Controlling the coherence of a diamond spin qubit through its strain environment

Abstract

The uncontrolled interaction of a quantum system with its environment is detrimental for quantum coherence. For quantum bits in the solid state, decoherence from thermal vibrations of the surrounding lattice can typically only be suppressed by lowering the temperature of operation. Here, we use a nano-electro-mechanical system to mitigate the effect of thermal phonons on a spin qubit - the silicon-vacancy colour centre in diamond - without changing the system temperature. By controlling the strain environment of the colour centre, we tune its electronic levels to probe, control, and eventually suppress the interaction of its spin with the thermal bath. Strain control provides both large tunability of the optical transitions and significantly improved spin coherence. Finally, our findings indicate the possibility to achieve strong coupling between the silicon-vacancy spin and single phonons, which can lead to the realisation of phonon-mediated quantum gates and nonlinear quantum phononics.

Fig. 1

Description of the SiV⁻ and NEMS system. a Electronic level structure of the SiV⁻ showing the mean zero phonon line (ZPL) wavelength, frequency splittings between orbital branches in the ground state (GS) and excited state (ES) (Δ_gs and Δ_es, respectively) at zero strain, and the four optical transitions A, B, C, and D. Also shown are single-phonon transitions in the GS and ES manifolds. b Scanning electron microscope (SEM) image of a representative diamond NEMS cantilever. Dark regions correspond to diamond, and light regions correspond to metal electrodes. Scale bar corresponds to 2 μm. (Inset) Confocal photoluminescence image of three adjacent cantilevers. The array of bright spots in each cantilever is fluorescence from SiV⁻ centres. Inset scale bar corresponds to 10 μm. c Simulation of the displacement of the cantilever due to the application of a DC voltage of 200 V between the top and bottom electrodes. The component of the strain tensor along the long axis of the cantilever is displayed using the colour scale. Scale bar corresponds to 2 μm. Crystal axes of diamond are indicated in relation to the geometry of the cantilever. Arrows on top of the cantilever indicate the highest symmetry axes of four possible SiV⁻ orientations, and their colour indicates separation into two distinct classes upon application of strain. SiV⁻ centres studied in this work are shown by blue arrows and are oriented along $\left[1\overline{1}1\right]$, $\left[\overline{1}11\right]$ directions. They are orthogonal to the cantilever long-axis, and experience strain predominantly in the plane normal to their highest symmetry axis. Inset shows the molecular structure of such a transverse-orientation SiV⁻ along with its internal axes, when viewed in the plane normal to the [110] axis

Fig. 2

Strain-tuning of the SiV⁻ energy levels. a Strain response of a transverse-orientation SiV⁻ as shown in Fig. 1c. Wavelengths of the four optical transitions A, B, C, and D are recorded against strain. Raw PLE data with applied voltages can be found in Supplementary Fig. 7. The lower panel shows orbital splittings within GS (solid green squares) and ES (open blue circles) extracted from the optical transition wavelengths. Solid curves are fits to group theory-based strain response model.^, b Thermal relaxation rates between GS orbital branches vs. their energy splitting. Error bars represent standard deviation of the estimated rate, and are under 5% for all data points. Fit to model in Supplementary Discussion allows extraction of the phonon-absorption rate γ_up and phonon-emission rate γ_down. c Calculated phonon-absorption rate γ_up(Δ_gs) (solid yellow line) as a function of GS-orbital splitting Δ_gs at temperature T = 4 K. Left y-axis indicates the magnitude of this rate normalized to the value at zero strain, γ_up(46 GHz). Right y-axis indicates the two competing factors whose product determines γ_up: the phonon density of states (normalized to its value at zero strain), shown with the solid violet line, and the thermal occupation of acoustic modes shown with the dashed violet line

Fig. 3

Spin coherence measurements. a SiV⁻ level structure in the presence of strain and external magnetic field. A spin qubit is defined with levels $∣1\downarrow ⟩$ and $∣1\uparrow ⟩$ on the lower orbital branch of the GS. This qubit can be polarized, and prepared optically using the Λ-scheme provided by transitions C1 and C2. Phonon transitions within ground- and excited-state manifolds are also indicated. The upward phonon transition (phonon absorption process) can be suppressed at high strain, thereby mitigating the effect of phonons on the coherence of the spin qubit. b Coherent population trapping (CPT) spectra probing the spin transition at increasing values of the GS orbital splitting Δ_gs from top to bottom. Scale bar in bottom left represents a fluorescence signal contrast of 10%. Measurements are carried till the noise in the fluorescence signal is below 1.5%. Bold solid curves are Lorentzian fits. Optical power is adjusted in each measurement to minimize power-broadening. c Linewidth of CPT dips as a function of GS orbital splitting Δ_gs indicating improvement in spin coherence with increasing strain. Error bars represent standard deviation of the estimated linewidths from the Lorentzian fits. d Power dependence of CPT-linewidth at the highest strain condition (Δ_gs = 467 GHz). Data points are estimated linewidths from CPT measurements, and the solid curve is a linear fit, which reveals a linewidth of 0.64 ± 0.06 MHz corresponding to $T_2^{*}$ = 0.25 ± 0.02 μs