Strain Coupling of a Nitrogen-Vacancy Center Spin to a Diamond Mechanical Oscillator

Abstract

We report on single electronic spins coupled to the motion of mechanical resonators by a novel mechanism based on crystal strain. Our device consists of single-crystal diamond cantilevers with embedded nitrogen-vacancy center spins. Using optically detected electron spin resonance, we determine the unknown spin-strain coupling constants and demonstrate that our system resides well within the resolved sideband regime. We realize coupling strengths exceeding 10 MHz under mechanical driving and show that our system has the potential to reach strong coupling. Our novel hybrid system forms a resource for future experiments on spin-based cantilever cooling and coherent spin-oscillator coupling. DOI: 10.1103/PhysRevLett.113.020503 PACS numbers: 03.67.Lx, 42.50.Wk, 76.30.Mi, 85.85.+j Recent years have brought significant advances in the control of nanoscale mechanical oscillators, which culminated in experiments to prepare such oscillators close to their quantum ground state [1,2] or a single-phonon excited state [3]. Generating and studying such states and further extending quantum control of macroscopic mechanical oscillators brings exciting perspectives for high precision sensing, quantum technologies [4], and fundamental studies of the quantum-to-classical crossover [5][6][7]. An attractive route towards these goals is to couple individual quantum two-level systems to mechanical oscillators and thereby enable efficient oscillator cooling [8] or state transfer [9] between a quantum system and oscillator in analogy to established concepts in ion trapping [10]. A prerequisite for most of these schemes [8,10,11] is the resolved sideband regime, where the transition between the two quantum states exhibits well-resolved, frequency-modulated sidebands at the oscillator eigenfrequency. Various hybrid systems are currently being explored in this context and include mechanical oscillators coupled to cold atoms [12], superconducting qubits [3], quantum dots [13,14], or solid-state spin systems [15,16]. None of these systems, however, have reached the resolved sideband regime thus far and novel approaches are needed to further advance quantum control of macroscopic mechanical systems.An important aspect that distinguishes existing hybrid systems is the physical mechanism they exploit to couple quantum system and oscillator. Coupling through electric [13], magnetic [15,16], or strain fields [14], as well as through optical forces [12] has been demonstrated as of now. Strain coupling is based on electronic level shifts [8,17] induced by crystal strain during mechanical motion and is particularly appealing in the context of hybrid systems. On one hand, strain coupling is predicted to result in interesting and unique system dynamics, such as spin squeezing [18] or phonon lasing [19] and can be used for mechanical spin driving [20]. On the other hand, strain coupling brings decisive technological advantages as it is intrinsic to the system. It thereby allows for monolithic and compact devices which are robust against manufacturi...

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