Reducing the instability of an optical lattice clock using multiple atomic ensembles

The stability of an optical atomic clock is a critical figure of merit for almost all clock applications. To this end, much optical atomic clock research has focused on reducing clock instability by increasing the atom number, lengthening the coherent interrogation times, and introducing entanglement to push beyond the standard quantum limit. In this work, we experimentally demonstrate an alternative approach to reducing clock instability using a phase estimation approach based on individually controlled atomic ensembles in a strontium (Sr) optical lattice clock. We first demonstrate joint Ramsey interrogation of two spatially-resolved atom ensembles that are out of phase with respect to each other, which we call "quadrature Ramsey spectroscopy," resulting in a factor of 1.36(5) reduction in absolute clock instability as measured with interleaved self-comparisons. We then leverage the rich hyperfine structure of ${}^{87}$Sr to realize independent coherent control over multiple ensembles with only global laser addressing. Finally, we utilize this independent control over 4 atom ensembles to implement a form of phase estimation, achieving a factor of greater than 3 enhancement in coherent interrogation time and a factor of 2.08(6) reduction in instability over an otherwise identical single ensemble clock with the same local oscillator and the same number of atoms. We expect that multi-ensemble protocols similar to those demonstrated here will result in reduction in the instability of any optical lattice clock with an interrogation time limited by the local oscillator.Comment: Main text: 9 pages, 4 figures. Appendix: 9 pages, 10 figures, 1 table. 74 references tota

Sensing distant nuclear spins with a single electron spin

We experimentally demonstrate the use of a single electronic spin to measure the quantum dynamics of distant individual nuclear spins from within a surrounding spin bath. Our technique exploits coherent control of the electron spin, allowing us to isolate and monitor nuclear spins weakly coupled to the electron spin. Specifically, we detect the evolution of distant individual carbon-13 nuclear spins coupled to single nitrogen vacancy centers in a diamond lattice with hyperfine couplings down to a factor of 8 below the electronic spin bare dephasing rate. Potential applications to nanoscale magnetic resonance imaging and quantum information processing are discussed.Comment: Corrected typos, updated references. 5 pages, 4 figures, and supplemental materia

Detection and control of individual nuclear spins using a weakly coupled electron spin

We experimentally isolate, characterize and coherently control up to six individual nuclear spins that are weakly coupled to an electron spin in diamond. Our method employs multi-pulse sequences on the electron spin that resonantly amplify the interaction with a selected nuclear spin and at the same time dynamically suppress decoherence caused by the rest of the spin bath. We are able to address nuclear spins with interaction strengths that are an order of magnitude smaller than the electron spin dephasing rate. Our results provide a route towards tomography with single-nuclear-spin sensitivity and greatly extend the number of available quantum bits for quantum information processing in diamond

Sensing Distant Nuclear Spins with a Single Electron Spin

We experimentally demonstrate the use of a single electronic spin to measure the quantum dynamics of distant individual nuclear spins from within a surrounding spin bath. Our technique exploits coherent control of the electron spin, allowing us to isolate and monitor nuclear spins weakly coupled to the electron spin. Specifically, we detect the evolution of distant individual C13 nuclear spins coupled to single nitrogen vacancy centers in a diamond lattice with hyperfine couplings down to a factor of 8 below the electronic spin bare dephasing rate. Potential applications to nanoscale magnetic resonance imaging and quantum information processing are discussed.Physic

Depth dependence of the radiative lifetime of shallow color centers in single crystalline diamond

Optically active defects in diamond are widely used as bright single-photon sources for quantum sensing, computing, and communication. For many applications, it is useful to place the emitter close to the diamond surface, where the radiative properties of the emitter are strongly modified by its dielectric environment. It is well-known that the radiative power from an electric dipole decreases as the emitter approaches an interface with a lower-index dielectric, leading to an increase in the radiative lifetime. For emitters in crystalline solids, modeling of this effect needs to take into account the crystal orientation and direction of the surface cut, which can greatly impact the emission characteristics. In this paper, we provide a framework for analyzing the emission rates of shallow (<100 nm) defects, in which optical transitions are derived from electric dipoles in a plane perpendicular to their spin axis. We present our calculations for the depth-dependent radiative lifetime for color centers in (100)-, (110)-, and (111)-cut diamond, which can be extended to other vacancy defects in diamond

A lab-based test of the gravitational redshift with a miniature clock network

Einstein's theory of general relativity predicts that when two clocks are compared using light, a clock at a higher gravitational potential will tick faster than an otherwise identical clock at a lower potential, an effect known as the gravitational redshift. This prediction has been tested by comparing separated atomic clocks over a wide range of height differences. Here we perform a laboratory-based, blinded test of the gravitational redshift using differential clock comparisons within an evenly spaced array of 5 atomic ensembles spanning a height difference of 1 cm. We measure a fractional frequency gradient of $[-12.4\pm0.7_{\rm{(stat)}}\pm2.4_{\rm{(sys)}}]\times10^{-19}/$cm, consistent with the expected gravitational redshift gradient of $-10.9\times10^{-19}/$cm. Our measurements can also be viewed as a demonstration of relativistic geodesy with millimeter scale resolution. These results illustrate how local-oscillator-independent differential clock comparisons can be harnessed for geodesy, and highlight their potential for emerging applications of optical atomic clocks such as searches for new physics, gravitational wave detection, the realization of entanglement enhanced clocks, and in explorations of the interplay between quantum mechanics and gravity.Comment: Main text: 22 pages, 4 figures, 1 table, 51 references. Extended data: 8 figures, 1 table. Methods: 20 pages, 9 reference

Measuring mechanical motion with a single spin

We study theoretically the measurement of a mechanical oscillator using a single two level system as a detector. In a recent experiment, we used a single electronic spin associated with a nitrogen vacancy center in diamond to probe the thermal motion of a magnetized cantilever at room temperature {Kolkowitz et al., Science 335, 1603 (2012)}. Here, we present a detailed analysis of the sensitivity limits of this technique, as well as the possibility to measure the zero point motion of the oscillator. Further, we discuss the issue of measurement backaction in sequential measurements and find that although backaction heating can occur, it does not prohibit the detection of zero point motion. Throughout the paper we focus on the experimental implementation of a nitrogen vacancy center coupled to a magnetic cantilever; however, our results are applicable to a wide class of spin-oscillator systems. Implications for preparation of nonclassical states of a mechanical oscillator are also discussed.Comment: 17 pages, 6 figure