effect, distinguishing between the two-mode squeezed vacuum and coherent states. Moreover, our experimental scheme, employing two FWM atomic ensembles with long-coherent photons, provides valuable insights into the complementarity of which-path information in induced and stimulated coherences.
We report a systematic approach for establishing a complementary relationship between the interference visibility, concurrence, and predictability in the crossing of induced and stimulated coherences of two-mode squeezed coherent states. This is achieved using a double-path interferometer involving two independent four-wave mixing (FWM) atomic samples generated via spontaneous and stimulated FWM processes from a warm atomic ensemble of 87Rb. We demonstrate that the transition from quantum to classical behavior can be characterized by the induced coherence effect, distinguishing between the two-mode squeezed vacuum and coherent states. Moreover, our experimental scheme, employing two FWM atomic ensembles with long-coherent photons, provides valuable insights into the complementarity of which-path information in induced and stimulated coherences.
Abstract Induced coherence was first demonstrated three decades ago in a proof‐of‐principle experiment using entangled photons from spontaneous parametric down‐conversion in nonlinear crystals. This phenomenon is considered an interesting instance of complementarity, which lies at the heart of quantum optics. Here, the first demonstration of induced coherence across two coupled interferometers based on spontaneous four‐wave mixing (SFWM) in two independent hot‐atomic‐vapor‐based entangled photon sources is reported. When both the pump and coupling lasers are split and interact with two warm 87 Rb atomic ensembles, single‐photon interference is observed between the two idler photons of the narrowband photon pairs, generated via SFWM from the two cascade‐type atomic systems. Furthermore, it is found that the phase memory effect arises from the phase of the bidirectional counter‐propagating pump and coupling lasers, respectively. This work takes an important step toward the transition to the era of quantum optics being driven by atomic ensembles from solid‐state systems.
A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality characterized by an interference visibility and a which-path information has trade-off relation known as complementarity. These quantities are related to the first-order coherence, and the interference is based on the phase correlation between lights coming from two arms. However according to quantum optics theory, such a simple wave-particle picture is not enough to understand the nature because the theory showed an importance of higher-order coherence in the sense of both interference and statistical distribution of photons. Second-order intensity correlation is especially crucial to reveal distinctive quantum features of photons with no classical analogue. Here, in an intensity interferometric scenario as represented by the Hong-Ou-Mandel interferometer, we discuss a wave-particle duality of light based on a which-path information and a quantity characterizing a magnitude of the intensity interferometric effect. We show, for classical light, the two quantities obey the complementary principle similar to the case of the double-slit experiment, but do not for nonclassical light. The nonclassical light such as photons at two arms is allowed to show larger which-path information and intensity interference simultaneously beyond the complementary relation. Moreover, the violation reveals a new nonclassical nature of light although both of the above two quantities seem to be understandable classically, which is never found from a consideration of only one side of wave-particle duality.
Complementarity, or more specifically, the wave-particle duality, and quantum coherence are two fundamental concepts in quantum mechanics. Recently, motivated by the progress of the quantification of quantum coherence, the complementary relation between coherence and path information is investigated by many authors, and various duality relations between them are established. Such relations not only provide insights into fundamental problems of quantum mechanics, such as the understanding of quantum coherence and wave-particle duality; but also are important in applications of quantum technologies. In this paper, based on the Bures distance and unambiguous quantum state discrimination, systematic analysis of the complementarity between the quantum coherence and path information in two path interferometers is carried out. Similarly as other related works, the wave aspect, or the visibility of the interferometer, is quantified by the l1-norm measure of quantum coherence, and the path information is considered via unambiguous quantum state discrimination. In this way, a novel duality relation in two path interferometers is obtained. Compared with known results, our work considers mixed states as well as pure states; considers the path predictability resulting from the intrinsic path asymmetry of the quantum state, as well as the path distinguishability resulting from the use of a which-path detector. Therefore, our work systematically generalizes known results in two path interferometers by removing all the unnecessary restrictions. Specifically, the most general form of quantum states in two path interferometers is considered and the duality relation between quantum coherence and path information is proved based on the positivity property of density matrices. The cases of path predictability and path distinguishability are considered separately. For path predictability, the proof is straightforward; whereas some advanced mathematical techniques, such as the Schur-Weyl inequality, properties of the fidelity and properties of positive matrices, are required in order to give a rigorous proof of the duality relation between coherence and path distinguishability. Concrete examples are provided to illustrate the abstract method and results. Our work concerns about two path interferometers exclusively and depends heavily that the dimensionality is two, therefore it would be an interesting task to generalize the results in this paper to n-path interferometers.
Coherence can be induced or stimulated in parametric down-conversion using two or three crystals when, for example, the idler modes of the crystals are aligned. Previous experiments with induced coherence [Phys. Rev. Lett. 114, 053601 (2015)] focused on which-path information and the role of vacuum fields in realizing complementarity via reduced visibility in single-photon interference. Here we describe experiments comparing induced and stimulated coherence. Different single-photon interference experiments were performed by blocking one of the pump beams in a three-crystal setup. Each counted photon is emitted from one of two crystals and which-way information may or not be available, depending on the setup. Distinctly different results are obtained in the induced and stimulated cases, especially when a variable transmission filter is inserted between the crystals. A simplified theoretical model accounts for all the experimental results and is also used to address the question of whether the phases of the signal and idler fields in parametric down-conversion are correlated.