Two-Photon Interface of Nuclear Spins Based on the Optonuclear Quadrupolar Effect

Photons and nuclear spins are two well-known building blocks in quantum information science and technology. Establishing an efficient interface between optical photons and nuclear spins, while highly desirable for hybridizing these two quantum systems, is challenging, because the interactions between nuclear spins and the environment are usually weak in magnitude, and there is also a formidable gap between nuclear spin frequencies and optical frequencies. In this work, we propose an optonuclear quadrupolar (ONQ) effect, whereby optical photons can be efficiently coupled to nuclear spins, similar to Raman scattering. Compared to previous works, ancilla electron spins are not required for the ONQ effect. This leads to advantages such as applicability in defect-free nonmagnetic crystals and longer nuclear spin coherence time. In addition, the frequency of the optical photons can be arbitrary, so they can be fine-tuned to minimize the material heating and to match telecom wavelengths for long-distance communications. Using perturbation theory and first-principles calculations, we demonstrate that the ONQ effect is stronger by several orders of magnitude than other nonlinear optical effects that could couple to nuclear spins. Based on this rationale, we propose promising applications of the ONQ effect, including quantum memory, quantum transduction, and materials isotope spectroscopy. We also discuss issues relevant to the experimental demonstration of the ONQ effect.

Popular Summary

The rapid growth of quantum information science and technology in recent years is enabled by the remarkable success of various platforms for realizing quantum bits, or qubits, among which optical photons and nuclear spins play crucial roles. Hybridizing these two quantum systems, while highly desirable, is challenging due to their formidable frequency mismatch and the weak interaction between nuclear spins and the environment. Here, we propose a mechanism whereby optical photons and nuclear spins can be efficiently coupled.

Our mechanism is an optonuclear quadrupolar (ONQ) effect. The basic idea is that optical photons affect the electron-generated electrical field gradient near the nuclear spin, thereby modulating the nuclear quadrupole interaction. Consequently, nuclear spin can be coupled to two photons whose frequency difference matches the nuclear spin frequency.

In contrast to previous approaches for optical control over nuclear spins, the ONQ effect does not require ancilla electron spins, and is thus applicable in defect-free nonmagnetic crystals. The ONQ effect is also stronger than other nonlinear optonuclear effects by several orders of magnitude. With this in mind, we suggest several promising applications of the ONQ effect, ranging from materials spectroscopy to quantum technologies such as quantum memory and quantum transduction. For example, we show that using the ONQ effect, the transduction fidelity between optical and microwave or radio frequency photons can reach nearly 90%.

The ONQ effect establishes an efficient interface between optical photons and nuclear spins. Future work could focus on demonstrating more applications of the ONQ effect, designing photonic structures, and searching for materials to enable strong ONQ responses.

Figure 1

Illustration of the ONQ effect. (a) A semiclassical illustration of the ONQ effect. Under two photons with frequencies ${\omega }_{o1}$ and ${\omega }_{o2}$, respectively, the electron cloud vibrates with frequency $|{\omega }_{o1}-{\omega }_{o2}|$ and modulates the quadrupolar interaction of the nuclear spin. (b) Quantum energy level diagram of the ONQ effect. Electrons do (virtual) transitions between three orbitals and modulate the EFG at the nuclear site. Nuclear spins can transit between two energy levels if the frequency matching condition is satisfied.

Figure 2

(a),(b) Atomic structure of wurtzite GaN. The dashed line in (a) labels the mirror symmetry ${\mathcal{M}}_x$ of wGaN. Green, Ga; yellow, N. (c) Change in EFG tensor $\mathrm{\Delta }{\mathcal{V}}_{ij}$ of Ga nuclei as a function of ${\mathcal{E}}_x$. Because of the ${\mathcal{M}}_x$ symmetry, four of six components of the ${\mathcal{V}}_{ij}$ tensor have first-order response $(\partial {\mathcal{V}}_{ij}/\partial {\mathcal{E}}_x){|}_{{\mathcal{E}}_{\mathit{x}}=0}=0$ (inset). (d) $({\partial }^2{\mathcal{V}}_{xx}/\partial {\mathcal{E}}_x^2){|}_{{\mathcal{E}}_{\mathit{x}}=0}$ against the band gap $E_g$ for all wurtzite III-V materials with $E_g>0$ in DFT calculations.

Figure 3

Simulation results of optical to MW or rf transduction. (a) Population of different subsystems as a function of time $t$. Here, we take ${\mathrm{\Gamma }}_n=1\mathrm{kHz}$. In the light-red shaded region, the optical-nuclear interaction is turned on, while in the light-blue shaded region, the MW-nuclear interaction is turned on. (b) Fidelity of the optical to MW transition as a function of NSE relaxation rate ${\mathrm{\Gamma }}_n$. In the simulations, we take $G_o\approx 0.24\mathrm{MHz}$ and $G_m\sim 0.3\mathrm{MHz}$.

Figure 4

Readout of the quantum state of the NSE. Left box: the cavity is on resonance with the ONQ transition, and one can detect whether the ${\omega }_{o1}$ photon is emitted to determine the state of the NSE. Right box: an anharmonic cavity is off resonance with the ONQ transition. One can detect the shift in the resonance frequency of the cavity to determine the quantum state of the NSE.

Figure 5

The ${\mathcal{V}}_{zz}$ component of the EFG at the site of Ga nuclei in wurtzite GaN as a function of uniaxial strain along the $z$ direction.

Figure 6

The EFG $\mathcal{V}$ tensor as a function of electric field ${\mathcal{E}}_x$ for (a) zinc-blende GaAs and (b) Sb defect in silicon.