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The transverse spatial effects observed in photon pairs produced by parametric down-conversion provide a robust and fertile testing ground for studies of quantum mechanics, non-classical states of light, correlated imaging and quantum information. Over the last 20 years there has been much progress in this area, ranging from technical advances and...
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Citations
... Next, we sent spatially entangled photons generated via SPDC [65] through the MMF. Similar to classical light, which is scrambled in the fiber and exhibits a speckle pattern, the spatial correlations between the two photons get scrambled, yielding a two-photon speckle [66]. ...
Multimode optical fibers support the dense, low-loss transmission of many spatial modes, making them attractive for technologies such as communications and imaging. However, information propagating through multimode fibers is scrambled, due to modal dispersion and mode mixing. This is usually rectified using wavefront shaping techniques with devices such as spatial light modulators. Recently, we demonstrated an all-fiber system for controlling light propagation inside multimode fibers using mechanical perturbations, called the fiber piano. In this tutorial we explain the design considerations and experimental methods needed to build a fiber piano, and review applications where fiber pianos have been used.
... is proportional to the well-known two-photon probability amplitude generated by SPDC [21]. Note that two-photon terms do not contribute to the phenomenon in which we are interested and the probability of generation of six or more photon terms is negligible. ...
... In the interaction picture, the Hamiltonian of the SPDC process can be written as [21] ...
... where V P is the complex amplitude of the pump wave, k P is the associated wave vector, and ω P is the angular frequency. Quantum fields associated with signal and idler photons are represented by their plane wave mode decomposition [21] E (+) ...
We present a quantum interference phenomenon in which four-photon quantum states generated by two independent sources are used to create a two-photon interference pattern without detecting two of the photons. Contrary to the common perception, the interference pattern can be made fully independent of phases acquired by the photons detected to construct it. However, it still contains information about spatially dependent phases acquired by the two undetected photons. This phenomenon can also be observed with fermionic particles. We show that the phenomenon can be applied to develop an interferometric, quantum phase imaging technique that is immune to uncontrollable phase fluctuations in the interferometer and allows image acquisition without detecting the photons illuminating the object.
... Spontaneous parametric down-conversion (SPDC) is the most well-known process for this task wherein a pump photon is down-converted to two photons, namely, signal and idler [4,5]. Down-converted photons offer entanglement in various degrees of freedom [6] or entanglement can be prepared in a specific degree of freedom through the use of interferometers [7,8]. By entangling more than one degree of freedom, the so-called hyper-entangled states are obtained. ...
... QIUL combines elements of non-linear interferometry and quantum optics, in which a laser pumps a non-linear crystal to generate spatially correlated photon-pairs, historically named as signal and idler, via SPDC [25][26][27]. The wavelengths of the signal and idler beams can be easily tuned by controlling the pump and crystal parameters. ...
... This overlap ensures that there is no knowledge of the which-path information, in other words, the two idler beams become indistinguishable and the observer is incapable of knowing whether the signal photon that strikes the camera plane was generated in the forward or backward path resulting in a single-photon interference pattern [35,36,39,40]. The reconstruction of the object information is also attributed to the spatial correlations shared by the photon-pair, namely momentum correlations which are the result of momentum conservation in the SPDC process [27,37]. Furthermore, the undetected light scheme grants the opportunity to work in a very distinct wavelength range for the illumination and detection parts, taking advantage of a mature silicon based detection technology at the visible wavelength range [26,28,29]. ...
... The MZI offers a better control of the optical paths between the two beams providing a large relative angle, which can optimize the imaging capabilities of the system [32,33]. The signal beam allows the image reconstruction despite never interacting with the object as a result of the induced coherence and the spatial correlations between signal and idler beams [27,35]. ...
... In this proof-of-principle work, we introduce and implement quantum SHWS (QSHWS) by measuring the JPD of photon pairs from spontaneous parametric down-conversion (SPDC) [32,33] at the focal plane of the microlens array. To our knowledge, this is the first single-measurement and reference-free biphoton phase measurement method. ...
With an extremely high dimensionality, the spatial degree of freedom of entangled photons is a key tool for quantum foundation and applied quantum techniques. To fully utilize the feature, the essential task is to experimentally characterize the multiphoton spatial wave function including the entangled amplitude and phase information at different evolutionary stages. However, there is no effective method to measure it. Quantum state tomography is costly, and quantum holography requires additional references. Here we introduce quantum Shack-Hartmann wavefront sensing to perform efficient and reference-free measurement of the biphoton spatial wave function. The joint probability distribution of photon pairs at the back focal plane of a microlens array is measured and used for amplitude extraction and phase reconstruction. In the experiment, we observe that the biphoton amplitude correlation becomes weak while phase correlation shows up during free-space propagation. Our work is a crucial step in quantum physical and adaptive optics and paves the way for characterizing quantum optical fields with high-order correlations or topological patterns.
... A bandpass filter at 810 ± 10 nm is used to remove ambient light and most non-degenerate pairs. Due to the phase matching conditions in the SPDC process, the photons at the plane of the crystal are strongly correlated in transverse position (r) and strongly anti-correlated in transverse momentum (k) [40]. Both of these types of correlations can be exploited, hence the two experimental configurations. ...
Quantum imaging enhances imaging systems performance, potentially surpassing fundamental limits such as noise and resolution. However, these schemes have limitations and are still a long way from replacing classical techniques. Therefore, there is a strong focus on improving the practicality of quantum imaging methods, with the goal of finding real-world applications. With this in mind, in this tutorial we describe how the concepts of classical light shaping can be applied to imaging schemes based on entangled photon pairs. We detail two basic experimental configurations in which a spatial light modulator is used to shape the spatial correlations of a photon pair state and highlight the key differences between this and classical shaping. We then showcase two recent examples that expand on these concepts to perform aberration and scattering correction with photon pairs. We include specific details on the key steps of these experiments, with the goal that this can be used as a guide for building photon-pair-based imaging and shaping experiments.
... As described in Section 2.2, the source used for our experiments generates pairs of photons. These pairs are entangled spatially, with a wavefunction that can be approximated as a double Gaussian [48,49] that exhibits spatial and momentum correlation among pairs [50,51]: ...
Electron multiplying charge-coupled devices (EMCCDs), owing to their high quantum efficiency and spatial resolution, are widely used to study typical quantum optical phenomena and related applications. Researchers have already developed a procedure that enables one to statistically determine whether a pixel detects a single photon, based on whether its output is higher or lower than the estimated noise level. However, these techniques are feasible at extremely low photon numbers (≈0.15 mean number of photons per pixel per exposure), allowing for at most one photon per pixel. This limitation necessitates a very large number of frames required for any study. In this work, we present a method to estimate the mean rate of photons per pixel per frame for arbitrary exposure time. Subsequently, we make a statistical estimate of the number of photons (≥ 1) incident on each pixel. This allows us to effectively use the EMCCD as a photon number resolving device. This immediately augments the acceptable light levels in the experiments, leading to significant reduction in the required experimentation time. As evidence of our approach, we quantify contrast in quantum correlation exhibited by a pair of spatially entangled photons generated by a spontaneous parametric down conversion process. In comparison with conventional methods, our method realizes an enhancement in the signal-to-noise ratio (SNR) by approximately a factor of 3 for half the data collection time. This SNR can be easily enhanced by minor modifications in experimental parameters such as exposure time, etc.
... Given the orthogonality and completeness of OAM eigenstates [30], twisted photons are the ideal candidates to construct a qutrit state for performing this evolution. Here, utilizing the single-photon OAM state generated by spontaneous parametric down-conversion (SPDC) [31], we translate the aforementioned theoretical strategy into an experimental implementation. Without loss of generality, we choose three OAM modes |+1⟩ ≡ (1, 0, 0) T , |−1⟩ ≡ (0, 1, 0) T and |0⟩ ≡ (0, 0, 1) T to construct a three-dimensional Hilbert space, and thus the state vector in Eq. (1) is naturally the superposition of these OAM modes. ...
Photonic orbital angular momentum (OAM) offers a promising platform for high-dimensional quantum information processing. While geometric phase (GP) is the crucial tool in enabling intrinsically fault-tolerant quantum computation, the measurement of GP using linear optics remains relatively unexplored in the OAM state space. Here, we propose an experimental scheme to detect GP shifts resulting from the cyclic evolution of OAM qutrit states. Distinguished with the conventional evolution along cyclic path on the Poincaré sphere (PS), the nontrivial evolution in our theoretical scheme is along a cyclic path residing within the SU(3)/U(2) parameter space. By employing a combination of X-gates, dove prisms, and double cylindrical lenses, we achieve the cyclic evolution and analyse the resultant GP through our designed Sagnac interferometer. Our theoretical study may find potential in high-dimensional quantum computation using twisted photons and in exploring the geometric structure of such optical systems.
... SPDC was theoretically introduced by D. Klishko [29] and experimentally realized by D. C. Burnham and D. L. Weinberg. [30] The properties of photon pairs produced in SPDC processes have been extensively studied in terms of their spatial properties [31] or for the generation of entanglement in two [32] and high dimensions. [33] In this review, we mainly present results within the paraxial regime, where the wavelengths of the photons involved in the SPDC process are much smaller than the crystal length, and the angles of the pump beam and both SPDC photons are small. ...
... Quantum imaging usually employs photon pairs spatially correlated in two planes: far field and near field. [31,66,67] The far field plane was analyzed in the previous section and shows how photon pairs are anticorrelated in momentum. In the near field plane, photon pairs are "position correlated," which can also be employed to perform QIUL. ...
Nonlinear interferometers are a ubiquitous tool in quantum photonics. As such, they allow spooky‐like imaging with undetected light. On the one side their working principle is based on the principle of induced coherence, which is deeply rooted in the heart of quantum mechanics. On the other side, they bear the strong potential to serve as new tool for biomedical imaging. In this review, an extensive overview about nonlinear interferometers and their working principle is given. A particular focus is set on their exploitation for quantum imaging and sensing. In addition, related side topics and further application fields as well as perspectives are provided.
... Parametric down-conversion (PDC) is a nonlinear optical process that has revolutionized the field of quantum optics [20,21], and is one of the most important experimental tools for investigating quantum entanglement in quantum information and computation [22]. This process can be understood as the coupling between three optical modes via a χ(2) interaction inside a nonlinear crystal [23]. ...
... all classical states satisfy this inequality) is violated [24]. Other quantum signatures stem from the correlations between transverse components of the wave vectors of the signal and idler photons [20]. In addition to the quantum properties that can be observed in sources of parametric down-conversion without any special arrangement, one can also prepare and measure entanglement in other degrees of freedom, such as polarization. ...
In this paper, we utilize an analog model of the general relativity and investigate the influence of spatial curvature on quantum properties of stimulated parametric down-conversion process. For this purpose, we use two-mode sphere coherent state as the input beams of the aforementioned process. These states are realization of coherent states of two-dimensional harmonic oscillator, which lies on a two-dimension sphere. We calculate the entanglement of output states of stimulated parametric down conversion process, measured by linear entropy, and show that it depends on the spatial curvature. So, by preparing the suitable two-mode sphere coherent states, it is possible to control the entanglement between the output states in the laboratory. In addition, we consider mean number and Mandel parameter of the output states of the process and also, their cross-correlation function, as the convince measures of non-classical behaviors.
