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Low Temperature Physics

Microwave transmission and dynamical response of three on-chip superconducting resonators coupled to the same molecular spin ensemble

Carolina del Rio, Sebastián Roca-Jerat, Paweł Pakulski, José Luis García-Palacios, María Carmen Pallarés, Javier Sese, Dawid Pinkowicz, Anabel Lostao, David Zueco, Fernando M. Luis

Published Jul 1, 2026• 0 citations
Publisher

Abstract

We study the simultaneous interaction of a sample of organic free radicals, which realize the spin-1/2 model with a quasi-isotropic g factor ≈ 2, with three ≈ 5.5 GHz lumped-element superconducting resonators in a chip. Each resonator consists of a finger capacitor in parallel with a single wire inductor, which maximizes the coupling intensity of the spins to the photon magnetic field. Their frequencies have been detuned relative to one another in order to make them individually addressable. Each resonator within the trio is capacitively coupled to its nearest neighbor and inductively coupled to a common readout transmission line, and only the central one hosts a molecular deposit. The device has been characterized by microwave transmission experiments performed as a function of frequency (between 5.3 and 5.7 GHz) and magnetic field (170–220 mT) at very low temperatures (T ≃ 13 mK). The results evidence a strong local interaction of the spins to the central resonator, which reaches the coherent coupling regime. In addition, they show that the same spins also couple to the modes associated with the distant resonators. These data have been analyzed on the basis of a theoretical model that incorporates the direct spin-photon interactions as well as those mediated by the circuit. The results provide a relatively simple, practical method for investigating spin resonance of a material at multiple frequencies. Besides, this method allows designing each resonator differently, to fulfill a specific role, e.g., for optimized control or readout of the spin states, which can be of relevance for the implementation of hybrid quantum computation schemes based on molecular spin qubits.

DOI
10.1063/10.0044346

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•Mar 6, 2026•0 citations
We study the simultaneous interaction of a sample of organic free radicals, which realize the spin-1/2 model with a quasi-isotropic g factor ≈ 2, with three ≈ 5.5 GHz lumped-element superconducting resonators in a chip. Each resonator consists of a finger capacitor in parallel with a single wire inductor, which maximizes the coupling intensity of the spins to the photon magnetic field. Their frequencies have been detuned relative to one another in order to make them individually addressable. Each resonator within the trio is capacitively coupled to its nearest neighbor and inductively coupled to a common readout transmission line, and only the central one hosts a molecular deposit. The device has been characterized by microwave transmission experiments performed as a function of frequency (between 5.3 and 5.7 GHz) and magnetic field (170–220 mT) at very low temperatures (T ≃ 13 mK). The results evidence a strong local interaction of the spins to the central resonator, which reaches the coherent coupling regime. In addition, they show that the same spins also couple to the modes associated with the distant resonators. These data have been analyzed on the basis of a theoretical model that incorporates the direct spin-photon interactions as well as those mediated by the circuit. The results provide a relatively simple, practical method for investigating spin resonance of a material at multiple frequencies. Besides, this method allows designing each resonator differently, to fulfill a specific role, e.g., for optimized control or readout of the spin states, which can be of relevance for the implementation of hybrid quantum computation schemes based on molecular spin qubits.
The ability to establish coherent communication channels is key for scaling up quantum devices. Here, we engineer interactions between distant polaritons, hybrid spin-photon excitations formed at different lumped-element superconducting resonators within a chip. The chip consists of several resonator pairs, slightly detuned in frequency to make them addressable, capacitively coupled within each pair and inductively coupled to a common readout line. They interact locally with samples of PTMr and Tripak−^{-}− organic free radicals, deposited onto their inductors, which provide model S=1/2S = 1/2S=1/2, g≃2g \simeq 2g≃2 spin ensembles. Frequency-dependent microwave transmission experiments, performed at very low temperatures, measure polariton frequencies as a function of magnetic field in different scenarios. When only one resonator within a pair hosts a molecular sample, the results evidence that spins couple remotely to the empty LER as well as to the local cavity mode. If both resonators interact with a spin ensemble, the magnetic field tunes the polariton frequencies relative to each other, on account of the different spin-photon interactions at each LER. When polaritons are brought into mutual resonance, an avoided level crossing emerges that gives direct spectroscopic evidence for a coherent polariton-polariton interaction mediated by the circuit. Pump-probe experiments reveal that the excitation of a polariton within a connected pair is felt, thus it can be read out, by the other one. These observations, backed by model calculations, illustrate the control and detection of distant photon-photon and spin-spin correlations and entanglement in a scalable modular chip.
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.
Within the quest for solid state quantum systems to be used for fundamental as well as applied research, molecular spins have recently emerged as a versatile platform with interesting performances in terms of quantum coherence and correlation. Molecular units provide well defined environment to electronic spins and they represent elementary bricks for complex nano-architectures and nano-devices. Here we review our recent efforts and results on their efficient integration in circuit Quantum ElectroDynamics and, more specifically, in reaching their coherent coupling with microwave photons in planar resonators. To monitor molecular spin performances over a wide temperature and magnetic field range we have first developed microwave planar resonators made of high T c superconductors, obtaining excellent performances up to liquid Nitrogen temperature and in magnetic fields up to 7 Tesla. Ensembles of different molecular spins systems are then systematically tested. The regime of high spin-photon cooperativity is achieved with molecular spins diluted in non-magnetic matrix at 0.5 K, while the strong coupling regime is observed with concentrated samples of organic radicals up to 50 K. The possibility to create coherent states among distinct spin ensembles is further explored in similar spectroscopic experiments. These results show that molecular spins can be efficiently integrated in quantum devices.
We implement superconducting Yttrium barium copper oxide planar resonators with two fundamental modes for circuit quantum electrodynamics experiments. We first demonstrate good tunability in the resonant microwave frequencies and in their interplay, as emerges from the dependence of the transmission spectra on the device geometry. We then investigate the magnetic coupling of the resonant modes with bulk samples of 2,2-diphenyl-1-picrylhydrazyl organic radical spins. The transmission spectroscopy performed at low temperature shows that the coherent spin-photon coupling regime with the spin ensembles can be achieved by each of the resonator modes. The analysis of the results within the framework of the input-output formalism and by means of entropic measures demonstrates coherent mixing of the degrees of freedom corresponding to two remote spin ensembles and, with a suitable choice of the geometry, the approaching of a regime with spin-induced mixing of the two photon modes.
Hybrid quantum systems play an essential role in efforts towards the advancements of quantum information technology and quantum sensing by bridging distinct technological platforms. In particular, hybrid systems comprising superconducting microwave circuits are being pursued intensely in light of existing achievements in superconducting qubits and precise quantum control in microwave circuits. Their realization relies on the design of superconducting resonators capable of coupling to an oscillatory mode of a second quantum system, facilitating the probing and manipulation of one via the other. In order to accommodate the coupled system, its particular constraints and requirements must be respected, which may be quite extreme from the perspective of established superconducting circuit design and operation. Overcoming this challenge has proved to be a substantial obstacle for the attainment of strongly coupled hybrid systems, despite spectacular advances in superconducting microwave circuits individually. In this work, we examine two approaches tackling this issue for different hybrid quantum systems, focusing on the optimization and characterization of the superconducting circuits. The first device aims at a superconductor-atom hybrid system through the coupling to Rydberg-Rydberg transitions in ultra-cold Rb-87 atoms trapped near the superconducting chip. Using simulations in conjunction with theoretical considerations, we demonstrate a comprehensive geometry parameter optimization procedure for maximum coupling rate. Presenting an experimental implementation of the resulting circuit, we validate its suitability for use under the intended operation conditions, including the option of tuning the electronic transition frequencies using a dc voltage. Secondly, we investigate a device designed for applications in large magnetic in-plane fields used to mediate coupling to integrated micromechanical oscillators; more specifically it is a flux-tunable SQUID resonator comprising Josephson nano-constrictions as nonlinear inductive components. Performing a thorough characterization of its frequency and Kerr anharmonicity tuning behavior at fields up to several hundred mT, we discover a pronounced asymmetry in its flux response at large fields. We show this asymmetry to be caused by the nano-constrictions turning into Josephson diodes, develop an intuitive macroscopic model for its field-induced emergence and reconstruct the diode current-phase relation from the flux tuning data. Several figures of merit informing the suitability of the SQUID resonators for optomechanical systems as well as other applications are improved by the diode effect, highlighting the potential of Josephson diodes in superconducting microwave circuits. Our results provide a promising stepping stone for the advancement of hybrid systems involving superconducting microwave circuits, putting new and exciting operation and coupling regimes within reach.