We combine top-down and bottom-up nanolithography to optimize the coupling of small molecular spin ensembles to 1.4 GHz on-chip superconducting resonators. Nanoscopic constrictions, fabricated with a focused ion beam at the central transmission line, locally concentrate the microwave magnetic field. Drops of free-radical molecules have been deposited from solution onto the circuits. For the smallest ones, the molecules were delivered at the relevant circuit areas by means of an atomic force microscope. The number of spins N eff effectively coupled to each device was accurately determined combining Scanning Electron and Atomic Force Microscopies. The collective spin-photon coupling constant has been determined for samples with N eff ranging between 2 × 10 6 and 10 12 spins, and for temperatures down to 44 mK. The results show the well-known collective enhancement of the coupling proportional to the square root of N eff . The average coupling of individual spins is enhanced by more than 4 orders of magnitude (from 4 mHz up to above 180 Hz), when the transmission line width is reduced from 400 μm down to 42 nm, and reaches maximum values near 1 kHz for molecules located on the smallest nanoconstrictions.

We report on the design, fabrication, and characterization of superconducting coplanar waveguide resonators with nanoscopic constrictions. By reducing the size of the center line down to 50 nm, the radio frequency currents are concentrated and the magnetic field in its vicinity is increased. The device characteristics are only slightly modified by the constrictions, with changes in resonance frequency lower than 1% and internal quality factors of the same order of magnitude as the original ones. These devices could enable the achievement of higher couplings to small magnetic samples or even to single molecular spins and have applications in circuit quantum electrodynamics, quantum computing, and electron paramagnetic resonance.

In this paper, a new pseudorandom number generator (PRNG) based on the logistic map has been proposed. To prevent the system to fall into short period orbits as well as increasing the randomness of the generated sequences, the proposed algorithm dynamically changes the parameters of the chaotic system. This PRNG has been implemented in a Virtex 7 field-programmable gate array (FPGA) with a 32-bit fixed point precision, using a total of 510 lookup tables (LUTs) and 120 registers. The sequences generated by the proposed algorithm have been subjected to the National Institute of Standards and Technology (NIST) randomness tests, passing all of them. By comparing the randomness with the sequences generated by a raw 32-bit logistic map, it is shown that, by using only an additional 16% of LUTs, the proposed PRNG obtains a much better performance in terms of randomness, increasing the NIST passing rate from 0.252 to 0.989. Finally, the proposed bitwise dynamical PRNG is compared with other chaos-based realizations previously proposed, showing great improvement in terms of resources and randomness.Index Terms-Chaos, digital circuits, field-programmable gate array (FPGA), logistic map, pseudorandom number generator (PRNG), random number generation. Carlos Sánchez-Azqueta was born in Zaragoza, Spain. He received the B.Sc., M.Sc., and Ph.D. degrees in physics from the University of Zaragoza, Zaragoza, Spain, in 2006, 2010 the Dipl.-Ing. degree in electronic engineering from the Complutense University of Madrid, Madrid, Spain, in 2009.His current research interests include mixed-signal integrated circuits, high-frequency analog communications, and cryptography applications.Dr. Sánchez-Azqueta is a member of the

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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 173Yb(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 [173Yb(trensal)] spin transitions, a necessary ingredient for the implementation of qudit protocols with molecular spins using a hybrid architecture.