Synchronizing the Dynamics of a Single Nitrogen Vacancy Spin Qubit on a Parametrically Coupled Radio-Frequency Field through Microwave Dressing

A hybrid spin-oscillator system in parametric interaction is experimentally emulated using a single nitrogen vacancy (NV) spin qubit immersed in a radio frequency (rf) field and probed with a quasiresonant microwave (MW) field. We report on the MW-mediated locking of the NV spin dynamics onto the rf field, appearing when the MW-driven Rabi precession frequency approaches the rf frequency and for sufficiently large rf amplitudes. These signatures are analogous to a phononic Mollow triplet in the MW rotating frame for the parametric interaction and promise to have impact in spin-dependent force detection strategies.

Figure 1

An emulated spin-mechanical hybrid system. (a) A single NV spin qubit is coupled to a rf field (frequency ${\mathrm{\Omega }}_m/2\pi$), which parametrically modulates its energy splitting ($\hslash {\omega }_0$) with an amplitude $\hslash \delta {\omega }_0$ while quasiresonant MW irradiation (pulsation $\omega$) is used to manipulate the spin state, drive Rabi precessions of the two-level system (frequency ${\mathrm{\Omega }}_R/2\pi$), and realize resonant spectroscopy of the system. (b) Experimental setup: a single NV defect hosted in a diamond nanocrystal deposited on a glass plate is optically read out through a confocal microscope apparatus, and the spin-state-dependent fluorescence [34] is read out on an avalanche photodiode. MW and rf fields required for spin manipulation [34] and spin energy modulation, respectively, are delivered via a coplanar waveguide (see the Supplemental Material [35]).

Figure 2

Characterization of the spin-rf interaction in the adiabatic and resolved sideband regimes [${\mathrm{\Omega }}_m/2\pi =20\mathrm{kHz}$ in (a) and (b), 15 MHz in (c) and (d)]. Left: ESR spectra obtained in the absence of rf field (i) and for increasing oscillation amplitudes [$\delta {\omega }_0=2.5$, 4.7, 6.2, and 9.1 MHz from (ii) to (v), respectively]. Right: time-resolved ESR spectra obtained by gating the photon counts (20% duty cycle) at different rf oscillatory phases for $\delta {\omega }_0=9.1\mathrm{MHz}$. In the adiabatic case (b), the modulation observed has an amplitude of $\delta {\omega }_0$, while no temporal evolution is visible in the RSB case (d) since the spin dynamics is too slow to follow the imposed RF field.

Figure 3

Experimental [(a) and (b)] and numerically simulated [(c) and (d)] Rabi oscillations of NV spin in the presence [(b) and (d)] and absence [(a) and (c)] of rf modulation. The spin state is optically prepared in its $m_S=0$ ground state and subsequently irradiated with a MW field whose detuning is varied across the resolved sideband spectrum of Fig. 1. The substructures observed at large MW pulse duration are inherent to the NV defect’s hyperfine structure. Bottom: evolution of the Rabi frequency measured by tuning the MW frequency on the carrier ($\delta =0$) or on the first sidebands ($\delta =\pm {\mathrm{\Omega }}_m$) as a function of the driving amplitude ${\mathrm{\Omega }}_R$ (e), oscillation amplitude $\delta {\omega }_0$ (f), and oscillation frequency (${\mathrm{\Omega }}_m/2\pi$) (g). When nonvaried, parameters are $\delta {\omega }_0/2\pi =4.5\mathrm{MHz}$, ${\mathrm{\Omega }}_m/2\pi =15\mathrm{MHz}$, and 18 dBm MW power. Solid lines are fits based on Bessel functions and calibration measurements; see text.

Figure 4

Spin synchronization. Rabi oscillations (a) and their corresponding FFT spectra (b) measured for resonant MW pumping ($\delta =0$) in the absence (above) or presence (below) of rf modulation at a frequency close to the Rabi precession: ${\mathrm{\Omega }}_R\approx {\mathrm{\Omega }}_m$ ($5/6\mathrm{MHz}$ here). The triplet structure is the signature of spin locking, which is more easily evidenced in [(c) and (d)] experimental and simulated FFT spectra of the Rabi oscillations for varying MW power to scan the Rabi precession frequency across the rf/mechanical resonance. In the spin locking region, a gap appears in the energy spectrum of spin dynamics. (e) FFT spectra measured at the synchronization point (${\mathrm{\Omega }}_R={\mathrm{\Omega }}_m$) for increasing rf amplitudes $\delta {\omega }_0$. (f) Variation of the mechanical frequency across the synchronization point for fixed MW power (${\mathrm{\Omega }}_R/2\pi =5\mathrm{MHz}$) and rf amplitude $\delta {\omega }_0/2\pi =2.7\mathrm{MHz}$. (g) Interpretation of the synchronization mechanism in term of rf dressing of the MW dressed qubit. Transitions between doubly dressed states are detectable as frequency components of Rabi oscillations ${\mathrm{\Omega }}_m$, ${\mathrm{\Omega }}_m\pm \delta {\omega }_0/2$. (h) “rf light shifts”: dependence on the oscillation amplitude of MW powers ${\mathrm{\Omega }}_R^{\odot }$, which minimizes the triplet splitting. The dashed lines represent sixth-order expansions of the Bloch-Siegert light shifts (see text), whereas data points are derived from eight measurements similar to panel (c).