Using near-flat-band electrons for read-out of molecular spin qubit entangled states

Abstract

While molecular spin qubits (MSQs) are a promising platform for quantum computing, read-out has been largely limited to electron paramagnetic resonance which is often slow and requires a global system drive. Moreover, because one prerequisite for the Elzerman and Pauli spin blockade readout mechanisms typical of semiconductor spin qubits is tunneling of electrons between sites, these read-out modalities are unavailable in MSQs. Here, we theoretically demonstrate electrical read-out of entangled MSQs via driven many-electron spin unpolarized currents. In particular, using a time-dependent density matrix renormalization group approach we simulate a maximally entangled MSQ pair between two electronic leads. Driving itinerant electrons between the two leads, we find that the conductance is greater when the MSQs are in the entangled singlet state as compared to the entangled triplet state. This contrast in conductance is enhanced when the electronic density of states at the Fermi energy is large and for narrow bandwidth. Our results are readily applicable to molecules supramolecularly functionalizing semiconductors with relatively flat bands such as single-wall carbon nanotubes under a magnetic field.

Figures (9)

• Figure 1: Top: Exemplary schematic of a supramolecular device where MSQs (purple) retain their magnetic properties as they functionalize a $\pi$-conjugated nanowire. Bottom: Our model describes itinerant electrons in the nanowire interacting with the spin degree of freedom of the MSQs only, via an exchange interaction of strength$J_{sd} \approx 1$ meV . Image created with Gemini.
• Figure 2: Model system: itinerant electrons live in a finite 1D nanowire. After a quantum quench at time zero, they spread out and interact with MSQs (purple) atop the nanowire. When the itinerant electrons are close to the MSQs, virtual hopping onto the MSQs yields $sd$ exchange $J_{sd}$ but no Coulomb interactions.
• Figure 3: Panels show simulations of a system without MSQs, with $|T_0\rangle$ MSQs, and with $|S\rangle$ MSQs. Upper plot of each panel: color shows the electronic occupation $n_{j \mu}$ of a given site at a given time. The sites $|j\mu\rangle$ discretizing the 1D chain are along the vertical axis while time $t$, measured in units $\hbar/|v|$, is along the horizontal axis. Lower plot of each panel: perturbation of the MSQ entanglement, quantified by $I$ [Eq. (\ref{['eq:MI']})]. Hamiltonian parameters are $w=-1.00$, $J_{sd}=1.00$, $N_e = 10$, geometric parameters are $N_L=N_R=15$, $N_\text{total} = 31$, and td-DMRG parameters are $\chi_b = 250$, $dt=0.1$.
• Figure 5: Discrete $t>0$ single-particle energy eigenstates $E$ and associated wavenumbers $k_m$ and density of states $\rho(E)$. Spectrum computed for $w=-1$ (blue), $w=-0.60$ (green) and $w=-0.40$ (red) Rice-Mele bands. Dashed lines show Fermi energy $E_F$ and red circles show $\rho(E_F)$.
• Figure 6: Quantum spin valve efficiency $\eta$ [Eq. (\ref{['eq:efficiency_alt']})] at the end of our simulations as a function of $\rho(E_F)$. Entanglement retained by the $|S\rangle$ MSQs at the end of our simulations, quantified by the mutual information $I$ [Eq. (\ref{['eq:MI']})]. Both $\eta$ and $I$ correspond to a better quantum spin valve. Inset: the Rice-Mele hopping $w$ dictates one-to-one the bandwidth $E_\text{band}$ and the density of states at the Fermi energy $\rho(E_F)$.