Localized Nanoscale Formation of Vanadyl Porphyrin 2D MOF Nanosheets and Their Optimal Coupling to Lumped Element Superconducting Resonators
Ignacio Gimeno, Fernando M. Luis, Carlos Marcuello, María Carmen Pallarés, Anabel Lostao, Marina C. de Ory, A. Gómez, Daniel Granados, Inés Tejedor, Eva Natividad, Ainhoa Urtizberea, Olivier Roubeau
High Resolution Image Download MS PowerPoint Slide A strategy toward the realization of a quantum spin processor involves the coupling of spin qubits and qudits to photons within superconducting resonators. To enable the realization of such hybrid architecture, here we first explore the design of a chip with multiple lumped-element LC superconducting resonators optimized for their coupling to distinct transitions of a vanadyl porphyrin electronuclear qudit. The controlled integration of the vanadyl qudit onto the superconducting device, both in terms of number and orientation, is then attained using the in situ formation of nanosheets of a 2D framework built on the vanadyl qudit as a node. Low-temperature transmission experiments demonstrate the coupling of photons in resonators with different frequencies to the targeted electronuclear transitions of the vanadyl qudit, also confirming the control over the vanadyl qudit node orientation. The derived collective spin-photon couplings in the 0.3–1.6 MHz range then allow to estimate enhanced, optimal, single spin photon couplings up to 4 Hz.
High Resolution Image Download MS PowerPoint Slide A strategy toward the realization of a quantum spin processor involves the coupling of spin qubits and qudits to photons within superconducting resonators. To enable the realization of such hybrid architecture, here we first explore the design of a chip with multiple lumped-element LC superconducting resonators optimized for their coupling to distinct transitions of a vanadyl porphyrin electronuclear qudit. The controlled integration of the vanadyl qudit onto the superconducting device, both in terms of number and orientation, is then attained using the in situ formation of nanosheets of a 2D framework built on the vanadyl qudit as a node. Low-temperature transmission experiments demonstrate the coupling of photons in resonators with different frequencies to the targeted electronuclear transitions of the vanadyl qudit, also confirming the control over the vanadyl qudit node orientation. The derived collective spin-photon couplings in the 0.3–1.6 MHz range then allow to estimate enhanced, optimal, single spin photon couplings up to 4 Hz.
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.
Integration of molecular spin qubits onto superconducting circuits is one of the current proposals to build a hybrid quantum processor, in which their coupling to resonators would allow complex coherent quantum operations. As an alternative to large magnetically dilute crystals or concentrated nanoscale deposits of paramagnetic molecules studied so far, we consider here preformed nanoparticles of a Zr(IV)-based 3D MOF doped with Cu(II) and V(IV)O metalloporphyrin. Highly crystalline, phase-pure nanoparticles are obtained with an adjustable number of spin carriers and a homogeneous size that is adequate for nanoconstrictions in superconducting resonators. Continuous-wave and time-domain EPR spectroscopy show that the Cu(II) and V(IV) spins in these particles are potential qubits and qudits, respectively, with robust quantum coherence. These nanoparticles form good dispersions in methanol-chloroform mixtures, which allows the formation of monolayers of densely packed particles at the air-water interface. These Langmuir films are successfully transferred to very different substrates, including Nb resonators, homogeneously covering their most sensitive areas, i.e., the edges of the superconducting lines. Finally, the quantum coherence of the qubit nodes is maintained in the transferred nanoparticles, thereby demonstrating the viability of the present approach for the development of hybrid quantum processors.
We engineer lumped-element superconducting resonators that maximize magnetic coupling to molecular spin qubits, achieving record single-spin couplings up to 100 kHz and collective couplings exceeding 10 MHz. The resonators interact with PTMr organic free radicals, model spin systems with S=1/2 and a quasi-isotropic g≃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 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 50 nm wide constriction at the inductor center, single maximum G1 values reach ∼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.
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=1/2, g≃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.
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.
Abstract Electron spins are ideal two-level systems that may couple with microwave photons so that, under specific conditions, coherent spin-photon states can be realized. This represents a fundamental step for the transfer and the manipulation of quantum information. Along with spin impurities in solids, molecular spins in concentrated phases have recently shown coherent dynamics under microwave stimuli. Here we show that it is possible to obtain high cooperativity regime between a molecular Vanadyl Phthalocyanine (VOPc) spin ensemble and a high quality factor superconducting YBa2Cu3O7 (YBCO) coplanar resonator at 0.5 K. This demonstrates that molecular spin centers can be successfully integrated in hybrid quantum devices.