Spatially entangled four-photon states from a periodically poled potassium-titanyl-phosphate crystal

Torren, Alexander J. H. van der; Yorulmaz, S. Cigdem; Renema, Jelmer J.; Exter, M. P. van; Dood, M. J. A. de

doi:10.1103/physreva.85.043837

Cited by 8 publications

(10 citation statements)

References 23 publications

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“…(2) will never be separable in (ρ1, ρ2) coordinates, even when σ-= σ+. This means that the common experimental practice of measuring {σ±, σ} and evaluating Kamp [14,33] does not accurately capture the entirety of the spatial entanglement information content, but rather only a small portion [16,28].…”

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confidence: 99%

Quality of spatial entanglement propagation

2017

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We explore, both experimentally and theoretically, the propagation dynamics of spatially entangled photon pairs (biphotons). Characterization of entanglement is done via the Schmidt number, which is a universal measurement of the degree of entanglement directly related to the non-separability of the state into its subsystems. We develop expressions for the terms of the Schmidt number that depend on the amplitude and phase of the commonly used double-Gaussian approximation for the biphoton wave function, and demonstrate migration of entanglement between amplitude and phase upon propagation. We then extend this analysis to incorporate both phase curvature in the pump beam and higher spatial frequency content of more realistic non-Gaussian wave functions. Specifically, we generalize the classical beam quality parameter M 2 to the biphotons, allowing the description of more information-rich beams and more complex dynamics. Agreement is found with experimental measurements using direct imaging and Fourier optics.Entanglement is a key resource in quantum information. While entanglement in discrete variables, such as spin or polarization [1][2][3][4][5], forms the basis of qubits, of growing interest is entanglement in continuous variables, such as transverse spatial position and momentum. The conjugate nature of these variables underlies imaging and propagation, while their infinite-dimensional Hilbert space holds much potential for quantum computation [6][7][8][9]. Typically, the photon source for continuous-variable entanglement is spontaneous parametric down-conversion (SPDC) [10][11][12][13][14] but, remarkably, there have been few investigations into its amount and distribution upon propagation [15,16].A universal metric to quantify the degree of entanglement is the Schmidt number, which is directly related to the non-separability of the state's (two) subsystems [17][18][19]. While interferometric measurements of the Schmidt number have been proposed [15] and demonstrated [16], such methods do not examine the manifestation of the entanglement, i.e., non-separability of amplitude or phase. Furthermore, theoretical analysis has thus far focused primarily on Gaussian spatial profiles, which are not generated experimentally.Here, we present an analysis of the Schmidt number of realistic non-Gaussian entangled photon wave functions, explicitly revealing the migration of entanglement with propagation from amplitude to phase and back again [15]. First, we present a Schmidt decomposition of the commonly used double-Gaussian approximation for the biphoton wave function. We clearly identify amplitude and phase components and demonstrate migration between them during propagation. This migration depends on the focusing geometry of the pump used to generate the photon pairs, as its phase profile directly determines the far-field properties of the biphoton wave function. We then examine more realistic biphoton wave functions that have different propagation behavior from the ideal double-Gaussian. In particular, the higher spat...

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confidence: 99%

Quality of spatial entanglement propagation

2017

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“…(28), and the dashed lines correspond to the approximation given in Eq. (30). We see that as the noise probability increases the mean number of photon pairs to obtain the maximum visibility increases, whereas the maximum achievable visibility gets smaller.…”

Section: G Example: Multimode Correlations With a Uniform Marginal Dmentioning

confidence: 74%

“…Note that we are neglecting the probability of a four-photon emission, a process that increases the probability of having two pairs occupying the same mode due to stimulated emission [30]. In our case we consider n independent two-photon emissions during one exposure time of the detector arrays; for example, a pulsed pump laser with repetition rate of 100 MHz generating an average of 10…”

Section: Occupation Probabilities Of the Detection Modesmentioning

confidence: 99%

Optimizing the use of detector arrays for measuring intensity correlations of photon pairs

et al. 2013

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Intensity correlation measurements form the basis of many experiments based on spontaneous parametric down-conversion. In the most common situation, two single-photon avalanche diodes and coincidence electronics are used in the detection of the photon pairs, and the coincidence count distributions are measured by making use of some scanning procedure. Here we analyze the measurement of intensity correlations using multielement detector arrays. By considering the detector parameters such as the detection and noise probabilities, we found that the mean number of detected photons that maximizes the visibility of the two-photon correlations is approximately equal to the mean number of noise events in the detector array. We provide expressions predicting the strength of the measured intensity correlations as a function of the detector parameters and on the mean number of detected photons. We experimentally test our predictions by measuring far-field intensity correlations of spontaneous parametric down-conversion with an electron multiplying charge-coupled device camera, finding excellent agreement with the theoretical analysis.

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“…(2), keeping in mind that the photons are produced in pairs: the first term in Eq. (2) that contains photons with different OAM jlj occurs if the second pair is spontaneously emitted and uncorrelated to the first pair, while the second term corresponds to the case where the second pair is produced by a stimulated process giving a perfect clone of the first pair [35][36][37][38]. The different jlj values in the first term in Eq.…”

Section: Figmentioning

confidence: 99%

Observation of Four-Photon Orbital Angular Momentum Entanglement

2016

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We demonstrate genuine multipartite quantum entanglement of four photons in their orbital angular momentum degrees of freedom, where a high-dimensional discrete Hilbert space is attached to each photon. This can encode more quantum information compared to the qubit case, but it is a long-standing problem to entangle more than two such photons. In our experiment we use pulsed spontaneous parametric down-conversion to produce the photon quadruplets, which allows us to detect about one four-photon event per second. By means of quantum state reconstruction and a suitable witness operator we find that the photon quadruplets form a genuine multipartite entangled symmetric Dicke state. This opens a new tool for addressing foundational questions in quantum mechanics, and for exploration of novel high-dimensional multiparty quantum information applications such as secret sharing. DOI: 10.1103/PhysRevLett.116.073601 Experimental control over systems where more than two particles are entangled is of interest for the study of foundational questions in quantum mechanics, and for multiparty quantum information schemes. So far, up to 14 particles have been entangled [1,2], but in each case the single-particle Hilbert space was strictly two-dimensional, i.e., qubits. For photons, the spatial degrees of freedom enable high-dimensional single particle spaces, which can be discretized in the photon orbital angular momentum (OAM). This enables implementation of novel quantum information protocols [3][4][5], and the study of fundamentally new quantum states [6,7]. To date, only two such multidimensional particles have been entangled [8,9] albeit with ever increasing dimensionality [10][11][12]; only in continuous variables, a first study goes beyond this [13]. Here, we use pulsed spontaneous parametric downconversion (SPDC) [14] to produce photon quadruplets that are entangled in their OAM, or transverse-mode, degrees of freedom [8,15], and witness genuine multipartite Dicke-type entanglement [16][17][18]. Apart from addressing foundational questions [19][20][21], this could find applications in quantum metrology, imaging, and secret sharing [22,23].Photons that are generated by near-collinear SPDC are correlated in several degrees of freedom and exhibit quantum entanglement. Apart from the well-known polarization degrees, the photons can also be correlated in their spatial degrees; this manifests itself in continuous wave vector or (the Fourier-related) position entanglement. This can be discretized using transverse optical modes, and a particular useful choice for experiments is the LaguerreGauss (LG) modes. Their azimuthal part factorizes and describes phase vortices [24] exp ðilϕÞ, where ϕ is the azimuth and l ¼ −∞, …, ∞ determines the twisting number of the wave front, corresponding to an orbital angular momentum of lℏ per photon [25] (in addition to the spin angular momentum). The LG and the related Hermite-Gauss modes have well-known propagation dynamics; thus, they are suitable for the long-distance distribution of high-d...

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Spatially entangled four-photon states from a periodically poled potassium-titanyl-phosphate crystal

Cited by 8 publications

References 23 publications

Quality of spatial entanglement propagation

Quality of spatial entanglement propagation

Optimizing the use of detector arrays for measuring intensity correlations of photon pairs

Observation of Four-Photon Orbital Angular Momentum Entanglement

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