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arXiv:2007.09259 · Quantum Science and Technology

Einstein–Podolsky–Rosen paradox with position–momentum entangled macroscopic twin beams

Ashok Kumar, Gaurav Nirala, Alberto M. Marino

Published Aug 6, 2021• 24 citations
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Abstract

Abstract Spatial entanglement is at the heart of quantum enhanced imaging applications and high-dimensional quantum information protocols. In particular, for imaging and sensing applications, quantum states with a macroscopic number of photons are needed to provide a real advantage over the classical state-of-the-art. We demonstrate the Einstein–Podolsky–Rosen (EPR) paradox in its original position and momentum form with bright twin beams of light by showing the presence of EPR spatial (position–momentum) entanglement. An electron-multiplying charge-coupled-device camera is used to record images of the bright twin beams in the near and far field regimes to achieve an apparent violation of the uncertainty principle by more than an order of magnitude, which remains statistically significant even in the limit of a small number of images. We further show that the presence of quantum correlations in the spatial and temporal degrees of freedom leads to spatial squeezing of the bright twin beams in both the near and far fields. This provides another verification of the spatial entanglement and points to the presence of hyperentanglement in the bright twin beams.

DOI
10.1088/2058-9565/ac1b69

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Abstract Spatial entanglement is at the heart of quantum enhanced imaging applications and high-dimensional quantum information protocols. In particular, for imaging and sensing applications, quantum states with a macroscopic number of photons are needed to provide a real advantage over the classical state-of-the-art. We demonstrate the Einstein–Podolsky–Rosen (EPR) paradox in its original position and momentum form with bright twin beams of light by showing the presence of EPR spatial (position–momentum) entanglement. An electron-multiplying charge-coupled-device camera is used to record images of the bright twin beams in the near and far field regimes to achieve an apparent violation of the uncertainty principle by more than an order of magnitude, which remains statistically significant even in the limit of a small number of images. We further show that the presence of quantum correlations in the spatial and temporal degrees of freedom leads to spatial squeezing of the bright twin beams in both the near and far fields. This provides another verification of the spatial entanglement and points to the presence of hyperentanglement in the bright twin beams.
Spatially entangled twin photons provide both promising resources for modern quantum information protocols, because of the high dimensionality of transverse entanglement, and a test of the Einstein-Podolsky-Rosen paradox in its original form of position versus impulsion. Usually, photons in temporal coincidence are selected and their positions recorded, resulting in a priori assumptions on their spatiotemporal behavior. In this Letter, we record, on two separate electron-multiplying charge coupled devices cameras, twin images of the entire flux of spontaneous down-conversion. This ensures a strict equivalence between the subsystems corresponding to the detection of either position (image or near-field plane) or momentum (Fourier or far-field plane). We report the highest degree of paradox ever reported and show that this degree corresponds to the number of independent degrees of freedom, or resolution cells, of the images.
Spatially entangled twin photons provide a test of the Einstein-Podolsky-Rosen (EPR) paradox in its original form of position (image plane) versus impulsion (Fourier plane). We show that recording a single pair of images in each plane is sufficient to safely demonstrate an EPR paradox. On each pair of images, we have retrieved the fluctuations by subtracting the fitted deterministic intensity shape and then have obtained an intercorrelation peak with a sufficient signal to noise ratio to safely distinguish this peak from random fluctuations. A 95% confidence interval has been determined, confirming a high degree of paradox whatever the considered single pairs. Last, we have verified that the value of the variance of the difference between twin images is always below the quantum (poissonian) limit, in order to ensure the particle character of the demonstration. Our demonstration shows that a single image pattern can reveal the quantum and non-local behavior of light.
Spatially entangled twin photons provide a test of the Einstein-Podolsky-Rosen (EPR) paradox in its original form of position (image plane) versus impulsion (Fourier plane). We show that recording a single pair of images in each plane is sufficient to safely demonstrate an EPR paradox. On each pair of images, we have retrieved the fluctuations by subtracting the fitted deterministic intensity shape and then have obtained an intercorrelation peak with a sufficient signal to noise ratio to safely distinguish this peak from random fluctuations. A 95% confidence interval has been determined, confirming a high degree of paradox whatever the considered single pairs. Last, we have verified that the value of the variance of the difference between twin images is always below the quantum (poissonian) limit, in order to ensure the particle character of the demonstration. Our demonstration shows that a single image pattern can reveal the quantum and non-local behavior of light.
Summary form only given. With the rapid development of spatially-resolving single-photon detectors, spatially structured multidimensional entangled states start to play a key role in modern quantum science. In particular, they find extensive applications in emerging fields such as quantum imaging, holography, computation or quantum-enhanced metrology. Moreover, spatially-multiplexed schemes hold a promise to increase the capacity of quantum channels, essential for quantum key distribution. An appealing perspective is to apply these ideas to light-atom interfaces, that are capable of storing and processing continuous-variable (CV) entanglement, critical for novel quantum cryptography, computation and imaging schemes.Here we generate a hybrid bipartite entangled state of a photon and an atomic spin-wave excitation [1], exhibiting Einstein-Podolsky-Rosen (EPR) correlations in real space of continuous position-momentum variables, as in the original EPR proposal [2]. We verify the entanglement by measuring the coincidence patterns corresponding to modulus-squared spatial wavefunctions of the state. By studying temporal evolution and decoherence we find that the EPR entanglement may be stored for several microseconds. Our approach turns out to be by far more robust than the only hitherto performed experiment, based on quadratures of squeezed light and a slow-light medium, where time-delayed EPR correlations were demonstrated [3]. We achieve two orders of magnitude longer delay time using quantum memory setup and significantly stronger violation of EPR inequality [4], with product of variances 3 times below the EPR bound for the full two-dimensional coincidence distribution.
We demonstrate Einstein-Podolsky-Rosen (EPR) entanglement by detecting purely spatial quantum correlations in the near and far fields of spontaneous parametric down-conversion generated in a type-2 beta barium borate crystal. Full-field imaging is performed in the photon-counting regime with an electron-multiplying CCD camera. The data are used without any postselection, and we obtain a violation of Heisenberg inequalities with inferred quantities taking into account all the biphoton pairs in both the near and far fields by integration on the entire two-dimensional transverse planes. This ensures a rigorous demonstration of the EPR paradox in its original position-momentum form.
Spatial quantum correlations in the transverse degree of freedom promise to enhance optical resolution, image detection, and quantum communications through parallel quantum information encoding. In particular, the ability to observe these spatial quantum correlations in a single shot will enable such enhancements in applications that require real-time imaging, such as particle tracking and in situ imaging of atomic systems. Here, we report on measurements in the far field that show spatial quantum correlations in single images of bright twin beams with 108{10}^{8}108 photons in a 1-$\ensuremath{\mu}\mathrm{s}$ pulse using an electron-multiplying charge-coupled-device camera. A four-wave mixing process in hot rubidium atoms is used to generate narrowband, bright pulsed twin beams of light. Owing to momentum conservation in this process, the twin beams are momentum correlated, which leads to spatial quantum correlations in the far field. We show around 2 dB of spatial quantum noise reduction with respect to the shot-noise limit. The spatial squeezing is present over a large range of total number of photons in the pulsed twin beams.