Fig. 1: Sample description and characterization.
From: High cooperativity coupling to nuclear spins on a circuit quantum electrodynamics architecture
a Energy levels associated with the effective electronic S and nuclear I spin states of the different isotopical derivatives of [Yb(trensal)] molecules as a function of the magnetic field B. Solid colored lines correspond to [173Yb(trensal)] (S = 1/2, I = 5/2), dashed gray lines to [171Yb(trensal)] (S = 1/2, I = 1/2) and dashed-dotted gray lines to all remaining stable Yb isotopes having S = 1/2 and I = 0. The magnetic field is parallel to the C3 crystal axis, which also defines a common magnetic anisotropy axis for all molecules. For sufficiently strong B, levels can be labeled by their electronic (mS) and nuclear(mI) spin projections, but at lower B both spins become entangled and this identification is no longer possible. In this work, we instead assign a single index n( = 0, 1, …(2S + 1)(2I+1)) to each level that follows the order of increasing energy at high B. b Frequency of resonant transitions between the different spin levels of all these derivatives as a function of a magnetic field. Only those lying below 1.1 GHz, which mainly correspond to nuclear spin transitions, are shown. Dots mark the frequencies and magnetic fields at which resonant transitions are observed in the experiments. c Scheme of an [Yb(trensal)] crystal (yellow) interacting with a superconducting circuit composed of several LC resonators with different characteristic frequencies, which are inductively coupled to a common readout superconducting transmission line. The latter line is parallel to the external dc magnetic field and to the crystal C3 axis and can also be used to perform broadband magnetic spectroscopy on a single crystal located directly onto it. d Experimental results of on-chip broadband spectroscopy measurements for an [Yb:Lu(trensal)] crystal with a 7% Yb concentration. The normalized transmission derivative dS21/dB, measured at 10 mK, provides a direct map of all spin excitations as a function of B and energy (or frequency). e Theoretical simulation of the normalized dS21/dB. The conditions are the same as in d. Electronic spin transitions are clearly detected for the different isotopical derivatives. The labels in d and e mark transitions involving the ground spin state n = 0 of [171Yb(trensal)] (I = 1/2, 14% natural abundance), [173Yb(trensal)] (I = 5/2, 14% natural abundance) and all remaining derivatives with I = 0 (70% natural abundance).
