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arXiv:1508.06462 · Physical Review A

Einstein-Podolsky-Rosen–entangled motion of two massive objects

Roman Schnabel

Published Jul 28, 2015• 41 citations
arXivHTMLPDF

Abstract

In 1935, Einstein, Podolsky and Rosen (EPR) considered two particles in an entangled state of motion to illustrate why they questioned the completeness of quantum theory. In the past decades, microscopic systems with entanglement in various degrees of freedom have successfully been generated, representing compelling evidence to support the completeness of quantum theory. Today, the generation of an EPR-entangled state of motion of two massive objects of up to the kilogram-scale seems feasible with state-of-the-art technology. Recently, the generation and verification of EPR-entangled mirror motion in interferometric gravitational wave detectors was proposed, with the aim of testing quantum theory in the regime of macroscopic objects, and to make available nonclassical probe systems for future tests of modified quantum theories that include (non-relativistic) gravity. The work presented here builds on these earlier results and proposes a specific Michelson interferometer that includes two high-quality laser mirrors of about 0.1 kg mass each. The mirrors are individually suspended as pendula and located close to each other, and cooled to about 4 K. The physical concepts for the generation of the EPR-entangled centre of mass motion of these two mirrors are described. Apart from a test of quantum mechanics in the macroscopic world, the setup is envisioned to test predictions of yet-to-be-elaborated modified quantum theories that include gravitational effects.

DOI
10.1103/physreva.92.012126

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In 1935, Einstein, Podolsky and Rosen (EPR) considered two particles in an entangled state of motion to illustrate why they questioned the completeness of quantum theory. In the past decades, microscopic systems with entanglement in various degrees of freedom have successfully been generated, representing compelling evidence to support the completeness of quantum theory. Today, the generation of an EPR-entangled state of motion of two massive objects of up to the kilogram-scale seems feasible with state-of-the-art technology. Recently, the generation and verification of EPR-entangled mirror motion in interferometric gravitational wave detectors was proposed, with the aim of testing quantum theory in the regime of macroscopic objects, and to make available nonclassical probe systems for future tests of modified quantum theories that include (non-relativistic) gravity. The work presented here builds on these earlier results and proposes a specific Michelson interferometer that includes two high-quality laser mirrors of about 0.1 kg mass each. The mirrors are individually suspended as pendula and located close to each other, and cooled to about 4 K. The physical concepts for the generation of the EPR-entangled centre of mass motion of these two mirrors are described. Apart from a test of quantum mechanics in the macroscopic world, the setup is envisioned to test predictions of yet-to-be-elaborated modified quantum theories that include gravitational effects.
Recent ideas and technological developments have made possible studies of macroscopic objects deep in the quantum regime. In the talk I will discuss the experiment where an entangled Einstein-Podolsky-Rosen (EPR) state has been generated between distant mechanical and atomic oscillators [1]. The concept of an oscillator with an effective negative mass crucial for those experiments will be presented. Such entanglement allows to measure disturbances in the position and the momentum of an oscillator simultaneously, the trait which may seem counterintuitive. Using this entangled state, the trajectory of motion of the oscillator in phase space can be traced with, in principle, unlimited accuracy. Progress towards application of those ideas to gravitational wave detectors [2] following the proposals [3], [4] will be reported.
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.
We show that the generation of entanglement of two heavily macroscopic mirrors is feasible with state of the art techniques of high-precision laser interferometry. The basis of such a demonstration would be a Michelson interferometer with suspended mirrors and simultaneous homodyne detections at both interferometer output ports. We present the connection between the generation of entanglement and the standard quantum limit (SQL) for a free mass. The SQL is a well-known reference limit in operating interferometers for gravitational-wave detection and provides a measure of when macroscopic entanglement can be observed in the presence of realistic decoherence processes.
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.
We propose an experiment to test Bell nonlocality, a genuine nonclassicality, for the gravitational field. Two masses with embedded entangled spins (e.g., two diamonds with their NV-centre spins entangled) are placed well outside each other's light cones, ensuring a locality-loophole-free scenario. The spins are then coupled to the motion of their respective masses to generate spatial superpositions. Finally, local measurements are performed only on the gravitational fields of the two masses. If gravity is quantum, then the two entangled masses would entangle their gravitational fields, leading to correlations certifying Bell nonlocality of gravity. Trapped and ground-state cooled nano-objects with micron-sized spatial superposition are sufficient for this test. This goes beyond the recent proposals to test nonclassicality of gravity by providing, for the first time in the literature, a minimal tool to (i) create Einstein-Podolsky-Rosen (EPR) state of gravitational curvatures, (ii) witness entangled gravitational curvatures, (iii) rule out any local-realist description of gravity, and (iv) achieve a loophole-free test of gravity's nonclassicality in a fully device-independent way.