Biphoton transmission through non-unitary objects

Reichert, Matthew; Defienne, Hugo; Sun, Xiaohang; Fleischer, Jason W.

doi:10.1088/2040-8986/aa6175

Cited by 14 publications

(14 citation statements)

References 40 publications

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“…(11) of (1.89/1.0) 2 = 3.57. To confirm this behavior, we performed experiments using an electron multiplying CCD (EMCCD) camera, which has both single-photon sensitivity and massively parallel measurement capabilities, making it convenient for biphoton measurements [14,[37][38][39]. A spatially filtered 405 nm CW laser beam pumps a type I SPDC crystal (BBO, L = 3 mm), generating near-collinear entangled photons, and nearly degenerate pairs are selected via spectral filter.…”

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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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Quality of spatial entanglement propagation

2017

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“…Recent efforts with single-photon-sensitive cameras have characterized spatial entanglement 20 – 25 , but results relied on projection onto only two dimensions and considered only homogeneous distributions, limiting measurements to EPR-type entanglement. In these works, measurements were spatially averaged over the entire plane (losing local detail).…”

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confidence: 99%

Massively Parallel Coincidence Counting of High-Dimensional Entangled States

Reichert

Defienne

Fleischer

2018

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Entangled states of light are essential for quantum technologies and fundamental tests of physics. Current systems rely on entanglement in 2D degrees of freedom, e.g., polarization states. Increasing the dimensionality provides exponential speed-up of quantum computation, enhances the channel capacity and security of quantum communication protocols, and enables quantum imaging; unfortunately, characterizing high-dimensional entanglement of even bipartite quantum states remains prohibitively time-consuming. Here, we develop and experimentally demonstrate a new theory of camera detection that leverages the massive parallelization inherent in an array of pixels. We show that a megapixel array, for example, can measure a joint Hilbert space of 1012 dimensions, with a speed-up of nearly four orders-of-magnitude over traditional methods. The technique uses standard geometry with existing technology, thus removing barriers of entry to quantum imaging experiments, generalizes readily to arbitrary numbers of entangled photons, and opens previously inaccessible regimes of high-dimensional quantum optics.

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“…The advent of single-photon-sensitive cameras, such as intensified CCD (ICCD) and electron-multiplying CCD (EMCCD) cameras, has made rapid characterization of the spatially entangled photon pairs feasible [12][13][14][15][16][17][18][19][20][21]. We have recently developed a method of parallelizing such measurements using an EMCCD camera [19].…”

Section: Introductionmentioning

confidence: 99%

Optimizing the signal-to-noise ratio of biphoton distribution measurements

2018

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Single-photon-sensitive cameras can now be used as massively parallel coincidence counters for entangled photon pairs. This enables measurement of biphoton joint probability distributions with orders-of-magnitude greater dimensionality and faster acquisition speeds than traditional raster scanning of point detectors; to date, however, there has been no general formula available to optimize data collection. Here we analyze the dependence of such measurements on count rate, detector noise properties, and threshold levels. We derive expressions for the biphoton joint probability distribution and its signal-to-noise ratio (SNR), valid beyond the low-count regime up to detector saturation. The analysis gives operating parameters for global optimum SNR that may be specified prior to measurement. We find excellent agreement with experimental measurements within the range of validity, and discuss discrepancies with the theoretical model for high thresholds. This work enables optimized measurement of the biphoton joint probability distribution in highdimensional joint Hilbert spaces.

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Biphoton transmission through non-unitary objects

Cited by 14 publications

References 40 publications

Quality of spatial entanglement propagation

Quality of spatial entanglement propagation

Massively Parallel Coincidence Counting of High-Dimensional Entangled States

Optimizing the signal-to-noise ratio of biphoton distribution measurements

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