Figure 1

Comparison between conventional pulsed electron spin resonance (ESR) and qubit-detected ESR. (a) Conventional ESR: A spin ensemble is placed in a cavity with a frequency ${\omega }_c$ and driven with a microwave pulse resonant with the cavity. When the ESR frequency ${\omega }_s$ matches ${\omega }_c$, the spins absorb the microwave pulse, and emit immediately after a free-induction decay (FID) signal into the waveguide connected to the cavity. (b) Qubit-detected ESR: The cavity is now frequency tunable and embeds both the spin ensemble and a superconducting qubit with a frequency ${\omega }_{ge}$. In a first step (1), the spins are probed by a spectroscopy pulse with a frequency ${\omega }_p$, which excites them if its frequency matches ${\omega }_s$. In a second step (2), the cavity frequency is tuned to ${\omega }_c={\omega }_s$, receives the FID signal from the spins, and is afterwards tuned to transfer this signal to the superconducting qubit at ${\omega }_{ge}$. Finally (3) the qubit excited state probability $P_e\left({\omega }_p\right)$ is measured, mapping the spins absorption spectrum. Very low excitation powers can be used given the high sensitivity of the method.Reuse & Permissions

Figure 2

(a) Sketch of the implementation of qubit-based ESR. The spin ensemble $S$ consists of nitrogen-vacancy (NV) centers in a diamond crystal. They are coupled to the frequency-tunable coplanar waveguide resonator $C$ used as the ESR cavity. $C$ also embeds the ESR-detector qubit $Q$, a superconducting qubit of the transmon type whose state can be read-out with another resonator $R$. Microwave pulses for spin spectroscopy as well as for qubit read-out are sent via an input port coupled both to $C$ and to $R$. (b) and (c) Sketch and energy levels of NV centers in diamond. In our setup a DC magnetic field ${\mathbf{B}}_{\mathrm{NV}}$ is applied along the $[1,1,1]$ direction, resulting in different Zeeman splittings for centers having the $N-V$ axis parallel to ${\mathbf{B}}_{\mathrm{NV}}$ (ensemble I, in red) and those having their axis along the three other $\langle 1,1,1\rangle$ axes (ensemble III, in blue). The ESR frequencies ${\omega }_{\pm I,III}$ are further split in three resonance lines due to the hyperfine interaction with the spin-1 ${}^{14}N$ nuclear spin.[11]Reuse & Permissions

Figure 3

Single photon transfer between qubit and spins (Ref. 9). (inset) Pulse sequence used to excite the qubit in state $|e\rangle$ and transfer its excitation to $S$ via $C$ back and forth. (panel) Swap oscillations for the two spin frequencies ${\omega }_{+\mathrm{I}}$ and ${\omega }_{+\mathrm{III}}$. Swap times ${\tau }_{\mathrm{s},\mathrm{I}}$ and ${\tau }_{\mathrm{s},\mathrm{III}}$ are indicated by arrows. Note that the two curves are shifted vertically for clarity with corresponding scales on the left (for ensemble I) and the right axes (ensemble III).Reuse & Permissions

Figure 4

(a) Experimental pulse sequence used for qubit-detected ESR: (1) The spins are first weakly excited by a $2\mu$s microwave pulse with a frequency ${\omega }_p$; (2) the resulting spin excitation is transferred to the cavity $C$ by a fast flux pulse, which brings ${\omega }_c$ in resonance with ${\omega }_K$ ($K=+I,+III)$ for a swap time ${\tau }_{s,K}$, and then to the qubit $Q$ by an adiabatic swap (aSWAP). (3) The qubit excited state probability $P_e$ is finally measured. (b) Measured (open circles) and calculated (solid line) $P_e\left({\omega }_p\right)$ for spin ensemble $+$III (left) and $+$I (right). The spin density $\rho \left(\omega \right)$ used in the calculation is shown as a dashed line.Reuse & Permissions