Long-lived electronic spin qubits in single-walled carbon nanotubes

Abstract

Electron spins in solid-state systems offer the promise of spin-based information processing devices. Single-walled carbon nanotubes (SWCNTs), an all-carbon one-dimensional material whose spin-free environment and weak spin-orbit coupling promise long spin coherence times, offer a diverse degree of freedom for extended range of functionality not available to bulk systems. A key requirement limiting spin qubit implementation in SWCNTs is disciplined confinement of isolated spins. Here, we report the creation of highly confined electron spins in SWCNTs via a bottom-up approach. The record long coherence time of 8.2 µs and spin-lattice relaxation time of 13 ms of these electronic spin qubits allow demonstration of quantum control operation manifested as Rabi oscillation. Investigation of the decoherence mechanism reveals an intrinsic coherence time of tens of milliseconds. These findings evident that combining molecular approaches with inorganic crystalline systems provides a powerful route for reproducible and scalable quantum materials suitable for qubit applications.

Fig. 1. Confinement of electron spins with long coherence times in SWCNTs through chemical modification.

a Schematic of an electron spin (S = 1/2) confined in SWCNTs via chemical functionalization. B and m_s are the applied magnetic field and spin quantum number, respectively. b Hahn echo decay curve of the confined electron spins in SWCNTs (dots) and a stretched exponential fit (curve). Inset: Echo-detected field-swept spectra of SWCNTs with various spin densities. Average spin densities (in the units of spins/nm) are labeled. c Coherence decay under various numbers of CPMG decoupling pulses as a function of total evaluation time. Black curves are stretched exponential fits to the data. d Scaling of the extracted T₂ with the number n of CPMG pulses. The dashed line is a fit of the data to a power law: T₂ ∝ n^0.56.

Fig. 2. Coherent manipulation of spin-qubits in SWCNTs.

a Rabi oscillations of spin qubits measured using different microwave powers. b Fourier transformation of the nutation curves. Note that the shoulder at 15 MHz obtained at high powers is due to Hartman–Hahn effect from precessing ¹H nucleus. c Rabi frequencies obtained at various microwave powers versus the relative amplitudes of the applied microwave field. The line is a linear fit to the data.

Fig. 3. Environmental nuclear spin baths of the localized electron spins in SWCNTs.

a A representative saturation recovery trace of NO₂Ph-SWCNTs dispersed in toluene (dots) together with a biexponential fit (curve). b CP-ESEEM spectrum of NO₂Ph-SWCNTs dispersed in toluene. c HYSCORE spectrum of NO₂Ph-SWCNTs dispersed in toluene. d Zoomed in view of the area marked in (c). A_x,y,z represent the hyperfine tensors. e Simulated HYSCORE spectrum of NO₂Ph-SWCNTs using the experimentally obtained hyperfine tensors. f HYSCORE spectrum of NO₂Ph-SWCNTs dispersed in deuterated toluene measured at 5 K.

Fig. 4. Decoherence sources and simulation of T₂.

a, b Hahn echo decay curves (a) and saturation recovery traces (b) of NO₂Ph-SWCNTs with various spin densities. The spin densities (spins/nm) are labeled next to the data. The dashed lines are stretched and biexponential fits. c Illustration of the decoherence mechanism in the SWCNT spin system. Inter-tube spin-spin interaction and hyperfine couplings to ¹³C and ¹H are the main sources. d–g Simulated dynamics (dots) of a spin experiencing decoherence due to instantaneous diffusion (d) and hyperfine coupling to spin active nuclei including ¹H, ²H, and ¹³C in the solvents (e) and ¹³C in the SWCNT bundles (f), as well as the simulated dynamics of an isolated spin in a single SWCNT without solvent or bundling (g) using the CCE method. The curves are stretched exponential fits.