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arXiv:1911.07541 · Physical Review Applied

Optimal coupling of HoW10 molecular magnets to superconducting circuits near spin clock transitions

Ignacio Gimeno, Víctor Rollano, David Zueco, Yan Duan, Marina C. de Ory, A. Gómez, Alejandro Gaita‐Ariño, Carlos Sánchez‐Azqueta, Thomas Astner, Daniel Granados, Stephen Hill, Johannes Majer, Eugenio Coronado, Fernando M. Luis

Published Oct 26, 2023• 10 citations
arXivHTMLPDF

Abstract

A central goal in quantum technologies is to maximize $G{T}_{2}$, where $G$ stands for the coupling of a qubit to control and readout signals and ${T}_{2}$ is the qubit's coherence time. This is challenging, as increasing $G$ (e.g., by coupling the qubit more strongly to external stimuli) often leads to deleterious effects on ${T}_{2}$. Here, we study the coupling of pure and magnetically diluted crystals of ${\mathrm{Ho}\mathrm{W}}_{10}$ magnetic clusters to microwave superconducting coplanar waveguides. Absorption lines give a broadband picture of the magnetic energy level scheme and, in particular, confirm the existence of level anticrossings at equidistant magnetic fields determined by the combination of crystal field and hyperfine interactions. Such ``spin clock transitions'' are known to shield the electronic spins against magnetic field fluctuations. The analysis of the microwave transmission shows that the spin-photon coupling also becomes maximum at these transitions. The results show that engineering spin-clock states of molecular systems offers a promising strategy to combine sizable spin-photon interactions with a sufficient isolation from unwanted magnetic noise sources.

DOI
10.1103/physrevapplied.20.044070

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A central goal in quantum technologies is to maximize GT2G{T}_{2}GT2​, where GGG stands for the coupling of a qubit to control and readout signals and T2{T}_{2}T2​ is the qubit's coherence time. This is challenging, as increasing GGG (e.g., by coupling the qubit more strongly to external stimuli) often leads to deleterious effects on T2{T}_{2}T2​. Here, we study the coupling of pure and magnetically diluted crystals of HoW10{\mathrm{Ho}\mathrm{W}}_{10}HoW10​ magnetic clusters to microwave superconducting coplanar waveguides. Absorption lines give a broadband picture of the magnetic energy level scheme and, in particular, confirm the existence of level anticrossings at equidistant magnetic fields determined by the combination of crystal field and hyperfine interactions. Such ``spin clock transitions'' are known to shield the electronic spins against magnetic field fluctuations. The analysis of the microwave transmission shows that the spin-photon coupling also becomes maximum at these transitions. The results show that engineering spin-clock states of molecular systems offers a promising strategy to combine sizable spin-photon interactions with a sufficient isolation from unwanted magnetic noise sources.
A central goal in quantum technologies is to maximize GT2, where G stands for the rate at which each qubit can be coherently driven and T2 is the qubit's phase coherence time. This is challenging, as increasing G (e.g. by coupling the qubit more strongly to external stimuli) often leads to deleterious effects on T2. Here, we study a physical situation in which both G and T2 can be simultaneously optimized. We measure the coupling to microwave superconducting coplanar waveguides of pure (i.e. non magnetically diluted) crystals of HoW10 magnetic clusters, which show level anticrossings, or spin clock transitions, at equidistant magnetic fields. The absorption lines give a complete picture of the magnetic energy level scheme and, in particular, confirm the existence of such clock transitions. The quantitative analysis of the microwave transmission allows monitoring the overlap between spin wave functions and gives information about their coupling to the environment and to the propagating photons. The formation of quantum superpositions of spin-up and spin-down states at the clock transitions allows simultaneously maximizing the spin-photon coupling and minimizing environmental spin perturbations. Using the same experimental device, we also explore the coupling of these qubits to a 11.7 GHz cavity mode, arising from a nonperfect microwave propagation at the chip boundaries and find a collective spin to single photon coupling GN = 100 MHz. The engineering of spin states in molecular systems offers a promising strategy to combine sizeable photon-mediated interactions, thus scalability, with a sufficient isolation from unwanted magnetic noise sources.
Abstract Enhanced coherence in HoW10 molecular spin qubits has been demonstrated by use of clock-transitions (CTs). More recently it was shown that, while operating at the CTs, it was possible to use an electrical field to selectively address HoW10 molecules pointing in a given direction, within a crystal that contains two kinds of identical but inversion-related molecules. Herein we theoretically explore the possibility of employing the electric field to effect entangling two-qubit quantum gates within a 2-qubit Hilbert space resulting from dipolar coupling of two CT-protected HoW10 molecules in a diluted crystal. We estimate the thermal evolution of T1, T2, find that CTs are also optimal operating points from the point of view of phonons, and lay out how to combine a sequence of microwave and electric field pulses to achieve coherent control within a switchable two-qubit operating space between symmetric and asymmetric qubit states that are protected both from spin-bath and from phonon-bath decoherence. This two-qubit gate approach presents an elegant correspondence between physical stimuli and logical operations, meanwhile avoiding any spontaneous unitary evolution of the qubit states. Finally, we found a highly protected 1-qubit subspace resulting from the interaction between two clock molecules.
Quantum information processing (QIP) concerns communication between qubits in quantum computer. Coplanar waveguide (CPW) resonators which could easily be fabricated with the micro-techniques in integrated circuits started to show its potentiality in QIP in last few years. So far CPW resonators were used to arrange communication between Josephson q-bits which have relatively short decoherence time. The q-bits based on molecular spins mountain quantum coherence for much longer time, but they have too weak coupling to microwave field to allow effective spin manipulation. In this project we aimed to optimize CPW resonators in order to achieve strong coupling to molecular spins. \nWe present results for standard Coplanar Waveguide (CPW) Nb resonators fabricated on sapphire substrate. To achieve strong coupling between microwave field and molecular spins constrictions of the central conductor at the antinode of current were made to get local enhancement of magnetic field. We also present the simulation results for the key design elements: T-junctions and constrictions, which gave a good guideline for design and fabrication. Low temperature measurements of resonators with (and without) local constrictions were made and verified the accuracy of simulations. Finally, we discuss the temperature and power dependence of resonators transmission spectra.
Strong coupling of semiconductor spin qubits to superconducting microwave resonators was recently demonstrated [X. Mi et al., Nature 555, 599 (2018); A. J. Landig et al., Nature 560, 179 (2018); N. Samkharadze et al., Science 359, 1123 (2018); T. Cubaynes et al., NPJ Quant. Inf. 5, 47 (2019)]. These breakthroughs pave the way for quantum information processing that combines the long coherence times of solid-state spin qubits with the long-distance connectivity, fast control, and fast high-fidelity quantum-non-demolition readout of existing superconducting qubit implementations. Here we theoretically analyze and optimize the dispersive readout of a single spin in a semiconductor double quantum dot (DQD) coupled to a microwave resonator via its electric dipole moment. The strong spin-photon coupling arises from the motion of the electron spin in a local magnetic field gradient. We calculate the signal-to-noise ratio (SNR) of the readout accounting for both Purcell spin relaxation and spin relaxation arising from intrinsic electric noise within the semiconductor. We express the maximum achievable SNR in terms of the cooperativity associated with these two dissipation processes. We find that while the cooperativity increases with the strength of the dipole coupling between the DQD and the resonator, it does not depend on the strength of the magnetic field gradient. We then optimize the SNR as a function of experimentally tunable DQD parameters. We identify wide regions of parameter space where the unwanted backaction of the resonator photons on the qubit is small. Moreover, we find that the coupling of the resonator to other DQD transitions can enhance the SNR by at least a factor of two, a ``straddling'' effect [J. Koch et al., Phys. Rev. A 76, 042319 (2007)] that occurs only at nonzero energy detuning of the DQD double-well potential. We estimate that with current technology, single-shot readout fidelities in the range 82--95% can be achieved within a few $\ensuremath{\mu}\mathrm{s}$ of readout time without requiring the use of Purcell filters.
We review the progress made in integrating magnetic molecules containing transition metal ions into nanoelectronic solid-state devices and using them as molecular spin qubits. Molecular spin qubits offer numerous advantages over other material platforms, such as being inherently quantum systems with discrete energy levels, having a rich variety of possible chemical designs, and being synthesizable in large quantities with atomic precision. However, the integration of magnetic molecules into practical and scalable molecular spin qubit devices (MSQDs) that offer initialization, coherent control, and readout of quantum spin states remains one of the major bottlenecks on the way toward applications of these systems in quantum computing technologies. We discuss the evolution of the field of MSQDs and review the first successful implementation of essential qubit operations in a single-molecule transistor based on a TbPc 2 molecule. Further development has been achieved through the merging of molecular electronics with the circuit quantum electrodynamics (cQED) approach where molecular spin states can be manipulated by the microwave frequency photons confined in a superconducting waveguide resonator. We discuss examples of such hybrid devices operating via coupling of a superconducting resonator to large spin ensembles, such as bulk samples and thin films. We also review a possible architecture for single-molecule cQED devices and the potential advantages that it offers. Then, we highlight the possibility and benefits of the optical initialization and readout of molecular spin states. This approach has been realized by using an optical pumping technique for the initialization and changes in photoluminescence for the readout of large molecular spin ensembles coupled to a superconducting resonator. The field of MSQDs is highly interdisciplinary, bringing together progress in synthetic chemistry, molecular electronics, cQED, and optical measurements. While it is still in its infancy, there are promising theoretical designs and encouraging proof-of-concept experiments, and we discuss several proposed device architectures that are eagerly awaiting experimental realization. Advances in hybrid MSQDs will open horizons for quantum technologies.
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.