Quantum mechanics predicts that the equilibrium state of a resistive electrical circuit contains a dissipationless current. This persistent current has been the focus of considerable theoretical and experimental work, but its basic properties remain a topic of controversy. The main experimental challenges in studying persistent currents have been the small signals they produce and their exceptional sensitivity to their environment. To address these issues we have developed a new technique for detecting persistent currents which offers greatly improved sensitivity and reduced measurement back action. This allows us to measure the persistent current in metal rings over a wider range of temperature, ring size, and magnetic field than has been possible previously. We find that measurements of both a single ring and arrays of rings agree well with calculations based on a model of non-interacting electrons.An electrical current induced in a resistive circuit will rapidly decay in the absence of an applied voltage. This decay reflects the tendency of the circuit's electrons to dissipate energy and relax to their ground state. However quantum mechanics predicts that the electrons' many-body ground state (and, at finite temperature, their thermal equilibrium state) may itself contain a "persistent" current which flows through the resistive circuit without dissipating energy or decaying. A dissipationless equilibrium current flowing through a resistive circuit is highly counterintuitive, but it has a familiar analog in atomic physics: some atomic species' electronic ground states possess non-zero orbital angular momentum, equivalent to a current circulating around the atom.Theoretical treatments of persistent currents (PC) in resistive metal rings have been developed over a number of decades (see [1,2] and references therein). Calculations which take 1

Mechanical systems can be influenced by a wide variety of small forces, ranging from gravitational to optical, electrical, and magnetic. When mechanical resonators are scaled down to nanometer-scale dimensions, these forces can be harnessed to enable coupling to individual quantum systems. We demonstrate that the coherent evolution of a single electronic spin associated with a nitrogen vacancy center in diamond can be coupled to the motion of a magnetized mechanical resonator. Coherent manipulation of the spin is used to sense driven and Brownian motion of the resonator under ambient conditions with a precision below 6 picometers. With future improvements, this technique could be used to detect mechanical zero-point fluctuations, realize strong spin-phonon coupling at a single quantum level, and implement quantum spin transducers.

The development of hybrid quantum systems is central to the advancement of emerging quantum technologies, including quantum information science and quantum-assisted sensing. The recent demonstration of high-quality single-crystal diamond resonators has led to significant interest in a hybrid system consisting of nitrogen–vacancy centre spins that interact with the resonant phonon modes of a macroscopic mechanical resonator through crystal strain. However, the nitrogen–vacancy spin–strain interaction has not been well characterized. Here, we demonstrate dynamic, strain-mediated coupling of the mechanical motion of a diamond cantilever to the spin of an embedded nitrogen–vacancy centre. Via quantum control of the spin, we quantitatively characterize the axial and transverse strain sensitivities of the nitrogen–vacancy ground-state spin. The nitrogen–vacancy centre is an atomic scale sensor and we demonstrate spin-based strain imaging with a strain sensitivity of 3 × 10−6 strain Hz−1/2. Finally, we show how this spin-resonator system could enable coherent spin–phonon interactions in the quantum regime.

We demonstrate nanometer-precision depth control of nitrogen-vacancy (NV) center creation near the surface of synthetic diamond using an in situ nitrogen delta-doping technique during plasma-enhanced chemical vapor deposition. Despite their proximity to the surface, doped NV centers with depths (d) ranging from 5 - 100 nm display long spin coherence times, T2 > 100 \mus at d = 5 nm and T2 > 600 \mus at d \geq 50 nm. The consistently long spin coherence observed in such shallow NV centers enables applications such as atomic-scale external spin sensing and hybrid quantum architectures.Comment: 14 pages, 4 figures, 11 pages of additional supplementary materia