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Quantum photon correlations at the single atom level in free space

D. Goncalves

Published Aug 31, 2019• 0 citations
OpenAlex

Abstract

In this project, we present a novel approach to calculate and engineer the photon correlations emerging from the interference between an input field and the field scattered by an atom in free space. Historically, it has been difficult to observe robust quantum correlations in the total field, as the inefficient atom-light coupling in free space usually causes the scattered field to be small in comparison to the input. To overcome this issue, we propose the use of separate pump and probe beams, where the former effectively enhances the atomic emission to be comparable to the probe. Additionally, we elucidate the physical origin of the non-classical correlations predicted, by studying the transient atomic state after the measurement of a photon.

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Unconventional quantum correlations of light emitted by a single atom in free space

D. Goncalves, Morgan W. Mitchell, Darrick E. Chang

We present an approach to engineer the photon correlations emerging from the interference between an input field and the field scattered by a single atom in free space. Nominally, the inefficient atom-light coupling causes the quantum correlations to be dominated by the input field alone. To overcome this issue, we propose the use of separate pump and probe beams, where the former increases the atomic emission to be comparable to the probe. Examining the second-order correlation function ${g}^{(2)}(\ensuremath{\tau})$ of the total field in the probe direction, we find that the addition of the pump formally plays the same role as increasing the coupling efficiency, even though the physical atom-light coupling efficiency remains unchanged. We show that one can tune the correlation function ${g}^{(2)}(0)$ from zero (perfect antibunching) to infinite (extreme bunching) by a proper choice of pump amplitude. We further elucidate the origin of these correlations in terms of the transient atomic state following the detection of a photon, and show that these correlations can be observed under realistic conditions.

arXiv:2004.01993•Physical Review A•Jul 29, 2021•8 citations

Entanglement and Superradiance in the Light of Non-Classical and Classical Photon Sources

Ralph Wiegner

In the present thesis we investigate spatial and temporal intensity correlations which are created by statistically independent or by entangled light sources. Even though this classification may appear quite technical, the diverseness of the statistical properties of the considered photon sources naturally brings into our focus two different lines of research. In the first part of this thesis we will quantitatively study the non-classical and potentially entangled character of light fields which originate from a variety of different statistically independent light sources. To this end quantum correlations between light fields are analyzed which either stem from non-classical single-photon emitters (like ensembles of uncorrelated atoms) or from a mixture of non-classical and classical photon sources (like lasers with uncorrelated fluctuating initial phase). In the second part of this thesis we study correlations between initially entangled lightsources, namely localized atoms which share an entangled state. In the course of the investigations we physically reinterpret in particular the so called superradiance effect in a quantum-path formalism: superradiance denotes an enhanced mean radiated intensity in a particular direction, i.e., a focussing of the photons scattered by an atomic gas. This effect is commonly explained by a successive synchronization of the dipole moments of all participating atoms leading to a photon emission predominantly in one direction. For more than 60 years this focussing has been physically interpreted as a cooperative effect depending on the dipole-dipole interaction between the atoms. In contrast, we will show that it is rather a quantum-interference effect which is caused by non-synchronized and potentially widely separated entangled atoms.

•Jan 1, 2012•0 citations

Quantum Information and Quantum Correlations of Single-Photon Emitters

Christoph Thiel

This thesis summarizes investigations on quantum correlations in the fluorescence light of single trapped atoms. The results found have applications in the broad field of quantum information science: it is shown how to overcome classical imaging boundaries using a new developed scheme of quantum imaging, how to project and engineer correlated quantum states in the ground states of multi-level atoms by detecting their fluorescence light and how to prove the quantum nature of these correlations using fundamental tests of quantum information science. Without the need of further introduction to these topics it is interesting to note at this early point that all correlations observed are indeed of quantum nature and show in particular entanglement features, while initially the system under consideration is entirely uncorrelated and the only intervention comes along with the measurement process itself. Therefore, this thesis is embedded into a current field of research activities in the area of quantum information science which is commonly referred to as measurement-induced entanglement. In the first part of this thesis, the correlated photon signal as measured in the fluorescence light of single-photon emitters is at the focus of investigations. It is shown that this correlated signal can be used to overcome classical signals in terms of resolution when applied to image processing. In the second part, the fluorescence signal of a system of multi-level atoms is used to project correlated quantum states into the long-lived ground levels of the atoms. Hereby, a broad variety of entangled quantum states can be generated, ranging from symmetric states like the W-states and GHZ-states to arbitrary total angular momentum eigenstates. Finally, the last part of this thesis takes a closer look at the fundamental physical processes inherent in all schemes and applications investigated throughout the thesis. There, amongst others we investigate Bell-type inequalities that are able to prove the quantum nature of the correlations.

•Jan 4, 2010•1 citation

Strong-coupling quantum optics in free space with holes in a Fermi sea

Hao Wang, Hayden C. Orth, Duo Xu +1 more

Coherent and efficient light-matter interfaces between an atom and a single mode of the electromagnetic field are essential for quantum technologies. Traditionally, these systems employ optical cavities or waveguides to isolate a specific mode of light, but a more recent approach is to engineer antennas from ordered configurations of trapped ultracold atoms that exhibit controllable and directed scattering. In this work, we propose a method to engineer an antenna from the center-of-mass wavefunction of a single atom, which can produce directed emission and thereby exhibit strong coupling to a target mode of light in free space. We predict that the resulting single-atom cooperativity can be comparable to the current state of the art in optical cavity and waveguide QED experiments. Building on this approach, we show that a wavepacket antenna becomes a single-atom mirror in the linear response regime. We study the modified dipole-dipole interactions and band structure of chains of such emitters, which can exhibit sub- and superradiance at spacings much larger than the wavelength of the light. Extending our approach to multi-level atoms, we propose a method to achieve arbitrary spatial scattering from a single atom, including uni-directional spontaneous emission. Finally, we elucidate how our approach can enhance cooperative scattering in conventional arrays of tightly trapped atoms.

quant-pharXiv:2609.15935•Sep 15, 2026•0 citations

Coupling Single Electrons to Single Photons and Probing their Entanglement

Jan-Wilke Henke, Hao Jeng, Claus Ropers

Electron beams are a formidable tool for probing nanophotonic systems [1]. Combining electron microscopy with external optical excitation in ultrafast transmission electron microscopes has enabled the mapping of optical near-fields [2] and the bunching of electrons in attosecond pulses [3, 4]. These developments are based on the stimulated inelastic scattering between electrons and light [5, 6], in which the electrons gain energy from or lose energy to the optical field. Recently, the underlying interaction strength of this process has been increased significantly by harnessing resonant enhancement of the optical field and velocity phase matching [7]. Such an increased interaction strength also benefits the spontaneous scattering of electrons with light, thus promising applications like generating complex quantum states of light [8]. In this presentation, we discuss a set of experiments on free electron quantum optics that investigate single-electron-single-photon interactions and probe the resulting entanglement. Specifically, we consider scenarios in which optical waveguide structures are placed inside a transmission electron microscope (TEM) facilitating the interaction. Electrons passing by, for example, an integrated photonic structure (cf. Fig. 1a) can inelastically scatter with the optical mode, leading to the emergence of electron-photon pair states [9]. The resulting correlation between energy-loss electrons and photons, illustrated in Fig. 1b, can be probed employing time- and energy-resolved detection of both particles, revealing a pronounced coincidence peak between their arrival times, schematically shown in Fig. 1c. Extending the photon detection setup by a second detector to allow for Hanbury Brown and Twiss (HBT) measurements, the photon statistics heralded by such energy-loss electrons can be studied [10]. The observed anti-bunching behavior indicates a nonclassical optical state with single-photon properties. The inelastic electron-light scattering underlying the electron-photon pair generation is further expected to induce entanglement in the particle energies [11], however, direct observation of quantum entanglement would be exceedingly difficult given the large number of independent quantum states available in these degrees of freedom. Therefore, we propose experiments based on the quantum eraser scheme to demonstrate this free-electron-photon entanglement in different degrees of freedom [12,13]. Specifically, we consider a double-slit geometry coherently illuminated by an electron beam such that an interference pattern can be observed on a distant screen (cf. Fig. 2a). If electrons passing through the left or right (denoted |Land |R⁠, respectively) slit generate distinct marker photons with vertical (|V)or horizontal (|H) polarization, this interference pattern would disappear due to the entanglement of electron path and photon polarisation (cf. Fig. 2b). However, if this which-path information carried by the marker photon is erased, e.g. by mixing the polarisation states, the interference pattern can be recovered when detecting electrons and photons in coincidence. We describe an extension of this idea to an entanglement test, before discussing possible realistic implementations and presenting preliminary results on several experimental key aspects. In summary, we discuss the inelastic electron-light scattering at integrated photonic structures with applications ranging from coherent electron beam modulation using continuous-wave optical fields to the electron-driven generation of quantum optical states of light. Delving deeper into single electron-single photon interactions, we outline feasible experiments to generate and verify electron-photon entanglement with a potential extension to electron pairs based on entanglement swapping. All this adds to the toolbox of free electron quantum optics, potentially enabling novel sources of quantum light as well as quantum-enhanced sensing in electron microscopy. Generation of correlated electron-photon pairs. (a) Electrons pass over a photonic integrated circuit placed in the sample plane of a TEM, generating photons in the optical waveguides via inelastic scattering. Energy-loss electrons are detected and time-tagged behind an imaging spectrometer in coincidence with photons exiting the waveguide. (b) Inelastic scattering links the electron energy loss (green, right ladder) to the generation of photons (red, left ladder), creating correlations in energy and time. (c) A strong temporal correlation between the loss electrons and detected photons, indicated by the red dot, is observed relative to the uncorrelated zero-loss background electrons (blue line). Free-electron-photon quantum eraser. (a) Coherent electron illumination of a double-slit structure results in interference between the two pathways |Land |R.(b) If the electrons generate distinguishable marker photons, e.g. of orthogonal polarizations |Vand |H⁠, no interference pattern can be observed due to the electron-photon entanglement. (c) Collecting these marker photons and erasing the which-path information, e.g. using a half-wave plate (⁠λ/2⁠), the electron interference can be recovered using electron-photon coincidence detection with single-photon detectors (SPDs) placed behind a polarizing beam splitter (PBS).

Microscopy and Microanalysis•Jul 1, 2025•0 citations

Theory of two-photon interference

H. Fearn, R. Loudon

The interference effects that can be observed in the two output arms of a lossless beam splitter are calculated for incident light in the form of a photon-pair excitation in the two input arms. The output state that occurs when the photon pair is excited in a single input arm resembles that expected for independent classical particles, whereas quantum interference effects occur when the photon pair is divided between the two input arms. Detailed output photocount correlation functions are calculated for two-photon input states produced by a two-atom light source, a degenerate or nondegenerate parametric oscillator in a high-Q cavity, and an atomic cascade emission light source.

Journal of the Optical Society of America B•May 1, 1989•124 citations
In this project, we present a novel approach to calculate and engineer the photon correlations emerging from the interference between an input field and the field scattered by an atom in free space. Historically, it has been difficult to observe robust quantum correlations in the total field, as the inefficient atom-light coupling in free space usually causes the scattered field to be small in comparison to the input. To overcome this issue, we propose the use of separate pump and probe beams, where the former effectively enhances the atomic emission to be comparable to the probe. Additionally, we elucidate the physical origin of the non-classical correlations predicted, by studying the transient atomic state after the measurement of a photon.
We present an approach to engineer the photon correlations emerging from the interference between an input field and the field scattered by a single atom in free space. Nominally, the inefficient atom-light coupling causes the quantum correlations to be dominated by the input field alone. To overcome this issue, we propose the use of separate pump and probe beams, where the former increases the atomic emission to be comparable to the probe. Examining the second-order correlation function ${g}^{(2)}(\ensuremath{\tau})$ of the total field in the probe direction, we find that the addition of the pump formally plays the same role as increasing the coupling efficiency, even though the physical atom-light coupling efficiency remains unchanged. We show that one can tune the correlation function g(2)(0){g}^{(2)}(0)g(2)(0) from zero (perfect antibunching) to infinite (extreme bunching) by a proper choice of pump amplitude. We further elucidate the origin of these correlations in terms of the transient atomic state following the detection of a photon, and show that these correlations can be observed under realistic conditions.
In the present thesis we investigate spatial and temporal intensity correlations which are created by statistically independent or by entangled light sources. Even though this classification may appear quite technical, the diverseness of the statistical properties of the considered photon sources naturally brings into our focus two different lines of research. In the first part of this thesis we will quantitatively study the non-classical and potentially entangled character of light fields which originate from a variety of different statistically independent light sources. To this end quantum correlations between light fields are analyzed which either stem from non-classical single-photon emitters (like ensembles of uncorrelated atoms) or from a mixture of non-classical and classical photon sources (like lasers with uncorrelated fluctuating initial phase). In the second part of this thesis we study correlations between initially entangled lightsources, namely localized atoms which share an entangled state. In the course of the investigations we physically reinterpret in particular the so called superradiance effect in a quantum-path formalism: superradiance denotes an enhanced mean radiated intensity in a particular direction, i.e., a focussing of the photons scattered by an atomic gas. This effect is commonly explained by a successive synchronization of the dipole moments of all participating atoms leading to a photon emission predominantly in one direction. For more than 60 years this focussing has been physically interpreted as a cooperative effect depending on the dipole-dipole interaction between the atoms. In contrast, we will show that it is rather a quantum-interference effect which is caused by non-synchronized and potentially widely separated entangled atoms.
This thesis summarizes investigations on quantum correlations in the fluorescence light of single trapped atoms. The results found have applications in the broad field of quantum information science: it is shown how to overcome classical imaging boundaries using a new developed scheme of quantum imaging, how to project and engineer correlated quantum states in the ground states of multi-level atoms by detecting their fluorescence light and how to prove the quantum nature of these correlations using fundamental tests of quantum information science. Without the need of further introduction to these topics it is interesting to note at this early point that all correlations observed are indeed of quantum nature and show in particular entanglement features, while initially the system under consideration is entirely uncorrelated and the only intervention comes along with the measurement process itself. Therefore, this thesis is embedded into a current field of research activities in the area of quantum information science which is commonly referred to as measurement-induced entanglement. In the first part of this thesis, the correlated photon signal as measured in the fluorescence light of single-photon emitters is at the focus of investigations. It is shown that this correlated signal can be used to overcome classical signals in terms of resolution when applied to image processing. In the second part, the fluorescence signal of a system of multi-level atoms is used to project correlated quantum states into the long-lived ground levels of the atoms. Hereby, a broad variety of entangled quantum states can be generated, ranging from symmetric states like the W-states and GHZ-states to arbitrary total angular momentum eigenstates. Finally, the last part of this thesis takes a closer look at the fundamental physical processes inherent in all schemes and applications investigated throughout the thesis. There, amongst others we investigate Bell-type inequalities that are able to prove the quantum nature of the correlations.
Coherent and efficient light-matter interfaces between an atom and a single mode of the electromagnetic field are essential for quantum technologies. Traditionally, these systems employ optical cavities or waveguides to isolate a specific mode of light, but a more recent approach is to engineer antennas from ordered configurations of trapped ultracold atoms that exhibit controllable and directed scattering. In this work, we propose a method to engineer an antenna from the center-of-mass wavefunction of a single atom, which can produce directed emission and thereby exhibit strong coupling to a target mode of light in free space. We predict that the resulting single-atom cooperativity can be comparable to the current state of the art in optical cavity and waveguide QED experiments. Building on this approach, we show that a wavepacket antenna becomes a single-atom mirror in the linear response regime. We study the modified dipole-dipole interactions and band structure of chains of such emitters, which can exhibit sub- and superradiance at spacings much larger than the wavelength of the light. Extending our approach to multi-level atoms, we propose a method to achieve arbitrary spatial scattering from a single atom, including uni-directional spontaneous emission. Finally, we elucidate how our approach can enhance cooperative scattering in conventional arrays of tightly trapped atoms.
Electron beams are a formidable tool for probing nanophotonic systems [1]. Combining electron microscopy with external optical excitation in ultrafast transmission electron microscopes has enabled the mapping of optical near-fields [2] and the bunching of electrons in attosecond pulses [3, 4]. These developments are based on the stimulated inelastic scattering between electrons and light [5, 6], in which the electrons gain energy from or lose energy to the optical field. Recently, the underlying interaction strength of this process has been increased significantly by harnessing resonant enhancement of the optical field and velocity phase matching [7]. Such an increased interaction strength also benefits the spontaneous scattering of electrons with light, thus promising applications like generating complex quantum states of light [8]. In this presentation, we discuss a set of experiments on free electron quantum optics that investigate single-electron-single-photon interactions and probe the resulting entanglement. Specifically, we consider scenarios in which optical waveguide structures are placed inside a transmission electron microscope (TEM) facilitating the interaction. Electrons passing by, for example, an integrated photonic structure (cf. Fig. 1a) can inelastically scatter with the optical mode, leading to the emergence of electron-photon pair states [9]. The resulting correlation between energy-loss electrons and photons, illustrated in Fig. 1b, can be probed employing time- and energy-resolved detection of both particles, revealing a pronounced coincidence peak between their arrival times, schematically shown in Fig. 1c. Extending the photon detection setup by a second detector to allow for Hanbury Brown and Twiss (HBT) measurements, the photon statistics heralded by such energy-loss electrons can be studied [10]. The observed anti-bunching behavior indicates a nonclassical optical state with single-photon properties. The inelastic electron-light scattering underlying the electron-photon pair generation is further expected to induce entanglement in the particle energies [11], however, direct observation of quantum entanglement would be exceedingly difficult given the large number of independent quantum states available in these degrees of freedom. Therefore, we propose experiments based on the quantum eraser scheme to demonstrate this free-electron-photon entanglement in different degrees of freedom [12,13]. Specifically, we consider a double-slit geometry coherently illuminated by an electron beam such that an interference pattern can be observed on a distant screen (cf. Fig. 2a). If electrons passing through the left or right (denoted |Land |R⁠, respectively) slit generate distinct marker photons with vertical (|V)or horizontal (|H) polarization, this interference pattern would disappear due to the entanglement of electron path and photon polarisation (cf. Fig. 2b). However, if this which-path information carried by the marker photon is erased, e.g. by mixing the polarisation states, the interference pattern can be recovered when detecting electrons and photons in coincidence. We describe an extension of this idea to an entanglement test, before discussing possible realistic implementations and presenting preliminary results on several experimental key aspects. In summary, we discuss the inelastic electron-light scattering at integrated photonic structures with applications ranging from coherent electron beam modulation using continuous-wave optical fields to the electron-driven generation of quantum optical states of light. Delving deeper into single electron-single photon interactions, we outline feasible experiments to generate and verify electron-photon entanglement with a potential extension to electron pairs based on entanglement swapping. All this adds to the toolbox of free electron quantum optics, potentially enabling novel sources of quantum light as well as quantum-enhanced sensing in electron microscopy. Generation of correlated electron-photon pairs. (a) Electrons pass over a photonic integrated circuit placed in the sample plane of a TEM, generating photons in the optical waveguides via inelastic scattering. Energy-loss electrons are detected and time-tagged behind an imaging spectrometer in coincidence with photons exiting the waveguide. (b) Inelastic scattering links the electron energy loss (green, right ladder) to the generation of photons (red, left ladder), creating correlations in energy and time. (c) A strong temporal correlation between the loss electrons and detected photons, indicated by the red dot, is observed relative to the uncorrelated zero-loss background electrons (blue line). Free-electron-photon quantum eraser. (a) Coherent electron illumination of a double-slit structure results in interference between the two pathways |Land |R.(b) If the electrons generate distinguishable marker photons, e.g. of orthogonal polarizations |Vand |H⁠, no interference pattern can be observed due to the electron-photon entanglement. (c) Collecting these marker photons and erasing the which-path information, e.g. using a half-wave plate (⁠λ/2⁠), the electron interference can be recovered using electron-photon coincidence detection with single-photon detectors (SPDs) placed behind a polarizing beam splitter (PBS).
The interference effects that can be observed in the two output arms of a lossless beam splitter are calculated for incident light in the form of a photon-pair excitation in the two input arms. The output state that occurs when the photon pair is excited in a single input arm resembles that expected for independent classical particles, whereas quantum interference effects occur when the photon pair is divided between the two input arms. Detailed output photocount correlation functions are calculated for two-photon input states produced by a two-atom light source, a degenerate or nondegenerate parametric oscillator in a high-Q cavity, and an atomic cascade emission light source.