The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schrödinger's famous remark about it [Proc. Camb. Phil. Soc. 31, 555 (1935)], prompts examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments, and report here values of the Bell parameter greater than B = 2.54. This is many standard deviations outside the limit B = 2 established by the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit B = 2.828.... These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it.Introduction: For many decades the term "entanglement" has been attached to the world of quantum mechanics [1]. However, it is true that non-quantum optical entanglement can exist (realized very early by Spreeuw [2]) and its applications have concrete consequences. These are based on entanglements between two, or more than two, degrees of freedom, which are easily avalable classically [2][3][4][5][6]. Multi-entanglements of the same kind are also being explored quantum mechanically [7]. Applications in the classical domain have included, for example, resolution of a long-standing issue concerning Mueller matrices [8], an alternative interpretation of the degree of polarization [9], introduction of the Bell measure as a new index of coherence in optics [10], and innovations in polarization metrology [11]. Here we present theoretical and experimental results extending these results by showing that probabilistic classical optical fields can exhibit violations of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [12] of quantum strength. This is evidence of a new kind that asks for reconsideration of the common understanding that Bell violation signals quantum physics. We emphasize that our discussion focuses on non-quantum entanglement of nondeterministic classical optical fields, and does not engage issues such as non-locality that are important for some applications in quantum information.The observations and applications of non-quantum wave entanglement noted above [2-6, 8-11] exploited nonseparable correlations among two or more modes or degrees of freedom (DOF) of optical wave fields. Nonseparable correlations among modes are an example of entanglement [13], but are not enough for our present purpose. In addition, we want to conform to three criteria that Shimony has identified for Bell tests [1], facts of quantum Nature that must be satisfied when examining possible tests of the quantum-classical border. Fortuitously, the ergodic stochastic optical fields of the classical theory of partial coherence and partial polarization (see Wolf [15]) satisfy these criteria fully (see Suppl. Materials [16]), and we have used such fields as our test bed. Background Theory: We will deal here only wit...

Quantum optics and classical optics are linked in ways that are becoming apparent as a result of numerous recent detailed examinations of the relationships that elementary notions of optics have with each other. These elementary notions include interference, polarization, coherence, complementarity and entanglement. All of them are present in both quantum and classical optics. They have historic origins, and at least partly for this reason not all of them have quantitative definitions that are universally accepted. This makes further investigation into their engagement in optics very desirable. We pay particular attention to effects that arise from the mere co-existence of separately identifiable and readily available vector spaces. Exploitation of these vector-space relationships are shown to have unfamiliar theoretical implications and new options for observation. It is our goal to bring emerging quantum-classical links into wider view and to indicate directions in which forthcoming and future work will promote discussion and lead to unified understanding.

Compact cold-atom sensors depend on vacuum technology. One of the major limitations to miniaturizing these sensors is the active pumps—typically ion pumps—that are required to sustain the low pressure needed for laser cooling. Although passively pumped chambers have been proposed as a solution to this problem, technical challenges have prevented successful operation at the levels needed for cold-atom experiments. The authors present the first demonstration of a vacuum package successfully independent of ion pumps for more than a week; their vacuum package is capable of sustaining a cloud of cold atoms in a magneto-optical trap (MOT) for greater than 200 days using only non-evaporable getters and a rubidium dispenser. Measurements of the MOT lifetime indicate that the package maintains a pressure of better than 2×10−7 Torr. This result will significantly enable the development of compact atomic sensors, including those sensitive to magnetic fields, where the absence of an ion pump will be advantageous.

We present an atomic prism spectrometer that utilizes the steep linear dispersion between two strongly absorbing hyperfine resonances of rubidium. We resolve spectral lines 50 MHz apart and, utilizing a larger part of the available spectrum than only between the two resonances, we spatially separate collinear pump, signal and idler beams resulting from a four-wave mixing process. Due to the high transparency possible between the resonances, these results have applications in the filtering of narrow band entangled photons and interaction free measurements.

Slow-light media are of interest in the context of quantum computing and enhanced measurement of quantum effects, with particular emphasis on using slow-light with single photons. We use light-inflight imaging with a single photon avalanche diode camera-array to image in situ pulse propagation through a slow light medium consisting of heated rubidium vapour. Light-in-flight imaging of slow light propagation enables direct visualisation of a series of physical effects including simultaneous observation of spatial pulse compression and temporal pulse dispersion. Additionally, the singlephoton nature of the camera allows for observation of the group velocity of single photons with measured single-photon fractional delays greater than 1 over 1 cm of propagation.