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If the boundary conditions of the quantum vacuum are changed in time, quantum field theory predicts that real, observable particles can be created in the initially empty modes. Here, we realize this effect by changing the boundary conditions of a spinor Bose–Einstein condensate, which yields a population of initially unoccupied spatial and spin excitations. We prove that the excitations are created as entangled pairs by certifying continuous-variable entanglement within the many-particle output state. © 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.

Splitting the entanglement When particles in a quantum mechanical system are entangled, a measurement performed on one part of the system can affect the results of the same type of measurement performed on another part—even if these subsystems are physically separated. Kunkel et al. , Fadel et al. , and Lange et al. achieved this so-called distributed entanglement in a particularly challenging setting: an ensemble of many cold atoms (see the Perspective by Cavalcanti). In all three studies, the entanglement was first created within an atomic cloud, which was then allowed to expand. Local measurements on the different, spatially separated parts of the cloud confirmed that the entanglement survived the expansion. Science , this issue p. 413 , p. 409 , p. 416 ; see also p. 376

Since the pioneering work of Ramsey, atom interferometers are employed for precision metrology, in particular to measure time and to realize the second. In a classical interferometer, an ensemble of atoms is prepared in one of the two input states, whereas the second one is left empty. In this case, the vacuum noise restricts the precision of the interferometer to the standard quantum limit (SQL). Here, we propose and experimentally demonstrate a novel clock configuration that surpasses the SQL by squeezing the vacuum in the empty input state. We create a squeezed vacuum state containing an average of 0.75 atoms to improve the clock sensitivity of 10,000 atoms by 2.05 dB. The SQL poses a significant limitation for today's microwave fountain clocks, which serve as the main time reference. We evaluate the major technical limitations and challenges for devising a next generation of fountain clocks based on atomic squeezed vacuum. Since the pioneering work of Ramsey, atom interferometers are employed for precision metrology, in particular to measure time and to realize the second. In a classical interferometer, an ensemble of atoms is prepared in one of the two input states, whereas the second one is left empty. In this case, the vacuum noise restricts the precision of the interferometer to the standard quantum limit (SQL). Here, we propose and experimentally demonstrate a novel clock configuration that surpasses the SQL by squeezing the vacuum in the empty input state. We create a squeezed vacuum state containing an average of 0.75 atoms to improve the clock sensitivity of 10000 atoms by 2.05+0.34−0.37 dB. The SQL poses a significant limitation for today’s microwave fountain clocks, which serve as the main time reference. We evaluate the major technical limitations and challenges for devising a next generation of fountain clocks based on atomic squeezed vacuum.

Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Science 344, 1256 (2014)]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states---ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures., 46 pages (25.2 + appendices), 7 figures

Quantum mechanics predicts that our physical reality is influenced by events that can potentially happen but factually do not occur. Interaction-free measurements (IFMs) exploit this counterintuitive influence to detect the presence of an object without requiring any interaction with it. Here we propose and realize an IFM concept based on an unstable many-particle system. In our experiments, we employ an ultracold gas in an unstable spin configuration, which can undergo a rapid decay. The object—realized by a laser beam—prevents this decay because of the indirect quantum Zeno effect and thus, its presence can be detected without interacting with a single atom. Contrary to existing proposals, our IFM does not require single-particle sources and is only weakly affected by losses and decoherence. We demonstrate confidence levels of 90%, well beyond previous optical experiments., The inherent strangeness of quantum mechanics means it is possible to detect objects using single-quantum particles even if they do not interact directly. Peise et al. realize such an ‘interaction-free measurement' by exploiting the quantum Zeno effect in a BEC, obviating the need for single-particle sources.

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 standard deviations 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., 8 pages, 7 figures

Recent experiments demonstrate the production of many thousands of neutral atoms entangled in their spin degrees of freedom. We present a criterion for estimating the amount of entanglement based on a measurement of the global spin. It outperforms previous criteria and applies to a wide class of entangled states, including Dicke states. Experimentally, we produce a Dicke-like state using spin dynamics in a Bose-Einstein condensate. Our criterion proves that it contains at least genuine 28-particle entanglement. We infer a generalized squeezing parameter of -11.4(5) dB., Comment: 5 pages, 4 figures

We present an analytical model for the theoretical analysis of spin dynamics and spontaneous symmetry breaking in a spinor Bose-Einstein condensate (BEC). This allows for an excellent intuitive understanding of the processes and provides good quantitative agreement with experimental results in Phys. Rev. Lett. 105, 135302 (2010). It is shown that the dynamics of a spinor BEC initially prepared in an unstable Zeeman state mF=0 (|0>) can be understood by approximating the effective trapping potential for the state |+-1> with a cylindrical box potential. The resonances in the creation efficiency of these atom pairs can be traced back to excitation modes of this confinement. The understanding of these excitation modes allows for a detailed characterization of the symmetry breaking mechanism, showing how a twofold spontaneous breaking of spatial and spin symmetry can occur. In addition a detailed account of the experimental methods for the preparation and analysis of spinor quantum gases is given., 12 pages, 14 figures

Interferometers with atomic ensembles constitute an integral part of modern precision metrology. However, these interferometers are fundamentally restricted by the shot noise limit, which can only be overcome by creating quantum entanglement among the atoms. We used spin dynamics in Bose-Einstein condensates to create large ensembles of up to $10^4$ pair-correlated atoms with an interferometric sensitivity $-1.61^{+0.98}_{-1.1}$ dB beyond the shot noise limit. Our proof-of-principle results point the way toward a new generation of atom interferometers., main text plus supporting online material: 12 pages 9 figures

Spin-changing collisions may lead under proper conditions to the parametric amplification of matter waves in spinor Bose-Einstein condensates. Magnetic dipole-dipole interactions, although typically very weak in alkalimetal atoms, are shown to play a very relevant role in the amplification process. We show that these interactions may lead to a strong dependence of the amplification dynamics on the angle between the trap axis and the magnetic-field orientation. We analyze as well the important role played by magnetic-field gradients, which also modify strongly the amplification process. Magnetic-field gradients, hence, must be carefully controlled in future experiments, in order to observe clearly the effects of the dipolar interactions in the amplification dynamics. © 2010 The American Physical Society. DFG/SFB/407 DFG/EXC/QUEST ESF/EuroQUASAR

Parametric amplification of quantum fluctuations constitutes a fundamental mechanism for spontaneous symmetry breaking. In our experiments, a spinor condensate acts as a parametric amplifier of spin modes, resulting in a twofold spontaneous breaking of spatial and spin symmetry in the amplified clouds. Our experiments permit a precise analysis of the amplification in specific spatial Bessel-like modes, allowing for the detailed understanding of the double symmetry breaking. On resonances that create vortex-antivortex superpositions, we show that the cylindrical spatial symmetry is spontaneously broken, but phase squeezing prevents spin-symmetry breaking. If, however, nondegenerate spin modes contribute to the amplification, quantum interferences lead to spin-dependent density profiles and hence spontaneously-formed patterns in the longitudinal magnetization., Comment: 5 pages, 4 figures

A phase-locked diode-laser system based on master-slave coupling of two-dimensional vertical-cavity surface-emitting laser (VCSEL) arrays by injection locking is presented. Frequencies and phases are adjusted by laser-trimmed microresistors. Additional beam-transformation optics consisting of two diffractive optical elements (DOEs) and a Fourier lens concentrates most of the far-field power in a nearly diffraction-limited beam. Both the VCSEL array and the microlens array are monolithically integrated and mounted in a compact module. With an array of 21 slave lasers a system coherence of 95% (for several hours) and of nearly 90% (for several months) has been demonstrated without any active phase control. The scalability of the output power has been verified by locking of an array of 77 slave lasers with a system coherence of 78%. The optical system efficiency is 20-23%; with beam-transformation optics this efficiency could be improved to 44%.

Phase tuning of injection-locked single-mode vertical-cavity surface-emitting laser diodes (VCSELs) is investigated experimentally with two slave VCSELs being locked by a master VCSEL. By slightly varying the laser current and thereby the frequency within the locking range, a maximum phase shift of more than 0.8 /spl pi/ is achieved. The method is applicable to large injection-locked VCSEL arrays.