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We demonstrate direct coupling between phonons and diamond nitrogen-vacancy (NV) center spins by driving spin transitions with mechanically generated harmonic strain at room temperature. The amplitude of the mechanically driven spin signal varies with the spatial periodicity of the stress standing wave within the diamond substrate, verifying that we drive NV center spins mechanically. These spin-phonon interactions could offer a route to quantum spin control of magnetically forbidden transitions, which would enhance NV-based quantum metrology, grant access to direct transitions between all of the spin-1 quantum states of the NV center, and provide a platform to study spin-phonon interactions at the level of a few interacting spins.

Coherent control of the nitrogen-vacancy (NV) center in diamond's triplet spin state has traditionally been accomplished with resonant ac magnetic fields under the constraint of the magnetic dipole selection rule, which forbids direct control of the |−1 ↔ |+1 spin transition. We show that high-frequency stress resonant with the spin state splitting can coherently control NV center spins within this subspace. Using a bulk-mode mechanical microresonator fabricated from single-crystal diamond, we apply intense ac stress to the diamond substrate and observe mechanically driven Rabi oscillations between the |−1 and |+1 states of an NV center spin ensemble. Additionally, we measure the inhomogeneous spin dephasing time (T * 2 ) of the spin ensemble using a mechanical Ramsey sequence and compare it to the dephasing times measured with a magnetic Ramsey sequence for each of the three spin qubit combinations available within the NV center ground state.These results demonstrate coherent spin driving with a mechanical resonator and could enable the creation of a phase-sensitive ∆-system within the NV center ground state. Here we use a mechanical microresonator to apply a large amplitude ac stress to a single crystal diamond. Building on recent spectroscopy experiments [8], we tune the frequency of this stress wave into resonance with the |(m s =) − 1 ↔ |+1 spin transition to mechanically drive Rabi oscillations of an NV center spin ensemble. Using this capability, we measure the inhomogeneous dephasing time for an ensemble of mechanically controlled NV center spin qubits to be T * 2 = 0.45±0.05 µs and compare this result to T * 2 for magnetically driven qubits constructed from the same NV center ensemble. We find that the mechanically driven {−1, +1} qubit coherence is similar to that of a magnetically driven {−1, +1} qubit, and these {−1, +1} qubits dephase twice as quickly as magnetically driven {0, −1} or {+1, 0} qubits.NV centers couple to mechanical stress (σ ⊥ and σ ) and magnetic fields (B ⊥ and B ) 2 through their ground-state spin Hamiltonian (shown schematically in Fig. 1a)where D 0 /2π = 2.87 GHz is the zero-field splitting, γ N V /2π = 2.8 MHz/G is the gyromagnetic ratio, ⊥ /2π = 0.015 MHz/MPa and /2π = 0.012 MHz/MPa are the perpendicular and axial stress coupling constants [10,14], P/2π = −4.945 MHz and A /2π = −2.166 MHz are the hyperfine parameters [15][16][17], and S x , S y , S z (I x , I y , I z ) are the x, y, and z components of the electronic (nuclear) spin-1 operator. The NV center symmetry axis defines the z-axis of our coordinate system as depicted in Fig. 1b In this work, we use two devices, both fabricated from type IIa, 100 "optical grade" diamonds purchased from Element Six. These samples are specified to contain fewer than 1 ppm nitrogen impurities, and each contained a native NV ensemble as received. The first sample, Sample A, has an NV center density of ∼ 110 NVs/µm 3 , while Sample B has a density of ∼ 120 NVs/µm 3 . To generate the large amplitude, high-frequency stress waves neede...

Inhomogeneous dephasing from uncontrolled environmental noise can limit the coherence of a quantum sensor or qubit. For solid state spin qubits such as the nitrogen-vacancy (NV) center in diamond, a dominant source of environmental noise is magnetic field fluctuations due to nearby paramagnetic impurities and instabilities in a magnetic bias field. In this work, we use ac stress generated by a diamond mechanical resonator to engineer a dressed spin basis in which a single NV center qubit is less sensitive to its magnetic environment. For a qubit in the thermally isolated subspace of this protected basis, we prolong the dephasing time T * 2 from 2.7 ± 0.1 µs to 15 ± 1 µs by dressing with a Ω = 581 ± 2 kHz mechanical Rabi field. Furthermore, we develop a model that quantitatively predicts the relationship between Ω and T * 2 in the dressed basis. Our model suggests that a combination of magnetic field fluctuations and hyperfine coupling to nearby nuclear spins limits the protected coherence time over the range of Ω accessed here. We show that amplitude noise in Ω will dominate the dephasing for larger driving fields.PACS numbers: 76.30. Mi, 63.20.kp, 76.60.Jx The triplet spin of the nitrogen-vacancy (NV) center in diamond has become a foundational component in both quantum metrology and future quantum information technologies. For sensing, the inhomogeneous dephasing time T * 2 of an NV center spin qubit can limit sensitivity to quasi-static fields. For quantum information applications, T * 2 can limit the number and the duration of gate operations that a qubit can undergo. Pulsed dynamical decoupling (PDD) techniques based on the principle of spin echoes refocus inhomogeneous dephasing and can extend T * 2 to the homogeneous spin dephasing time T 2 or longer [1][2][3][4][5][6]. These periodic pulse sequences enable precision sensing and long-lived quantum states, but they come with drawbacks. They usually limit sensing to a narrow bandwidth and erase signal built up from quasistatic fields. Moreover, commuting echo pulses with gate operations makes decoupling during multi-qubit gates a nontrivial task [7].Continuous dynamical decoupling (CDD) offers an alternative method for prolonging T * 2 that can be used when the limitations of PDD become too restrictive. NV center CDD protocols forego the standard Zeeman spin state basis {(m s =) + 1, 0, −1} in favor of an engineered basis in which the "dressed" eigenstates are less sensitive to environmental noise than the bare spin states [8][9][10][11][12][13][14][15][16]. For an NV center spin qubit, magnetic field fluctuations from nearby paramagnetic impurities and instabilities in a magnetic bias field typically dominate dephasing. A qubit composed of dressed states designed to be more robust to these fluctuations could have a prolonged T * 2 and could be used for precision sensing of quasi-static, nonmagnetic fields such as temperature [17] or strain. For quantum information processing, CDD allows decoupling to continue during gate operations, thus protecting both...

Efficient detection of the magnetic state at nanoscale dimensions is an important step to utilize spin logic devices for computing. Magnetoresistance effects have been hitherto used in magnetic state detection, but they suffer from energetically unfavorable scaling and do not generate an electromotive force that can be used to drive a circuit element for logic device applications. Here, we experimentally show that a favorable miniaturization law is possible via the use of spin-Hall detection of the in-plane magnetic state of a magnet. This scaling law allows us to obtain a giant signal by spin Hall effect in CoFe/Pt nanostructures and quantify an effective spin-to-charge conversion rate for the CoFe/Pt system. The spin-to-charge conversion can be described as a current source with an internal resistance, i.e., it generates an electromotive force that can be used to drive computing circuits. We predict that the spin-orbit detection of magnetic states can reach high efficiency at reduced dimensions, paving the way for scalable spin-orbit logic devices and memories.Modern computing transistor technology is scaled to tens of nanometers 1 in lateral dimensions driven by the favorable miniaturization (Moore's Law) 2 . Such a favorable miniaturization 3 is an essential requirement for enabling spin logic 4-7 in computing but it has so far been a missing focus in spintronics. In particular, energy efficient detection of the magnetic state at the nanoscale dimensions is an important step to realize spin logic devices for computing. Up to now, magnetic state sensing techniques have relied on magnetoresistances such as anisotropic magnetoresistance (AMR) 8 , giant magnetoresistance (GMR) 9,10 , colossal magnetoresistance (CMR) 11 , and tunneling magnetoresistance (TMR) 12 . Even if TMR has been steadily improved to large values (>1000%) 13 , the magnetoresistance techniques are unfavorable in terms of energy for sensing a magnetic state because the resistance of the device increases quadratically when scaling down the area of the device 14 . Also, importantly, magnetoresistance techniques cannot generate an electromotive force (i.e., an electric current) that can be used to drive another circuit element, a requirement for a