In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology.
In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology.
In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, as shown successfully with light fields. Here, we report on the production of massive particles which meet the EPR criterion for continuous phase/amplitude variables. The created quantum state of ultracold atoms shows an EPR parameter of 0.18(3), which is 2.4 standard deviations below the threshold of 1/4. Our state presents a resource for tests of quantum nonlocality with massive particles and a wide variety of applications in the field of continuous-variable quantum information and metrology.
Spin changing collisions in alkaline Bose-Einstein condensates can be employed to generate highly entangled atomic quantum states. Here, we will report on the generation of two classes of entangled states. Firstly, we demonstrate the generation of two-mode squeezed vacuum states and record their characteristic quadrature correlations by atomic homodyning. We prove that the correlations fulfill Reid’s criterion [1] for continuous-variable Einstein-Podolsky-Rosen entanglement. The homodyne measurements allow for a full tomographic reconstruction, yielding a two-mode squeezed state with a 78% fidelity. The created state can be directly applied to atom interferometry, as is exemplified by an atomic clock measurement beyond the Standard Quantum Limit. Secondly, we demonstrate entanglement between two spatially separated atomic modes. The entangled state is obtained by spatially splitting a Twin Fock state of indistinguishable atoms along a line of zero density. This structure of two separated atomic modes is obtained by utilizing an excited trap mode. The non-classical correlations between these atomic modes are verified by applying a novel entanglement criterion especially sensitive for our case. The method opens a path to exploit the recent success in the creation of many-particle entanglement in ultracold atoms for the field of quantum information, where individually addressable subsystems are required. Finally, we will show how the measurement protocol can be extended to perform a Bell test of quantum nonlocality. [1] M. Reid, Phys. Rev. A 40, 913-923 (1989)
Einstein-Podolsky-Rosen (EPR) entanglement introduced in 1935 deals with two particles that are entangled in their positions and momenta. Here we report the first experimental demonstration of EPR position-momentum entanglement of narrow-band photon pairs generated from cold atoms. By using two-photon quantum ghost imaging and ghost interference, we demonstrate explicitly that the narrow-band photon pairs violate the separability criterion, confirming EPR entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons. Our new source of EPR-entangled narrow-band photons is expected to play an essential role in spatially multiplexed quantum information processing, such as, storage of quantum correlated images, quantum interface involving hyperentangled photons, etc.
Certification and quantification of correlations for multipartite states of quantum systems appear to be a central task in quantum information theory. We give here a unitary quantum-mechanical perspective of both entanglement and Einstein-Podolsky-Rosen (EPR) steering of continuous-variable multimode states. This originates in the Heisenberg uncertainty relations for the canonical quadrature operators of the modes. Correlations of two-party (Nvs1)-mode states are examined by using the variances of a pair of suitable EPR-like observables. It turns out that the uncertainty sum of these nonlocal variables is bounded from below by local uncertainties and is strengthened differently for separable states and for each one-way unsteerable state. The analysis of the minimal properly normalized sums of these variances yields necessary conditions of separability and EPR unsteerability of (Nvs1)-mode states in both possible ways of steering. When the states and the performed measurements are Gaussian, then these conditions are precisely the previously known criteria of separability and one-way unsteerability.
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.
In 1935, Einstein, Podolsky, and Rosen (EPR) conceived a gedanken experiment which became a cornerstone of quantum technology and still challenges our understanding of reality and locality today.While the experiment has been realized with small quantum systems, a demonstration of the EPR paradox with massive many-particle systems remains an important challenge, as such systems are particularly closely tied to the concept of local realism in our everyday experience and may serve as probes for new physics at the quantum-to-classical transition.In this work we report an EPR experiment with two spatially separated Bose-Einstein condensates, each containing about 700 rubidium atoms.Entanglement between the condensates results in strong correlations of their collective spins, allowing us to demonstrate the EPR paradox between them.Our results represent the first observation of the EPR paradox with spatially separated, massive many-particle systems.They show that the conflict between quantum mechanics and local realism does not disappear as the system size increases to more than a thousand massive particles.Furthermore, EPR entanglement in conjunction with individual manipulation of the two condensates on the quantum level, as we demonstrate here, constitutes an important resource for quantum metrology and information processing with many-particle systems.