Quality of spatial entanglement propagation

Abstract

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...

Biphoton transmission through non-unitary objects

“…Spatial entanglement properties of the source are first characterized, without an object in the experiment, employing the technique described in [15,16,19]. Briefly, for spatially correlated biphotons, the auto-correlation of each frame is calculated and summed together to give a conditional probability distribution of the separation of coincidence counts.…”

“…The massively parallel capability of EMCCD's to detect the two-photon coincidence images has previously been used to measure correlation properties of the entangled photon pairs [15,16,19,20]. In the present work, this approach is extended to reconstruct the two-photon irradiance, 2 ( ), of the state, which is proportional to the marginal probability of detecting one photon of a pair at position = � + �.…”

“…Recently, the use of single-photon sensitive pixelarray detectors to measure coincidences-such as intensified [13,14] and electron multiplying (EM) CCD cameras [15,16]-has substantially increased the potential of this type of source for imaging purposes. Such cameras have previously been used to characterize spatial entanglement of photon pairs [17][18][19] and to demonstrate the EPR paradox [15,16,19]. In the present work, we exploit these detection techniques with an EMCCD camera to study the transmission of spatially entangled photon pairs through non-unitary objects, i.e., those with loss (| ( )| 2 ≠ 1).…”

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

“…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].…”

Fast camera spatial characterization of photonic polarization entanglement

“…However, these measurements used resource-intensive methods, such as sequential scanning or multiple standalone detectors.Early studies of entanglement with modern imagers used an electron-multiplying CCD (EM-CCD) camera with an effective area of 201 × 201 pixels and frame readout-rate of 5Hz [8].Albeit the EMCCD quantum efficiency was up to 90%, prolonged exposure time of about 1ms, requires this device to operate at very small photon-rates to avoid multiple photons in the same frame. Furthermore, to achieve single-photon level sensitivity the EMCCD camera operated at a low temperature of −85 o C.Further progression on quantum imaging with cameras was achieved using intensified CMOS and CCD cameras [12][13][14][15][16][17]. Flexible readout architectures allow kHz continuous framing rates in CMOS cameras.…”