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Bulletin of the American Physical Society

Coupling a single electron spin to a microwave resonator: Part I: controlling transverse and longitudinal couplings

Dany Lachance-Quirion, Félix Beaudoin, Julien Camirand Lemyre, W. A. Coish, Michel Pioro-Ladrière

Published Mar 16, 2017• 0 citations
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Microwave-frequency superconducting resonators are ideally suited to perform dispersive qubit readout, to mediate two-qubit gates, and to shuttle states between distant quantum systems. A prerequisite for these applications is a strong qubit-resonator coupling. Strong coupling between an electron-spin qubit and a microwave resonator can be achieved by correlating spin- and orbital degrees of freedom. This correlation can be achieved through the Zeeman coupling of a single electron in a double quantum dot to a spatially inhomogeneous magnetic field generated by a nearby nanomagnet. In this paper, we consider such a device and estimate spin-resonator couplings of order ∼1 MHz with realistic parameters. Further, through realistic simulations, we show that precise placement of the double-dot relative to the nanomagnet allows to select between a purely longitudinal coupling (commuting with the bare spin Hamiltonian) and a purely transverse (spin non-conserving) coupling. Additionally, we suggest methods to mitigate dephasing and relaxation channels that are introduced in this coupling scheme. This analysis gives a clear route toward the realization of coherent state transfer between a microwave resonator and a single electron spin in a GaAs double quantum dot with a fidelity above 90%. Improved dynamical decoupling sequences, low-noise environments, and longer-lived microwave cavity modes may lead to substantially higher fidelities in the near future.
We describe a method to tune, in situ, between transverse and longitudinal light-matter coupling in a hybrid circuit-QED device composed of an electron-spin degree of freedom coupled to a microwave transmission line cavity. Our approach relies on periodic modulation of the coupling itself, such that in a certain frame the interaction is both amplified and either transverse or, by modulating at two frequencies, longitudinal. The former realizes an effective simulation of certain aspects of the ultra-strong-coupling regime, while the latter allows one to implement a longitudinal readout scheme even when the intrinsic Hamiltonian is transverse, and the individual spin or cavity frequencies cannot be changed. We analyze the fidelity of using such a scheme to measure the state of the electron-spin degree of freedom, and argue that the longitudinal readout scheme can operate in regimes where the traditional dispersive approach fails.
While transverse coupling ( σ x ) is commonly used in qubit-resonator systems, longitudinal coupling via σ z presents a tantalizing alternative: it does not hybridize the modes, eliminating Purcell decay, and it enables quantum-nondemolition qubit readout independent of the qubit-resonator frequency detuning. Here, we demonstrate longitudinal coupling between a { Cr 7 Ni } molecular spin qubit ensemble and the kinetic inductance of a granular aluminum superconducting microwave resonator. The inherent frequency independence of this coupling allows for the utilization of a 7.8-GHz readout resonator to measure the full { Cr 7 Ni } magnetization curve spanning 0–600 mT, corresponding to a spin frequency range of f spin = 0 –15 GHz. For 2-GHz detuning from the readout resonator, we measure a 1 / e spin relaxation time of τ = 0.38 s, limited by phonon decay to the substrate. Based on these results, we propose a path towards longitudinal coupling of single spins to a superconducting fluxonium qubit.