Long-range quantum entanglement in dielectric mu-near-zero metamaterials

Entanglement is paramount in quantum information processing. Many quantum systems suffer from spatial decoherence in distances over a wavelength and cannot be sustained over short time periods due to dissipation. However, long range solutions are required for the development of quantum information processing on chip. Photonic reservoirs mediating the interactions between qubits and their environment are suggested. Recent research takes advantage of extended wavelength inside near-zero refractive index media to solve the long-range problem along with less sensitivity on the position of quantum emitters. However, those recent proposals use plasmonic epsilon near-zero waveguides that are intrinsically lossy. Here, we propose a fully dielectric platform, compatible with the Nitrogen Vacancy (NV) diamond centers on-chip technology, to drastically improve the range of entanglement over 17 free-space wavelengths, or approximatively 12.5 µm, using mu near-zero metamaterials. We evaluate transient and steady state concurrence demonstrating an order of magnitude enhancement compared to previous works. This is, to the best of our knowledge, the first time that such a long distance is reported using this strategy. Moreover, value of the zero time delay second order correlation function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>g</mml:mi></mml:mrow> <mml:mrow><mml:mn>12</mml:mn></mml:mrow> <mml:mrow><mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo></mml:mrow> </mml:msubsup> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>)</mml:mo></mml:mrow> </mml:math> are provided, showing antibunching signature correlated with a high degree of concurrence.