Figure 1

(a) Setup description. The NV center ensemble is magnetically coupled to the coplanar resonator containing a SQUID. The flux $\Phi$ through the SQUID loop can be tuned on a nanosecond scale by applying current pulses to an on-chip antenna. A magnetic field $B_{\mathrm{NV}}=1.7$ mT is applied to the spins, parallel to the sample and to the $[1,0,0]$ crystal axis (b). The amplitude $A\left(t\right)$ of microwave pulses transmitted through the resonator is measured by homodyne detection at room temperature after amplification. (c) Simplified energy level scheme of a NV center.Reuse & Permissions

Figure 2

Measurement setup and wiring. (a) Full configuration of the measurement apparatus at room temperature. (b) Schematic of the wiring inside the dilution refrigerator. LPF1, LPF2, LPF3, and LPF4 are low-pass filters having cutoff frequencies of 1.35 GHz, 450 MHz, 450 MHz, and 1.35 GHz, respectively. BPF1 actually consists of two series of low-pass ($<$5.4 GHz) and high-pass ($>$1.3 GHz) filters, and BPF2 is a bandpass filter ($2.5$ to 4 GHz). CuNi coax1, coax2, and coax4 are coaxial cables made of CuNi, and CuNi coax3 is a silver-plated CuNi coaxial cable. SC coax is a superconducting NbTi coaxial cable. Flex coax is a low-loss flexible coaxial cable. HEMT is a CITCRYO1-12 cryogenic microwave amplifier from Caltech, having a noise temperature of $T_N\sim 4$ K. The dc magnetic field $B{}_{NV}$ is generated by passing a current through a superconducting outer coil.Reuse & Permissions

Figure 3

(a) Photograph of the area where the four-SQUID array is placed in the resonator (taken before fabrication of the SQUIDs). The arrows show the flow of an applied fast current pulse. (b) Close-up schematic of the SQUID array [dotted square in (a)]. The applied (return) current pulse is represented by a solid (dashed) arrow. (c) Actual pulse sequence for the measurement: (i) excitation, (ii) interaction, (iii) data accumulation, and (iv) compensation in the sequence. After data sampling (iii), an inverted pulse (iv) is applied to compensate the time integral to 0 (see text). The whole length of one sequence is 5 $\mu$s.Reuse & Permissions

Figure 4

(a) Resonator transmission $|S_{21}|\left(\omega \right)$ at $B_{\mathrm{NV}}=1.7$ mT as a function of $\Phi$ (in units of the superconducting flux quantum ${\Phi }_0=h/2e$) showing two vacuum Rabi splittings. The solid line is a fit to the data using the coupled oscillators model [11]. (b) Vacuum Rabi splitting close to resonance with ${\omega }_{-}$. Black dots are experimental data; the red line is theory (rescaled in amplitude to fit the data) as explained in the text, assuming a spin-resonator detuning of $0.5$ MHz.Reuse & Permissions

Figure 5

(a) Sketch of an experimental sequence. (b) Output amplitude $A\left(t\right)$ measured for increasing flux pulse duration $\tau$, for a flux pulse amplitude such that ${\omega }_r({\Phi }_{\mathrm{OFF}}+\overline{\Delta \Phi })={\omega }_{-}$. The long-dashed orange line indicates $t=\tau$. The two white dashed lines indicate the time window on which averaging is performed to compute $a\left(\tau \right)$ (see text). (c) Amplitude $A\left(t\right)$ for $g_{\mathrm{ens}}\tau =0,\pi ,2\pi ,3\pi$. (d) Normalized amplitude $a\left(\tau \right)=\overline{A(\tau +t_{\mathrm{off}})}$ (see text). Red dots are experimental data; the continuous blue line is theory as explained in the text. (Inset) Sketch of the physical process leading to damping of the oscillations because of coupling of the superradiant state to the bath of subradiant states. (e) Optically detected magnetic resonance signal measured at room temperature (red dots), compared to the spin distribution $\rho \left(\omega \right)$ (see text) used in the theoretical calculations (blue line).Reuse & Permissions

Figure 6

Coherent field exchange between the resonator and the spins for varying flux pulse amplitude $\Delta \Phi$. Normalized amplitude $a\left(\tau \right)$ (see text) is plotted versus $\tau$ and $\Delta \Phi$. The left graph is experimental data; the right graph is theory. The white dashed line indicates $\overline{\Delta \Phi }$.Reuse & Permissions

Figure 7

Ramsey fringes experiment. The normalized microwave amplitude $a\left(\Delta t\right)$ after the pulse sequence shown in the inset is plotted. Red dots are experimental data; the black continuous line is theory.Reuse & Permissions