Dispersive Readout of Molecular Spin Qudits

We study the physics of a magnetic molecule described by a "giant"spin with multiple (d>2) spin states interacting with the quantized cavity field produced by a superconducting resonator. By means of the input-output formalism, we derive an expression for the output modes in the dispersive regime of operation. It includes the effect of magnetic anisotropy, which makes different spin transitions addressable. We find that the measurement of the cavity transmission allows us to uniquely determine the spin state of the qudits. We discuss, from an effective Hamiltonian perspective, the conditions under which the qudit readout is a nondemolition measurement and consider possible experimental protocols to perform it. Finally, we illustrate our results with simulations performed for realistic models of existing magnetic molecules.
We acknowledge funding from Spanish MCIN/AEI/10. 13039/501100011033/ Grants No. PGC2018-094792-BI00, No. RTI2018-096075-B-C21, and No. PCI2018-093116 (MCIU/AEI/FEDER, UE), the European Union’s Horizon 2020 research and innovation programme (QUANTERA project SUMO and FET-OPEN project FATMOLS, Grant No. 862893), the Gobierno de Aragón Grant No. E09-17R-Q-MAD, and the CSIC Quantum Technology Platform PT-001.