Controlling the coherence of a diamond spin qubit through strain engineering

TL;DR

This paper demonstrates how strain engineering in diamond can suppress thermal phonon interactions in silicon-vacancy centers, enhancing quantum coherence without cooling, and enabling potential phonon-based quantum gates.

Contribution

It introduces strain control as a method to mitigate phonon-induced decoherence in solid-state qubits, offering optical tunability and improved spin coherence.

Findings

Strain significantly affects SiV electronic levels and phonon interactions.

Strain control enhances spin coherence times.

Potential for strong spin-phonon coupling and quantum gate implementation.

Abstract

The uncontrolled interaction of a quantum system with its environment is detrimental for quantum coherence. In the context of solid-state qubits, techniques to mitigate the impact of fluctuating electric and magnetic fields from the environment are well-developed. In contrast, suppression of decoherence from thermal lattice vibrations is typically achieved only by lowering the temperature of operation. Here, we use a nano-electro-mechanical system (NEMS) to mitigate the effect of thermal phonons on a solid-state quantum emitter without changing the system temperature. We study the silicon-vacancy (SiV) colour centre in diamond which has optical and spin transitions that are highly sensitive to phonons. First, we show that its electronic orbitals are highly susceptible to local strain, leading to its high sensitivity to phonons. By controlling the strain environment, we manipulate the electronic levels of the emitter to probe, control, and eventually, suppress its interaction with the thermal phonon bath. Strain control allows for both an impressive range of optical tunability and significantly improved spin coherence. Finally, our findings indicate that it may be possible to achieve strong coupling between the SiV spin and single phonons, which can lead to the realisation of phonon-mediated quantum gates and nonlinear quantum phononics.

Full text

††thanks: These authors contributed equally††thanks: These authors contributed equally††thanks: These authors contributed equally

Controlling the coherence of a diamond spin qubit through strain engineering

Young-Ik Sohn

  

Srujan Meesala

John A. Paulson School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA

  

Benjamin Pingault

Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK

  

Haig A. Atikian

John A. Paulson School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA

  

Jeffrey Holzgrafe

John A. Paulson School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA

Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK

  

Mustafa Gündoğan

Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK

  

Camille Stavrakas

Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK

  

Megan J. Stanley

Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK

  

Alp Sipahigil

Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA

  

Joonhee Choi

John A. Paulson School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA

Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA

  

Mian Zhang

John A. Paulson School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA

  

Jose L. Pacheco

Sandia National Laboratories, Albuquerque, NM 87185, USA

  

John Abraham

Sandia National Laboratories, Albuquerque, NM 87185, USA

  

Edward Bielejec

Sandia National Laboratories, Albuquerque, NM 87185, USA

  

Mikhail D. Lukin

Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA

  

Mete Atatüre

Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK

  

Marko Lončar

John A. Paulson School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA

The uncontrolled interaction of a quantum system with its environment is detrimental for quantum coherence. In the context of solid-state qubits, techniques to mitigate the impact of fluctuating electric YiwenNanoLett ; Shanying ; IBM.glycerol and magnetic fields balasubramanian ; phosphorus.in.si ; optimal.dd ; dobrovitskii ; DD.review from the environment are well-developed. In contrast, suppression of decoherence from thermal lattice vibrations is typically achieved only by lowering the temperature of operation. Here, we use a nano-electro-mechanical system (NEMS) to mitigate the effect of thermal phonons on a solid-state quantum emitter without changing the system temperature. We study the silicon-vacancy (SiV) colour centre in diamond which has optical and spin transitions that are highly sensitive to phonons PhysRevLett.113.263601 ; PhysRevLett.113.263602 ; BeckerUltraFast ; SiVMicrowave ; SiVNJP . First, we show that its electronic orbitals are highly susceptible to local strain, leading to its high sensitivity to phonons. By controlling the strain environment, we manipulate the electronic levels of the emitter to probe, control, and eventually, suppress its interaction with the thermal phonon bath. Strain control allows for both an impressive range of optical tunability and significantly improved spin coherence. Finally, our findings indicate that it may be possible to achieve strong coupling between the SiV spin and single phonons, which can lead to the realisation of phonon-mediated quantum gates SAWquantum and nonlinear quantum phononics TahanPhonodynamics ; Lodahl ; Cleland ; Chu.Transmon .

Phonons couple to solid-state emitters directly through periodic deformation of the electronic wavefunctions stoneham . Electron-phonon interactions are responsible for relaxation and decoherence processes in a variety of quantum systems HansonReview ; qd.phonon.decay ; SiVNJP ; fuchs.motional.narrowing ; siyushev.gev ; bhaskar.gev ; orbach . In particular, for systems with spin-orbit coupling, phonon-mediated processes can demand operation at sub-Kelvin temperatures SiV.fridge ; faraon.cavity , or the use of magnetic fields of several Tesla kramers.highBfield to achieve long spin relaxation and coherence times. This requires cryogenic setups that are significantly more complex than common helium-4 cryostats employed to obtain coherent optical photons from solid state emitters. In contrast, our approach takes advantage of the fact that the large electron-phonon coupling responsible for such deocherence processes fundamentally arises from a high susceptibility of the electronic orbitals to lattice strain. We use this property to quench the effect of the thermal phonon bath on a single electronic spin qubit without lowering the operating temperature. Our experiments are performed on the negatively charged silicon-vacancy (SiV) centre in diamond, an emerging platform for photonic quantum networks SiVcqed with remarkable optical properties owing to its inversion symmetry AlpHOM . This inversion symmetry is also responsible for the particular electronic structure of the SiV, shown in Fig. 1a, with similar ground-state (GS) and excited-state (ES) manifolds, each containing two distinct orbital branches Hepp2014 . Orbital degeneracy in each manifold is lifted by spin-orbit coupling: $|1\rangle,|2\rangle$ in the GS split by 46 GHz, and $|3\rangle,|4\rangle$ in the ES split by 255 GHz in the absence of strain. Phonons with frequencies corresponding to these splittings can drive orbital transitions within the ground and excited manifolds SiVNJP .

As a first step towards controlling the electron-phonon interaction, we investigate the effect of static strain on these orbitals through strain-dependent photoluminescence excitation (PLE) of the optical transitions labelled A, B, C and D at 4 K. Static strain control at the location of the emitter is achieved with a NEMS device, a monolithic single-crystal diamond cantilever with metal electrodes patterned above and below it SuppInfo , as shown in the scanning electron microscope (SEM) image in Fig. 1b. An opening in the top electrode allows optical access to SiV centres located in an array (inset of Fig. 1b), precisely positioned by focused ion-beam (FIB) implantation of 28Si*+* ions japan.fib ; dirk.fib . A DC voltage applied across the electrodes deflects the cantilever downwards due to electrostatic attraction and generates controllable static strain oriented predominantly along the long axis of the cantilever. The strain profile can be simulated numerically via the finite-element-method (FEM), as shown in Fig. 1c. Of the two possible orientations of SiVs in our device, we address those with transverse orientation (labelled blue, and shown in detail in inset of Fig. 1c), which predominantly experience strain in the plane normal to their highest symmetry axis ($E_{g}$ $-$ symmetric strain Hepp.thesis ). Upon applying strain, transitions A and D shift towards shorter and longer wavelengths, respectively. These shifts indicate increasing GS and ES splittings as shown in Fig. 2a. This result is consistent with a previous experiment on a dense ensemble of SiVs Sternschulte . The variations in GS and ES splittings shown in Fig. 2a are quadratic at low strain, and linear at high strain. This indicates that $E_{g}$ $-$ symmetric strain mixes orbitals within the GS and ES manifolds, and thus phonon modes with corresponding strain components can induce resonant transitions between these orbitals. In contrast, strain along the SiV axis ($A_{1g}$ $-$ symmetric strain) is found to leave the GS and ES splittings unchanged, and therefore cannot cause electronic transitions. Complete characterisation of the strain response and relevant group theory analysis are detailed elsewhere SiVPRB .

With our device we can tune the splitting of the orbitals in the GS manifold from 46 GHz to typically up to 500 GHz, and in the best case, up to 1.2 THz SuppInfo . In doing so, we can probe the interaction between SiV and the phonon bath at different frequencies by measuring the thermal relaxation rate of the orbital with a time-resolved pump-probe technique (Fig. 2b). Measurements are performed in the frequency range $\Delta_{\mathrm{gs}}=$ 46 GHz to 110 GHz where this technique can be applied. The total relaxation rate is a sum of the rates of phonon absorption, $\gamma_{\mathrm{up}}$, and emission, $\gamma_{\mathrm{down}}$ (shown in Fig. 1a), which can be individually extracted using the theory described in SuppInfo . Over the range of $\Delta_{\mathrm{gs}}$ measured, phonon processes in both directions are observed to accelerate with increasing orbital splitting, thus indicating that the number of acoustic modes resonant with the GS splitting, i.e. the phonon density of states (DOS) at this frequency, increases with an expected dependence in $\Delta_{\mathrm{gs}}^{n}$ ($n$ depends on the geometry of material seen by resonant phonons SuppInfo ). However, if the orbital splitting is increased far above 120 GHz (at temperature $T$ = 4 K) as plotted in Fig. 2c, the phonon absorption rate ($\gamma_{\mathrm{up}}$) is theoretically expected to reverse its initial trend. In this regime, the polynomial increase in phonon DOS is outweighed by the exponentially decrease in thermal phonon occupation ($\sim\mathrm{exp}(-h\Delta_{\mathrm{gs}}/k_{B}T)$) SiVNJP , and consequently $\gamma_{\mathrm{up}}$ is rapidly quenched.

Such a suppression of phonon absorption at high strain can improve the spin coherence of the emitter. In the presence of magnetic field, the SiV electronic levels further split into spin sub-levels and provide an optically accessible spin qubit as shown in Fig. 3a PhysRevLett.113.263601 ; PhysRevLett.113.263602 ; Muller2014 . We use coherent population trapping (CPT) through simultaneous resonant laser excitation of the optical transitions labeled C1 and C2 to pump the SiV into a dark state, a coherent superposition of the spin sub-levels $|1\downarrow\rangle$, $|1\uparrow\rangle$. When the two-photon detuning is scanned, preparation of the dark state results in a fluorescence dip, whose linewidth is determined by the optical driving and spin dephasing rates. At low laser powers, the linewidth is limited by spin dephasing, which is dominated by phonon-mediated transitions within the GS manifold SiVNJP ; SuppInfo . In Fig. 3b, as the dark resonance narrows down due to prolonged spin coherence with increasing strain, we reveal a fine structure not visible before. Further measurements in Ref. SuppInfo suggest that the presence of two resonances is due to interaction of the SiV electron spin with a neighbouring spin such as a 13C nuclear spin. This indicates the possibility of achieving a local register of qubits as has been demonstrated with nitrogen vacancy (NV) centres Childress13102006 . Fig. 3c shows the decreasing linewidths of the CPT resonances with increasing GS orbital splitting, indicating an improved spin coherence time. Beyond a GS splitting of $\sim$400 GHz, the linewidths saturate at $\sim$1 MHz. At the highest strain condition, we perform a power dependent CPT measurement to eliminate the contribution of power broadening, and extract a spin coherence time of $T_{2}^{*}=0.25\pm 0.02\,\mathrm{\mu s}$ (compared with $T_{2}^{*}$ = 40 ns without strain control PhysRevLett.113.263601 ; PhysRevLett.113.263602 ). This saturation of $T_{2}^{*}$ suggests the mitigation of the primary dephasing source, single-phonon transitions between the GS orbitals, and the emergence of a secondary dephasing mechanism such as slowly varying magnetic fields from naturally abundant (1.1%) 13C nuclear spins in diamond. Our longest $T_{2}^{*}=0.25\pm 0.02\,\mathrm{\mu s}$ is on par with that of the NV center without dynamical decoupling balasubramanian ; emre.cpt , and of low-strain SiVs operated at a much lower temperature of 100 mK SiV.fridge , the conventional approach to suppress phonon-mediated dephasing.

In conclusion, we use a nano-electro-mechanical system to probe and control the interaction between a single electronic spin and the phonon bath of its solid-state environment. In doing so, we demonstrate six-fold prolongation of spin coherence by suppressing phonon-mediated dephasing as the dominant decoherence mechanism. As a next step, we can further improve the spin coherence by cancelling the effect of slowly-varying non-Markovian noise from the environment SiV.fridge using dynamical decoupling techniques that are well-studied with other spin systems optimal.dd ; dobrovitskii ; Childress13102006 . Our strain engineering approach can be applied to overcome phonon-induced decoherence in other emitters such as emerging inversion-symmetric centers in diamond siyushev.gev ; bhaskar.gev ; iwasaki.snv ; tchernij.snv , Kramers rare earth ions orbach ; faraon.cavity ; kramers.highBfield , and in general, systems with spin-orbit coupling in their ground state. High strain needed to quench phonon processes can be achieved simply by deposition of a thin film thin.film , which passively stresses the underlying crystal. A NEMS platform can provide the added benefit of active wavelength tuning, which can enable generation of indistinguishable photons from multiple emitters, and hence scalable photonic quantum networks SiVcqed ; BurekFiber . Another natural extension of our work is coherent coupling of the SiV spin to a well-defined mechanical mode, which will enable the use of phonons as quantum resource. In particular, we can combine the large strain susceptibility of the SiV SiVPRB with mechanical resonators of dimensions close to the phonon wavelength, such as optomechanical crystals BurekOMC to obtain orders of magnitude larger spin-phonon interaction strengths compared with previous works GregHBAR ; AniaCantilever ; PatrickCantilever ; LoncarCantilever ; Shimon ; Arcizet , leading to strong spin-phonon coupling. In this regime, one can realise phonon-mediated two-qubit gates SAWquantum analogous to those implemented with trapped ions cirac.zoller , and achieve quantum non-linearities required to deterministically generate single phonons and non-classical mechanical states TahanPhonodynamics ; Lodahl ; PhononCounting ; Cleland ; Chu.Transmon , a long sought-after goal since phonons can be used to interface spins with other quantum systems such as superconducting qubits hybrid .

Acknowledgements

This work was supported by STC Center for Integrated Quantum Materials (NSF Grant No. DMR-1231319), ONR MURI on Quantum Optomechanics (Award No. N00014-15-1-2761), NSF EFRI ACQUIRE (Award No. 5710004174), the University of Cambridge, the ERC Consolidator Grant PHOENICS, and the EPSRC Quantum Technology Hub NQIT (EP/M013243/1). B.P. thanks Wolfson College (University of Cambridge) for support through a research fellowship. Device fabrication was performed in part at the Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Infrastructure Network (NNIN), which is supported by the National Science Foundation under NSF award no. ECS-0335765. CNS is part of Harvard University. Focused ion beam implantation was performed under the Laboratory Directed Research and Development Program and the Center for Integrated Nanotechnologies, an Office of Science (SC) user facility at Sandia National Laboratories operated for the DOE (contract DE-NA0003525) by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc. We thank D. Perry for performing the focused ion beam implantation, and K. De Greve and M. W. Doherty for helpful discussions.