Ultrafast control of nuclear spins using only microwave pulses: Towards switchable solid-state quantum gates

We demonstrate the control of the $\alpha$-proton nuclear spin, $I$ $=1/2$, coupled to the stable radical ⋅CH(COOH)${}_2$, $S$ $=1/2$, in a $\gamma$-irradiated malonic acid single crystal using only microwave pulses. We show that, depending on the state of the electron spin ($m_S=\pm 1/2$), the nuclear spin can be locked in a desired state or oscillate between $m_I=+1/2$ and $m_I=-1/2$ on the nanosecond time scale. This approach provides a fast way of controlling nuclear spin qubits and also enables the design of switchable spin-based quantum gates by addressing only the electron spin.

Figure 1

(a) Bloch sphere showing the trajectories of nuclear-spin magnetization under free evolution assuming that the nuclear spin is polarized in the beginning ($m_I=+1/2$). The quantization axis of the effective magnetic field experienced by the nucleus depends on the state of the electron spin: for $m_S=+1/2$, the nuclear spin precesses about ${\mathbf{n̂}}_{\alpha }$ (yellow trace) with angular frequency ${\omega }_{\alpha }=\left|{\omega }_{12}\right|$; for $m_S=-1/2$, the nuclear spin precesses about ${\mathbf{n̂}}_{\beta }$ (green trace) with angular frequency ${\omega }_{\beta }=\left|{\omega }_{34}\right|$. (b) Exact cancellation case, ${\omega }_I=A/2$.

Figure 2

(a) Schematic representation of the stable radical ⋅CH(COOH)${}_2$ and the principal axes system of the hyperfine tensor. (b) Energy level diagram depicting the allowed (a1, a2) and forbidden (f1, f2) electron spin transitions. (c) EPR stick spectrum.

Figure 3

(a) Representation of the density matrix in the product basis $|\alpha \alpha \rangle$, $|\alpha \beta \rangle$, $|\beta \alpha \rangle$, $|\beta \beta \rangle$ during nutation or locking time periods. (b) Numerical simulation of the nuclear spin polarization $\langle I_z\rangle$ during the applied pulse sequence that uses semiselective mw $\pi$ pulses (shown at the top). Spin Hamiltonian parameters: nuclear Zeeman frequency, ${\omega }_I/2\pi =-14.58$ MHz; hyperfine coupling constants, $A/2\pi =-29.06$ MHz, $B/2\pi =6.45$ MHz. (c) Corresponding numerical simulation of the electron spin coherence $\langle S_x\rangle$ after the detection pulse sequence $(\pi /2){}_{2324}-\tau -(\pi ){}_{2324}-\tau -$ echo with $\tau =2\pi /{\omega }_{34}=310$ ns.

Figure 4

(a) Proposed pulse sequence consists of three parts: preparation, for creating the pseudopure state ${\sigma }_{\beta \alpha }$; manipulation, consisting of a time delay ${\tau }_n$ and a semiselective $(\pi ){}_{2324}$ or $(\pi ){}_{1314}$ pulse; detection of electron-spin coherence through a two-pulse echo with $\tau =2\pi /{\omega }_{34}$. (b) Free induction decay (FID)-detected EPR spectrum. The arrow indicates the observer position $B_0=343.7$ mT of the semiselective $(\pi ){}_{2324}$ pulses. (c) Three-pulse ESEEM spectrum. (d) Electron spin echo (ESE) intensity as a function of time $t_{\mathrm{detection}}$ between preparation and detection.