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Communications Physics

High cooperativity coupling to nuclear spins on a circuit quantum electrodynamics architecture

Víctor Rollano, Marina C. de Ory, Christian D. Buch, Marcos Rubín-Osanz, David Zueco, Carlos Sánchez‐Azqueta, Alessandro Chiesa, Daniel Granados, Stefano Carretta, A. Gómez, Stergios Piligkos, Fernando M. Luis

Published Oct 6, 2022• 32 citations
Publisher

Abstract

Abstract Nuclear spins are candidates to encode qubits or qudits due to their isolation from magnetic noise and potentially long coherence times. However, their weak coupling to external stimuli makes them hard to integrate into circuit quantum electrodynamics architectures, the leading technology for solid-state quantum processors. Here, we study the coupling of 173 Yb(III) nuclear spin states in an [Yb(trensal)] molecule to superconducting cavities. Experiments have been performed on magnetically dilute single crystals placed on the inductors of lumped-element LC superconducting resonators with characteristic frequencies spanning the range of nuclear and electronic spin transitions. We achieve a high cooperative coupling to all electronic and most nuclear [ 173 Yb(trensal)] spin transitions, a necessary ingredient for the implementation of qudit protocols with molecular spins using a hybrid architecture.

DOI
10.1038/s42005-022-01017-8

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Abstract Nuclear spins are candidates to encode qubits or qudits due to their isolation from magnetic noise and potentially long coherence times. However, their weak coupling to external stimuli makes them hard to integrate into circuit quantum electrodynamics architectures, the leading technology for solid-state quantum processors. Here, we study the coupling of 173 Yb(III) nuclear spin states in an [Yb(trensal)] molecule to superconducting cavities. Experiments have been performed on magnetically dilute single crystals placed on the inductors of lumped-element LC superconducting resonators with characteristic frequencies spanning the range of nuclear and electronic spin transitions. We achieve a high cooperative coupling to all electronic and most nuclear [ 173 Yb(trensal)] spin transitions, a necessary ingredient for the implementation of qudit protocols with molecular spins using a hybrid architecture.
Nuclear spins are candidates to encode qubits or qudits due to their isolation from magnetic noise and potentially long coherence times. However, their weak coupling to external stimuli makes them hard to integrate into circuit-QED architectures, the leading technology for solid-state quantum processors. Here, we study the coupling of 173^{173}173Yb(III) nuclear spin states in an [Yb(trensal)] molecule to superconducting cavities. Experiments have been performed on magnetically diluted single crystals placed on the inductors of lumped-element LCLCLC superconducting resonators with characteristic frequencies spanning the range of nuclear and electronic spin transitions. We achieve a high cooperative coupling to all electronic and most nuclear [173^{173}173Yb(trensal)] spin transitions. This result is a big leap towards the implementation of qudit protocols with molecular spins using a hybrid architecture.
A promising route toward the realization of a molecular spin quantum processor relies on coupling magnetic molecules to individual photons confined within superconducting resonators. As a simple approximation to such a hybrid scheme, here we explore the conditions that determine the collective coupling of DPPH organic free radicals to lumped-element LC superconducting resonators. In these chips, multiple resonators are coupled to a single readout line. This enables designing the relevant resonator properties, such as resonance frequency, cavity volume, and impedance while keeping a perfect transmission for the device. Here, we exploit these design possibilities to achieve a coherent spin-photon coupling regime. Besides, we study how this coupling depends on the relative orientation of the external dc magnetic field concerning the photon magnetic field and the spins locations concerning the chip surface.
We engineer lumped-element superconducting resonators that maximize magnetic coupling to molecular spin qubits, achieving record single-spin couplings up to 100100100 kHz and collective couplings exceeding 101010 MHz. The resonators interact with PTMr organic free radicals, model spin systems with S=1/2S=1/2S=1/2 and a quasi-isotropic g≃2g \simeq 2g≃2, dispersed in polymer matrices. The highest collective spin-photon coupling strengths are attained with resonators having large inductors, which therefore interact with most spins in the molecular ensemble. By contrast, the coupling of each individual spin G1G_{1}G1​ is maximized in resonators having a minimum size inductor, made of a single wire. The same platform has been used to study spin relaxation and spin coherent dynamics in the dispersive regime, when spins are energetically detuned from the resonator. We find evidences for the Purcell effect, i.e. the photon induced relaxation of those spins that are most strongly coupled to the circuit. The rate of this process gives access to the distribution of single spin photon couplings in a given device. For resonators with a 505050 nm wide constriction at the inductor center, single maximum G1G_{1}G1​ values reach ∼100\sim 100∼100 kHz. Pumping the spins with strong pulses fed through an independent transmission line induces coherent Rabi oscillations. The spin excitation then proceeds via either direct resonant processes induced by the main pulse frequency or, in the case of square-shaped pulses, via the excitation of the cavity by sideband frequency components. The latter process measures the cavity mode hybridization with the spins and can be eliminated by using Gaussian shaped pulses. These results establish a scalable route toward integrated molecular-spin quantum processors.
Interfacing photonic and solid-state qubits within a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. Ideal candidates for coherent qubit interconversion are optically active spins, magnetically coupled to a superconducting resonator. We report on an on-chip cavity QED experiment with magnetically anisotropic Er(3+)∶Y2SiO5 crystals and demonstrate collective strong coupling of rare-earth spins to a lumped element resonator. Moreover, the electron spin resonance and relaxation dynamics of the erbium spins are detected via direct microwave absorption, without the aid of a cavity.
Hybrid quantum systems with high-Tc_cc​ superconducting resonators
Superconducting microwave resonators are crucial elements of microwave circuits, offering a wide range of potential applications in modern science and technology. While conventional low-T[Formula: see text] superconductors are mainly employed, high-T[Formula: see text] cuprates could offer enhanced temperature and magnetic field operating ranges. Here, we report the realization of [Formula: see text] superconducting coplanar waveguide resonators, and demonstrate a continuous evolution from a lossy undercoupled regime, to a lossless overcoupled regime by adjusting the device geometry, in good agreement with circuit model theory. A high-quality factor resonator was then used to perform electron spin resonance measurements on a molecular spin ensemble across a temperature range spanning two decades. We observe spin-cavity hybridization indicating coherent coupling between the microwave field and the spins in a highly cooperative regime. The temperature dependence of the Rabi splitting and the spin relaxation time point toward an antiferromagnetic coupling of the spins below 2 K. Our findings indicate that high-Tc superconducting resonators hold great promise for the development of functional circuits. Additionally, they suggest novel approaches for achieving hybrid quantum systems based on high-T[Formula: see text] superconductors and for conducting electron spin resonance measurements over a wide range of magnetic fields and temperatures.