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arXiv:1805.05843 · Journal of Applied Physics

Microwave dual-mode resonators for coherent spin-photon coupling

Claudio Bonizzoni, Filippo Troiani, Alberto Ghirri, M. Affronte

Published Nov 20, 2018• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.5050869

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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.
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.
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-Tc{T}_{c}Tc​ 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 ggg 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.
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.
Coplanar microwave resonators made of 330 nm-thick superconducting YBa2Cu3O7 have been realized and characterized in a wide temperature (T, 2–100 K) and magnetic field (B, 0–7 T) range. The quality factor (QL) exceeds 104 below 55 K and it slightly decreases for increasing fields, remaining 90% of QL(B=0) for B = 7 T and T = 2 K. These features allow the coherent coupling of resonant photons with a spin ensemble at finite temperature and magnetic field. To demonstrate this, collective strong coupling was achieved by using di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium organic radical placed at the magnetic antinode of the fundamental mode: the in-plane magnetic field is used to tune the spin frequency gap splitting across the single-mode cavity resonance at 7.75 GHz, where clear anticrossings are observed with a splitting as large as ∼82 MHz at T = 2 K. The spin-cavity collective coupling rate is shown to scale as the square root of the number of active spins in the ensemble.
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.
Single-photon devices at microwave frequencies are important for applications in quantum information processing and communication in the microwave regime. In this work we describe a proposal of a multioutput single-photon device. We consider two superconducting resonators coupled to a gap-tunable qubit via both its longitudinal and transverse degrees of freedom. Thus, this qubit-resonator coupling differs from the coupling in standard circuit quantum-electrodynamic systems described by the Jaynes-Cummings model. We demonstrate that an effective quadratic coupling between one of the normal modes and the qubit can be induced and this induced second-order nonlinearity is much larger than that for conventional Kerr-type systems exhibiting photon blockade. Assuming that a coupled normal mode is resonantly driven, we observe that the output fields from the resonators exhibit strong sub-Poissonian photon-number statistics and photon antibunching. Contrary to previous studies on resonant photon blockade, the first-excited state of our device is a pure single-photon Fock state rather than a polariton state, i.e., a highly hybridized qubit-photon state. In addition, it is found that the optical state truncation caused by the strong qubit-induced nonlinearity can lead to an entanglement between the two resonators, even in their steady state under the Markov approximation.