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arXiv:0910.4216 · Physical Review A

Single atom-scale diamond defect allows a large Aharonov-Casher phase

Dougal Maclaurin, Andrew D. Greentree, Jared H. Cole, Lloyd C. L. Hollenberg, A. Martin

Published Oct 21, 2009• 10 citations
arXivHTMLPDF

Abstract

We propose an experiment that would produce and measure a large Aharonov-Casher (AC) phase in a solid-state system under macroscopic motion. A diamond crystal is mounted on a spinning disk in the presence of a uniform electric field. Internal magnetic states of a single nitrogen-vacancy $(\text{N-}V)$ defect, replacing interferometer trajectories, are coherently controlled by microwave pulses. The AC phase shift is manifested as a relative phase, of up to 17 radians, between components of a superposition of magnetic substates, which is two orders of magnitude larger than that measured in any other atom-scale quantum system.

DOI
10.1103/physreva.80.040104

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We propose an experiment that would produce and measure a large Aharonov-Casher (AC) phase in a solid-state system under macroscopic motion. A diamond crystal is mounted on a spinning disk in the presence of a uniform electric field. Internal magnetic states of a single nitrogen-vacancy (N-V)(\text{N-}V)(N-V) defect, replacing interferometer trajectories, are coherently controlled by microwave pulses. The AC phase shift is manifested as a relative phase, of up to 17 radians, between components of a superposition of magnetic substates, which is two orders of magnitude larger than that measured in any other atom-scale quantum system.
We demonstrate that the internal magnetic states of a single nitrogen-vacancy defect, within a rotating diamond crystal, acquire geometric phases. The geometric phase shift is manifest as a relative phase between components of a superposition of magnetic substates. We demonstrate that under reasonable experimental conditions a phase shift of up to four radians could be measured. Such a measurement of the accumulation of a geometric phase, due to macroscopic rotation, would be the first for a single atom-scale quantum system.
The Nitrogen-Vacancy(NV) center has recently emerged as a powerful quantum system, combining the good coherence properties and control techniques of atomic systems with the small size and fabrication capabilities of solid-state devices. We report on a measurement of a single electron-spin phase shift arising directly from physical rotation. This phase shift is observed by measuring the phase difference in a distortion microwave frequency of 2880 MHz, and it can accumulate nonlinearly in time. Carrier rotation information can be obtained by measuring the quantum geometric phase accumulation. We demonstrate quantum control of a NV center within a specific rotation system and a rotational period comparable to the NV spin coherence time T2*. These characteristics contribute as well to make this quantum system a sensitive and compact rotation sensor.
The force experienced by a spin in a magnetic field gradient underlies many proposals for hybrid quantum systems. These include schemes for mechanically mediated quantum gates, spin squeezing, searches for exotic forces, and motional superpositions for probing the interface between quantum and gravity. Yet, experimentally observing this spin-force for anything larger than atomic scales has proved challenging. In our work, we demonstrate controllable Center-of-Mass motion of a 128 mg128 \rm\: mg128mg diamagnetically levitated oscillator due to force from an ensemble of Nitrogen-Vacancy (NV) defects in diamond. We induce coherent motion in the oscillator by periodic optical initialisation of the NV spin states, achieving motional amplitudes exceeding 100 nm100 \rm\:nm100nm. Our results mark a key milestone towards spin-based engineering of motional states deep in the high-mass regime.
The nitrogen-vacancy (NV) center in diamond has garnered great interest over the past decade as its electronic spin shows promise as a quantum bit (qubit) and nanoscale sensor. Consisting of a substitutional nitrogen adjacent to a vacant site within the carbon lattice of diamond, this defect exhibits millisecond-long spin coherence times extending beyond room temperature, spin-dependent optical addressability, coupling to intrinsic and nearby nuclear spins, and it can be controlled and manipulated through electrical, magnetic, and optical means. In particular, at cryogenic temperatures (T < 25 K), the NV center's excited state becomes sharp and optically resolvable, providing a solid-state quantum optical testbed. In this thesis, I describe several experiments that explore this quantum optical interface to facilitate the development of a photonic network of single spins linked and controlled by light. We begin by exploring how electric fields tune the orbital levels within the NV center through the DC Stark effect, finding a surprising photo-induced field that aids in the ability to tune multiple NV centers' optical transitions to degeneracy. We then develop techniques to fully control the spin state of the NV center by coupling through a lambda system, an energy configuration consisting of two lower levels coupled to one of higher energy. When a lambda system is optically driven, the spin becomes trapped in a dark state, or the eigenstate of the system that is not coupled to the light fields through destructive interference, forming the basis for the various types of control demonstrated. We demonstrate arbitrary-basis initialization and readout of the spin state through coherent population trapping, as well as the ability to rotate about any arbitrary basis through stimulated Raman transitions. Combining these techniques, we measure the NV center's spin coherence through a completely optical measurement. We then extend these lambda system techniques to adiabatically move the dark state in trajectories around the Bloch sphere. Such trajectories accumulate a quantum mechanical phase that depends only on the geometry of the path enclosed, not on the energetics or time of the interaction. We characterize the interaction, measure this phase, known as Berry phase, and explore the limits of its control and resilience to noise. Finally, we demonstrate another all-optical control technique that uses strong ultrafast pulses of light to transfer the spin between the ground and excited states, deriving spin manipulation from the excited state dynamics. This technique also provides time-resolved spectroscopy of the excited state and its various decay and decoherence mechanisms. These experiments advance the progress toward the development of photonic networks coupling and controlling defects through light-matter interactions.
We use a combination of microwave fields and free precession to drive the spin of a nitrogen-vacancy (NV) center in diamond on different trajectories on the Bloch sphere and investigate the physical significance of the frame-dependent decomposition of the total phase into geometric and dynamic parts. The experiments are performed on a two-level subspace of the spin-1 ground state of the NV, where the Aharonov-Anandan geometric phase manifests itself as a global phase, and we use the third level of the NV ground-state triplet to detect it. We show that while the geometric Aharonov-Anandan phase retains its connection to the solid angle swept out by the evolving spin, it is generally accompanied by a dynamic phase that suppresses the geometric dependence of the system dynamics. These results offer insights into the physical significance of frame-dependent geometric phases.
Atom-scale defects in semiconductors are promising building blocks for quantum devices, but our understanding of their material-dependent electronic structure, optical interactions, and dissipation mechanisms is lacking. Using picosecond resonant pulses of light, we study the coherent orbital and spin dynamics of a single nitrogen-vacancy center in diamond over time scales spanning six orders of magnitude. We develop a time-domain quantum tomography technique to precisely map the defect's excited-state Hamiltonian and exploit the excited-state dynamics to control its ground-state spin with optical pulses alone. These techniques generalize to other optically addressable nanoscale spin systems and serve as powerful tools to characterize and control spin qubits for future applications in quantum technology.