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Double‐negative refractive index materials have attracted sustained experimental and theoretical interest because they can display a range of surprising optical phenomena, including negative Doppler shifts and perfect lensing. Double‐negative indexes have been achieved experimentally in engineered metamaterials; however, these materials become increasingly challenging to fabricate at shorter wavelengths, and at optical wavelengths only 2D negative index materials have been achieved. Here, it is shown that a double‐negative index can occur in a natural material, near narrow optical transitions of dielectric crystals stoichiometric in a rare‐earth ion. Optical measurements of two candidate materials, the magnetically‐ordered erbium crystals, ErCl3 ·6H2O and 7LiErF4, which have ultra‐narrow optical linewidths of 3 GHz and 250 MHz, respectively, in the telecom band are presented. It is shown that the spectral density of 7LiErF4 is sufficient to achieve a negative index at 1530 nm. This material can enable the exploration of negative refractive index effects at optical wavelengths in a truly 3D, natural medium. [ABSTRACT FROM AUTHOR]

Space-like separation of entangled quantum states is a central concept in fundamental investigations of quantum mechanics and in quantum communication applications. Optical approaches are ubiquitous in the distribution of entanglement because entangled photons are easy to generate and transmit. However, extending this direct distribution beyond a range of a few hundred kilometres (1,2) to a worldwide network is prohibited by losses associated with scattering, diffraction and absorption during transmission. A proposal to overcome this range limitation is the quantum repeater protocol (3,4), which involves the distribution of entangled pairs of optical modes among many quantum memories stationed along the transmission channel. To be effective, the memories must store the quantum information encoded on the optical modes for times that are long compared to the direct optical transmission time of the channel (5). Here we measure a decoherence rate of 8 X [10.sup.-5] per second over 100 milliseconds, which is the time required for light transmission on a global scale. The measurements were performed on a ground-state hyperfine transition of europium ion dopants in yttrium orthosilicate ([sup.151][Eu.sup.3+]: [Y.sub.2]Si[O.sub.5]) using optically detected nuclear magnetic resonance techniques. The observed decoherence rate is at least an order of magnitude lower than that of any other system suitable for an optical quantum memory. Furthermore, by employing dynamic decoupling, a coherence time of 370 ± 60 minutes was achieved at 2 kelvin. It has been almost universally assumed that light is the best long-distance carrier for quantum information. However, the coherence time observed here is long enough that nuclear spins travelling at 9 kilometres per hour in a crystal would have a lower decoherence with distance than light in an optical fibre. This enables some very early approaches (6,7) to entanglement distribution to be revisited, in particular those in which the spins are transported rather than the light., Mapping optical quantum states onto the hyperfine states of rare-earth optical centres in crystals (8-14) is an exciting avenue for ensemble-based quantum memories for light. Rare-earth-doped crystals possess optical transitions [...]

We propose a protocol to preserve the spin state of rare-earth ions when they are optically cycled. This technique uses large magnetic fields to increase the probability of an optically excited ion returning to its initial spin state. This Zeeman enhanced cyclicity is shown to be applicable to non-Kramers ions in various crystals irrespective of the site symmetry. The specific example of Pr3+:Y2SiO5 is investigated to demonstrate that the protocol can create closed optical transitions even where the point group symmetry of the site is C1. In this example, the predicted cyclicity exceeds 104. This high level of cyclicity extends the usefulness of rare-earth ion crystals for applications in quantum and classical information processing. We explore the use of this technique to enable single-ion, spin-state optical readout and the creation of ensemble-based spectral features that are robust against optical cycling. [ABSTRACT FROM AUTHOR]