Coherent coupling of molecular spins with microwave photons in planar superconducting resonators

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 Tc 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 nonmagnetic 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

Microstrip Resonators and Broadband Lines for X-band EPR Spectroscopy of Molecular Nanomagnets

We present a practical setup to perform continuous-wave X-band electron paramagnetic resonance spectroscopy by using planar microstrip lines and general purpose instrumentation. We fabricated Ag/alumina and Nb/sapphire microstrip resonators and transmission lines and compared their performance down to 2 K and under applied magnetic field. We used these devices to study single crystals of molecular Cr3 nanomagnets. By means of X-band planar resonators we measured angle-dependent spectra at fixed frequency, while broadband transmission lines were used to measure continuous wave spectra with varying frequency in the range 2–25 GHz. The spectra acquired at low temperatures allowed to extract the essential parameters of the low-lying energy levels of Cr3 and demonstrate that this method is particularly suitable to study small crystals of molecular nanomagnets

Coherently coupling distinct spin ensembles through a high-Tc superconducting resonator

The problem of coupling multiple spin ensembles through cavity photons is revisited by using (3,5-dichloro-4- pyridyl)bis(2,4,6-trichlorophenyl) methyl (PyBTM) organic radicals and a high-T-c superconducting coplanar resonator. An exceptionally strong coupling is obtained and up to three spin ensembles are simultaneously coupled. The ensembles are made physically distinguishable by chemically varying the g factor and by exploiting the inhomogeneities of the applied magnetic field. The coherent mixing of the spin and field modes is demonstrated by the observed multiple anticrossing, along with the simulations performed within the input-output formalism, and quantified by suitable entropic measures

Ultrastrong Magnon-Photon Coupling Achieved by Magnetic Films in Contact with Superconducting Resonators

Coherent coupling between spin wave excitations (magnons) and microwave photons in a cavity may disclose new paths to unconventional phenomena as well as for novel applications. Here, we present a systematic investigation on YIG (Yttrium Iron Garnet) films on top of coplanar waveguide resonators made of superconducting YBCO. We first show that spin wave excitations with frequency higher than the Kittel mode can be excited by putting in direct contact a 5~$\mu$m thick YIG film with the YBCO coplanar resonator (cavity frequency $\omega_c/2 \pi = 8.65$~GHz). With this configuration, we obtain very large values of the collective coupling strength $\lambda/2 \pi \approx 2$~GHz and cooperativity $C=5 \times 10^4$. Transmission spectra are analyzed by a modified Hopfield model for which we provide an exact solution that allows us to well reproduce spectra by introducing a limited number of free parameters. It turns out that the coupling of the dominant magnon mode with photons exceeds 0.2 times the cavity frequency, thus demonstrating the achievement of the ultrastrong coupling regime with this architecture. Our analysis also shows a vanishing contribution of the diamagnetic term which is a peculiarity of pure spin systems

Coupling molecular spin centers to microwave planar resonators: towards integration of molecular qubits in quantum circuits

We present spectroscopic measurements looking for the coherent coupling between molecular magnetic centers and microwave photons. The aim is to find the optimal conditions and the best molecular features to achieve the quantum strong coupling regime, for which coherent dynamics of hybrid photon-spin states take place. To this end, we used a high critical temperature YBCO superconducting planar resonator working at 7.7 GHz and at low temperatures to investigate three molecular mononuclear coordination compounds, namely (PPh4)2[Cu(mnt)2] (where mnt2- = maleonitriledithiolate), [ErPc2]-TBA+ (where pc2- is the phtalocyaninato and TBA+ is the tetra-n-butylammonium cation) and Dy(trensal) (where H3trensal = 2,2′,2′′-tris(salicylideneimino)triethylamine). Although the strong coupling regime was not achieved in these preliminary experiments, the results provided several hints on how to design molecular magnetic centers to be integrated into hybrid quantum circuits

Polymer-in-Ceramic Nanocomposite Solid Electrolyte for Lithium Metal Batteries Encompassing PEO-Grafted TiO2 Nanocrystals

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Machine-Learning-Assisted Manipulation and Readout of Molecular Spin Qubits

Machine learning finds application in the quantum control and readout of qubits. In this work we apply artificial neural networks to assist the manipulation and the readout of a prototypical molecular spin qubit-an oxovanadium(IV) moiety-in two experiments designed to test the amplitude and the phase recognition, respectively. We first successfully use an artificial network to analyze the output of a storage-retrieval protocol with four input pulses to recognize the echo positions and, with further post selection on the results, to infer the initial input pulse sequence. We then apply an artificial neural network to ascertain the phase of the experimentally measured Hahn echo, showing that it is possible to correctly detect its phase and to recognize additional single-pulse phase shifts added during manipulation.Machine learning finds application in the quantum control and readout of qubits. In this work we apply artificial neural networks to assist the manipulation and the readout of a prototypical molecular spin qubit-an oxovanadium(IV) moiety-in two experiments designed to test the amplitude and the phase recognition, respectively. We first successfully use an artificial network to analyze the output of a storage-retrieval protocol with four input pulses to recognize the echo positions and, with further post selection on the results, to infer the initial input pulse sequence. We then apply an artificial neural network to ascertain the phase of the experimentally measured Hahn echo, showing that it is possible to correctly detect its phase and to recognize additional single-pulse phase shifts added during manipulation

Photosynthetic Membranes Part 71. Laboratory-scale photomineralization of n-alkanols in aqueous solution by photocatalytic membranes immobilizing titianium dioxide

Kinetics of photocatalytic oxidn. of methanol, ethanol, n-propanol, n-heptanol, and n-decanol to yield intermediates, and photomineralization of intermediates to yield carbon dioxide and water, was studied in aq. soln. using a lab.-scale photoreactor and photocatalytic membranes immobilizing 30\ub13 wt.% of TiO2, in the presence of stoichiometric quantities of hydrogen peroxide as oxygen donor. The whole vol. of the irradiated soln. was 4.000\ub10.005 L, and the ratio between this vol. and the geometrical apparent surface of the irradiated side of the photocatalytic membrane 3.8\ub10.1 cm. A kinetic model was used, by which mineralization of substrate to CO2 was supposed to occur through one single intermediate (kinetic consts. k1), mediating the behavior of all the numerous real intermediates formed in the path from the substrate to CO2 (kinetic consts. k2). A competitive Langmuirian adsorption of both substrate and "intermediate" was also supposed to be operative, expressed by the apparent adsorption consts. K1 and K2. By Langmuir - Hinshelwood treatment of the initial rate data, the starting values of the k and K couples were obtained, from which, by a set of differential equations, the final optimized parameters, k1 and K1, k2 and K2 were calcd. While in the case of alkanoic acids, values of k1 and k2 were roughly coincident, in the case of n-alkanols investigated in this work, k2 values were higher than k1 of the same mols. This is interpreted on the basis of the closer behavior, from the photocatalytic point of view, of alkanols to hydrocarbons compared to their corresponding carboxylic acids. Furthermore, values of k2 for methanol were practically the same as those of k1 for the corresponding acid. This behavior confirms the suggestion of being methanoic acid the most representative intermediate for photodegrdn. of methanol

Coupling Sub-nanoliter BDPA Organic Radical Spin Ensembles with YBCO Inverse Anapole Resonators

We report the development and test of planar microwave Inverse Anapole Resonators (IARs) made of superconducting Yttrium Barium Copper Oxide (YBCO) for electron spin resonance spectroscopy on small samples. We first characterize our resonators in zero field and then by carrying out transmission spectroscopy on a diluted α,γ-bisdiphenylene-β-phenylally (BDPA) organic radical spin ensemble in an applied magnetic field. These IARs allow us to carry out electron spin resonance spectroscopy both in continuous-wave and pulsed-wave mode, and to estimate the spin memory time of BDPA. The comparison with the results obtained for the same sample on typical linear coplanar resonators shows an improvement by ≈2 - up to3 – orders of magnitude in spin sensitivity, with effective sensing volumes below 1 nanoliter. The best sensitivity we achieved is S≈10^7 spin/(Hz)^1/2 in the pulsed-wave regime. These results compare well with similar experiments reported in the literature