Strong coupling of a spin ensemble to a superconducting resonator

Superconducting Cavity-Based Sensing of Band Gaps in 2D Materials

The superconducting coplanar waveguide (SCPW) cavity plays an essential role in various areas like superconducting qubits, parametric amplifiers, radiation detectors, and studying magnon-photon and photon-phonon coupling. Despite its wide-ranging applications, the use of SCPW cavities to study various van der Waals 2D materials has been relatively unexplored. The resonant modes of the SCPW cavity exquisitely sense the dielectric environment. In this work, we measure the charge compressibility of bilayer graphene coupled to a half-wavelength SCPW cavity. Our approach provides a means to detect subtle changes in the capacitance of the bilayer graphene heterostructure, which depends on the compressibility of bilayer graphene, manifesting as shifts in the resonant frequency of the cavity. This method holds promise for exploring a wide class of van der Waals 2D materials, including transition metal dichalcogenides (TMDs) and their moiré, where DC transport measurement is challenging.

Molecular nanomagnets: a viable path toward quantum information processing?

Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.

Long-distance transmission of arbitrary quantum states between spatially separated microwave cavities

Long-distance transmission between spatially separated microwave cavities is a crucial area of quantum information science and technology. In this work, we present a method for achieving long-distance transmission of arbitrary quantum states between two microwave cavities, by using a hybrid system that comprises two microwave cavities, two nitrogen-vacancy center ensembles (NV ensembles), two optical cavities, and an optical fiber. Each NV ensemble serves as a quantum transducer, dispersively coupling with a microwave cavity and an optical cavity, which enables the conversion of quantum states between a microwave cavity and an optical cavity. The optical fiber acts as a connector between the two optical cavities. Numerical simulations demonstrate that our method allows for the transfer of an arbitrary photonic qubit state between two spatially separated microwave cavities with high fidelity. Furthermore, the method exhibits robustness against environmental decay, parameter fluctuations, and additive white Gaussian noise. Our approach offers a promising way for achieving long-distance transmission of quantum states between two spatially separated microwave cavities, which may have practical applications in networked large-scale quantum information processing and quantum communication.

A decouple-decomposition noise analysis model for closed-loop mode-localized tilt sensors

The development of mode-localized sensors based on amplitude output metrics has attracted increasing attention in recent years due to the potential of such sensors for high sensitivity and resolution. Mode-localization phenomena leverage the interaction between multiple coupled resonant modes to achieve enhanced performance, providing a promising solution to overcome the limitations of traditional sensing technologies. Amplitude noise plays a key role in determining the resolution of mode-localized sensors, as the output metric is derived from the measured AR (amplitude ratio) within the weakly coupled resonator system. However, the amplitude noise originating from the weakly coupled resonator's closed-loop circuit has not yet been fully investigated. This paper presents a decouple-decomposition (DD) noise analysis model, which is applied to achieve high resolution in a mode-localized tilt sensor based on a weakly coupled resonator closed-loop circuit. The DD noise model separates the weakly coupled resonators using the decoupling method considering the nonlinearity of the resonators. By integrating the decoupled weakly coupled resonators, the model decomposes the weakly coupled resonator's closed-loop circuit into distinct paths for amplitude and phase noise analyses. The DD noise model reveals noise effects at various circuit nodes and models the system noise in the closed-loop circuit of the weakly coupled resonators. MATLAB/Simulink simulations verify the model's accuracy when compared to theoretical analysis. At the optimal operating point, the mode-localized tilt sensor achieves an input-referred instability of 3.91 × 10-4° and an input-referred AR of PSD of 2.01 × 10-4°⁄√Hz using the closed-loop noise model. This model is also applicable to other varieties of mode-localized sensors.

Hybrid quantum systems with high-T[Formula: see text] superconducting resonators

Superconducting microwave resonators are crucial elements of microwave circuits, offering a wide range of potential applications in modern science and technology. While conventional low-T[Formula: see text] superconductors are mainly employed, high-T[Formula: see text] cuprates could offer enhanced temperature and magnetic field operating ranges. Here, we report the realization of [Formula: see text] superconducting coplanar waveguide resonators, and demonstrate a continuous evolution from a lossy undercoupled regime, to a lossless overcoupled regime by adjusting the device geometry, in good agreement with circuit model theory. A high-quality factor resonator was then used to perform electron spin resonance measurements on a molecular spin ensemble across a temperature range spanning two decades. We observe spin-cavity hybridization indicating coherent coupling between the microwave field and the spins in a highly cooperative regime. The temperature dependence of the Rabi splitting and the spin relaxation time point toward an antiferromagnetic coupling of the spins below 2 K. Our findings indicate that high-Tc superconducting resonators hold great promise for the development of functional circuits. Additionally, they suggest novel approaches for achieving hybrid quantum systems based on high-T[Formula: see text] superconductors and for conducting electron spin resonance measurements over a wide range of magnetic fields and temperatures.

Enhancement of the microwave photon-magnon coupling strength for a planar fabricated resonator

Planar resonators have a wide usage in modern microwave technologies and perspectives in novel quantum technologies development. As was demonstrated earlier, their utilization allows to achieve high values of microwave photon-magnon coupling strength-an important parameter in technologies of information coherent transfer from electromagnetic GHz range to the optical range. In the present work, the achievement of the high value of the microwave photon-magnon coupling strength by exploiting the increase of the spatial concentration of the magnetic component of the planar resonator electromagnetic field is reported. Starting from the conventional planar split-ring resonator design we increased the coupling strength up to 40% by modifying the resonator shape. The numerical simulation and experimental verification showed a predicted increase in the spatial concentration of the microwave magnetic component and showed the increased value of the microwave photon-magnon coupling strength as a sequence.

Silicon-Aluminum Phase-Transformation-Induced Superconducting Rings

The development of devices that exhibit both superconducting and semiconducting properties is an important endeavor for emerging quantum technologies. We investigate superconducting nanowires fabricated on a silicon-on-insulator (SOI) platform. Aluminum from deposited contact electrodes is found to interdiffuse with Si along the entire length of the nanowire, over micrometer length scales and at temperatures well below the Al-Si eutectic. The phase-transformed material is conformal with the predefined device patterns. The superconducting properties of a transformed mesoscopic ring formed on a SOI platform are investigated. Low-temperature magnetoresistance oscillations, quantized in units of the fluxoid, h/2e, are observed.

Spin-Echo Silencing Using a Current-Biased Frequency-Tunable Resonator

The ability to control microwave emission from a spin ensemble is a requirement of several quantum memory protocols. Here, we demonstrate such ability by using a resonator whose frequency can be rapidly tuned with a bias current. We store excitations in an ensemble of rare-earth ions and suppress on demand the echo emission ("echo silencing") by two methods: (1) detuning the resonator during the spin rephasing, and (2) subjecting spins to magnetic field gradients generated by the bias current itself. We also show that spin coherence is preserved during silencing.

Cavity Quantum Electrodynamics Effects with Nitrogen Vacancy Center Spins Coupled to Room Temperature Microwave Resonators

Cavity quantum electrodynamics (CQED) effects, such as Rabi splitting, Rabi oscillations, and superradiance, have been demonstrated with nitrogen vacancy (NV) center spins in diamond coupled to microwave resonators at cryogenic temperature. In this Letter, we explore the possibility to realize strong collective coupling and CQED effects with ensembles of NV spins at room temperature. Our calculations show that thermal excitation of the individual NV spins leads to population of collective Dicke states with low symmetry and a reduced collective coupling to the microwave resonators. Optical pumping can be applied to counteract the thermal excitation of the NV centers and to prepare the spin ensemble in Dicke states with high symmetry. The resulting strong coupling with high-quality resonators enables the study of intriguing CQED effects across the weak-to-strong coupling regime, and may have applications in quantum sensing and quantum information processing.

Coherent Coupling of Two Remote Magnonic Resonators Mediated by Superconducting Circuits

We demonstrate microwave-mediated distant magnon-magnon coupling on a superconducting circuit platform, incorporating chip-mounted single-crystal Y_{3}Fe_{5}O_{12} (YIG) spheres. Coherent level repulsion and dissipative level attraction between the magnon modes of the two YIG spheres are demonstrated. The former is mediated by cavity photons of a superconducting resonator, and the latter is mediated by propagating photons of a coplanar waveguide. Our results open new avenues toward exploring integrated hybrid magnonic networks for coherent information processing on a quantum-compatible superconducting platform.

Twenty-three-millisecond electron spin coherence of erbium ions in a natural-abundance crystal

Erbium ions embedded in crystals have unique properties for quantum information processing, because of their optical transition at 1.5 μm and of the large magnetic moment of their effective spin-1/2 electronic ground state. Most applications of erbium require, however, long electron spin coherence times, and this has so far been missing. Here, by selecting a host matrix with a low nuclear-spin density (CaWO₄) and by quenching the spectral diffusion due to residual paramagnetic impurities at millikelvin temperatures, we obtain a 23-ms coherence time on the Er³⁺ electron spin transition. This is the longest Hahn echo electron spin coherence time measured in a material with a natural abundance of nuclear spins and on a magnetically sensitive transition. Our results establish Er³⁺:CaWO₄ as a potential platform for quantum networks.

Focusing the electromagnetic field to 10-6λ for ultra-high enhancement of field-matter interaction

Focusing electromagnetic field to enhance the interaction with matter has been promoting researches and applications of nano electronics and photonics. Usually, the evanescent-wave coupling is adopted in various nano structures and materials to confine the electromagnetic field into a subwavelength space. Here, based on the direct coupling with confined electron oscillations in a nanowire, we demonstrate a tight localization of microwave field down to 10⁻⁶λ. A hybrid nanowire-bowtie antenna is further designed to focus the free-space microwave to this deep-subwavelength space. Detected by the nitrogen vacancy center in diamond, the field intensity and microwave-spin interaction strength are enhanced by 2.0 × 10⁸ and 1.4 × 10⁴ times, respectively. Such a high concentration of microwave field will further promote integrated quantum information processing, sensing and microwave photonics in a nanoscale system.

Subwavelength focusing of electromagnetic fields often uses evanescent waves and nanostructures to aid confinement. Here, the authors localize a microwave field to 6 orders of magnitude smaller than the wavelength, by coupling to confined electron oscillations in a hybrid nanowire-bowtie antenna.

Periodic Cavity State Revivals from Atomic Frequency Combs

Spin ensembles with a comb-shaped spectrum have shown exciting properties as efficient quantum memories. Here, we present a rigorous theoretical study of such atomic frequency combs in the strong coupling limit of cavity QED, based on a full quantum treatment using tensor-network methods. Our results demonstrate that arbitrary multiphoton states in the cavity are almost perfectly absorbed by the spin ensemble and reemitted as parity-flipped states at periodic time intervals. Fidelity values near unity are achieved in these revived states by compensating for energy shifts induced by the strong spin-cavity coupling through adjustments of individual coupling values of the teeth in the atomic frequency comb.

Photon Condensation and Enhanced Magnetism in Cavity QED

A system of magnetic molecules coupled to microwave cavities (LC resonators) undergoes the equilibrium superradiant phase transition. The transition is experimentally observable. The effect of the coupling is first illustrated by the vacuum-induced ferromagnetic order in a quantum Ising model and then by the modification of the magnetic phase diagram of Fe_{8} dipolar crystals, exemplifying the cooperation between intrinsic and photon-induced spin-spin interactions. Finally, a transmission experiment is shown to resolve the transition, measuring the quantum electrodynamical control of magnetism.

Strong single-photon optomechanical coupling in a hybrid quantum system

Engineering strong single-photon optomechanical couplings is crucial for optomechanical systems. Here, we propose a hybrid quantum system consisting of a nanobeam (phonons) coupled to a spin ensemble and a cavity (photons) to overcome it. Utilizing the critical property of the lower-branch polariton (LBP) formed by the ensemble-phonon interaction, the LBP-cavity coupling can be greatly enhanced by three orders magnitude of the original one, while the upper-branch polariton (UBP)-cavity coupling is fully suppressed. Our proposal breaks through the condition of the coupling strength less than the critical value in previous schemes using two harmonic oscillators. Also, strong Kerr effect can be induced in our proposal. This shows our proposed approach can be used to study quantum nonlinear and nonclassical effects in weakly coupled optomechanical systems.

Generating Long-Lived Macroscopically Distinct Superposition States in Atomic Ensembles

We propose to create and stabilize long-lived macroscopic quantum superposition states in atomic ensembles. We show that using a fully quantum parametric amplifier can cause the simultaneous decay of two atoms and, in turn, create stabilized atomic Schrödinger cat states. Remarkably, even with modest parameters these intracavity atomic cat states can have an extremely long lifetime, up to 4 orders of magnitude longer than that of intracavity photonic cat states under the same parameter conditions, reaching tens of milliseconds. This lifetime of atomic cat states is ultimately limited to several seconds by extremely weak spin relaxation and thermal noise. Our work opens up a new way toward the long-standing goal of generating large-size and long-lived cat states, with immediate interests both in fundamental studies and noise-immune quantum technologies.

Room-Temperature Quantum Memories Based on Molecular Electron Spin Ensembles

Whilst quantum computing has recently taken great leaps ahead, the development of quantum memories has decidedly lagged behind. Quantum memories are essential devices in the quantum technology palette and are needed for intermediate storage of quantum bit states and as quantum repeaters in long-distance quantum communication. Current quantum memories operate at cryogenic, mostly sub-Kelvin temperatures and require extensive and costly peripheral hardware. It is demonstrated that ensembles of weakly coupled molecular spins show long coherence times and can be used to store microwave pulses of arbitrary phase. These studies exploit strong coupling of the spin ensemble to special 3D microwave resonators. Most importantly, these systems operate at room temperature.

Quantum Interfaces to the Nanoscale

Scalable quantum information systems would store, manipulate, and transmit quantum information locally and across a quantum network, but no single qubit technology is currently robust enough to perform all necessary tasks. Defect centers in solid-state materials have emerged as potential intermediaries between other physical manifestations of qubits, such as superconducting qubits and photonic qubits, to leverage their complementary advantages. It remains an open question, however, how to design and to control quantum interfaces to defect centers. Such interfaces would enable quantum information to be moved seamlessly between different physical systems. Understanding and constructing the required interfaces would, therefore, unlock the next big steps in quantum computing, sensing, and communications. In this Perspective, we highlight promising coupling mechanisms, including dipole-, phonon-, and magnon-mediated interactions, and discuss how contributions from nanotechnologists will be paramount in realizing quantum information processors in the near-term.

Ballistic Hall Photovoltammetry of Magnetic Resonance in Individual Nanomagnets

We report on ballistic Hall photovoltammetry as a contactless probe of localized spin excitations. Spins resonating in the near field of a two-dimensional electron system are shown to induce a long range electromotive force that we calculate. We use this coupling mechanism to detect the spin wave eigenmodes of a single ferromagnet of sub-100 nm size. The high sensitivity of this detection technique, 380 spins/sqrt[Hz], and its noninvasiveness present advantages for probing magnetization dynamics and spin transport.

Cavity-enhanced microwave readout of a solid-state spin sensor

Overcoming poor readout is an increasingly urgent challenge for devices based on solid-state spin defects, particularly given their rapid adoption in quantum sensing, quantum information, and tests of fundamental physics. However, in spite of experimental progress in specific systems, solid-state spin sensors still lack a universal, high-fidelity readout technique. Here we demonstrate high-fidelity, room-temperature readout of an ensemble of nitrogen-vacancy centers via strong coupling to a dielectric microwave cavity, building on similar techniques commonly applied in cryogenic circuit cavity quantum electrodynamics. This strong collective interaction allows the spin ensemble’s microwave transition to be probed directly, thereby overcoming the optical photon shot noise limitations of conventional fluorescence readout. Applying this technique to magnetometry, we show magnetic sensitivity approaching the Johnson–Nyquist noise limit of the system. Our results pave a clear path to achieve unity readout fidelity of solid-state spin sensors through increased ensemble size, reduced spin-resonance linewidth, or improved cavity quality factor.

Conventional optical readout limits the sensitivity of solid state spin sensors due to photon shot noise and poor contrast. Here, the authors demonstrate room-temperature microwave detection of an ensemble of NV centers embedded in a microwave cavity, which offers high-fidelity readout without time overhead.

Hyperfine spectroscopy in a quantum-limited spectrometer

We report measurements of electron-spin-echo envelope modulation (ESEEM) performed at millikelvin temperatures in a custom-built high-sensitivity spectrometer based on superconducting micro-resonators. The high quality factor and small mode volume (down to 0.2 pL) of the resonator allow us to probe a small number of spins, down to 5 × 10 2 . We measure two-pulse ESEEM on two systems: erbium ions coupled to 183 W nuclei in a natural-abundance CaWO 4 crystal and bismuth donors coupled to residual 29 Si nuclei in a silicon substrate that was isotopically enriched in the 28 Si isotope. We also measure three- and five-pulse ESEEM for the bismuth donors in silicon. Quantitative agreement is obtained for both the hyperfine coupling strength of proximal nuclei and the nuclear-spin concentration.

Multimode Storage of Quantum Microwave Fields in Electron Spins over 100 ms

We report long coherence times (up to 300 ms) for near-surface bismuth donor electron spins in silicon coupled to a superconducting microresonator, biased at a clock transition. This enables us to demonstrate the partial absorption of a train of weak microwave fields in the spin ensemble, their storage for 100 ms, and their retrieval, using a Hahn-echo-like protocol. Phase coherence and quantum statistics are preserved in the storage.

Echo Trains in Pulsed Electron Spin Resonance of a Strongly Coupled Spin Ensemble

We report on a novel dynamical phenomenon in electron spin resonance experiments of phosphorus donors. When strongly coupling the paramagnetic ensemble to a superconducting lumped element resonator, the coherent exchange between these two subsystems leads to a train of periodic, self-stimulated echoes after a conventional Hahn echo pulse sequence. The presence of these multiecho signatures is explained using a simple model based on spins rotating on the Bloch sphere, backed up by numerical calculations using the inhomogeneous Tavis-Cummings Hamiltonian.

Universal coherence protection in a solid-state spin qubit

Decoherence limits the physical realization of qubits, and its mitigation is critical for the development of quantum science and technology. We construct a robust qubit embedded in a decoherence-protected subspace, obtained by applying microwave dressing to a clock transition of the ground-state electron spin of a silicon carbide divacancy defect. The qubit is universally protected from magnetic, electric, and temperature fluctuations, which account for nearly all relevant decoherence channels in the solid state. This culminates in an increase of the qubit's inhomogeneous dephasing time by more than four orders of magnitude (to >22 milliseconds), while its Hahn-echo coherence time approaches 64 milliseconds. Requiring few key platform-independent components, this result suggests that substantial coherence improvements can be achieved in a wide selection of quantum architectures.

Enhanced Molecular Spin-Photon Coupling at Superconducting Nanoconstrictions

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 × 10⁶ and 10¹² 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.

High-sensitivity DC magnetic field detection with ensemble NV centers by pulsed quantum filtering technology

Continuous wave optically detected magnetic resonance (CW-ODMR) is a practical way to study the sensitivity of the DC magnetic field. However, in large ensemble nitrogen-vacancy (NV) defects, the simultaneous excitation of microwave and laser will deteriorate the parameters of the ODMR spectrum and some unwanted sideband excitations caused by P1 electron spins will also bring challenges to further improve the sensitivity and signal quality. Here, we first achieve the CW-ODMR and acquire DC photon-shot-noise-limited magnetic sensitivity of 12nT/Hz. Different from the conventional method, we take advantage of pulsed quantum filtering (PQF) technology to eliminate such impacts above and demonstrate a sensitivity of about 1nT/Hz, which an order of magnitude enhancement over CW-ODMR. We find this method provides simple but effective support for relevant high-sensitivity DC magnetometry and obtains pure resonance signal when using large ensemble NV^- defects.

THz white light cavity with nonlinear dispersion in graphene

A white light cavity (WLC) scheme is proposed to achieve broadband response in the terahertz (THz) region by enhanced nonlinear dispersion in a magnetized graphene system. In the weak probe field limit, the cavity linewidth is narrowed due to electromagnetically induced transparency, and then it becomes nearly as broad as the empty-cavity linewidth under the condition of Autler-Towns splitting. It is interesting to find that the cavity linewidth can be further broadened by enhanced nonlinear dispersion. The simulation result shows that the response range of the cavity is from 6.273 THz to 6.308 THz under the given condition, which is nearly 11 times larger than the empty-cavity linewidth. Furthermore, the improvement in cavity transmission and the response of WLC at different frequencies are investigated.

Microwave probing of bulk dielectrics using superconducting coplanar resonators in distant-flip-chip geometry

Dielectric measurements on insulating materials at cryogenic temperatures can be challenging, depending on the frequency and temperature ranges of interest. We present a technique to study the dielectric properties of bulk dielectrics at GHz frequencies. A superconducting coplanar Nb resonator is deposited directly on the material of interest, and this resonator is then probed in distant-flip-chip geometry with a microwave feedline on a separate chip. Evaluating several harmonics of the resonator gives access to various probing frequencies in the present studies up to 20 GHz. We demonstrate the technique on three different materials (MgO, LaAlO₃, and TiO₂), at temperatures between 1.4 K and 7 K.

Projecting an ultra-strongly-coupled system in a non-energy-eigenbasis with a driven nonlinear resonator

We explore the problem of projecting the ground-state of an ultra-strong-coupled circuit-QED system into a non-energy-eigenstate. As a measurement apparatus we consider a nonlinear driven resonator. We find that the post-measurement state of the nonlinear resonator exhibits a large correlation with the post-measurement state of the ultra-strongly coupled system even when the coupling between measurement device and system is much smaller than the energy scales of the system itself. While the projection is imperfect, we argue that because of the strong nonlinear response of the resonator it works in a practical regime where a linear measurement apparatus would fail.

A high-N00N output of harmonically driven cavity QED

A harmonically driven cavity QED system consisting of two cavities and a two-level qubit is shown to enable the generation of a vast class of maximally entangled states suitable for measurements with a Heisenberg-limit precision. As one of its modalities, this system can serve as a quantum beam splitter, converting an |N〉 ⊗ |0〉 input into a maximally entangled N00N state (|N〉 ⊗ |0〉  +  |0〉 ⊗ |N〉)/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{{\bf{2}}}$$\end{document}2 at its output. A network of such quantum beam splitters is shown to provide a source of multimode N00N-type entanglement.

Single-crystalline boron-doped diamond superconducting quantum interference devices with regrowth-induced step edge structure

Superconducting quantum interference devices (SQUIDs) are currently used as magnetic flux detectors with ultra-high sensitivity for various applications such as medical diagnostics and magnetic material microstructure analysis. Single-crystalline superconducting boron-doped diamond is an excellent candidate for fabricating high-performance SQUIDs because of its robustness and high transition temperature, critical current density, and critical field. Here, we propose a fabrication process for a single-crystalline boron-doped diamond Josephson junction with regrowth-induced step edge structure and demonstrate the first operation of a single-crystalline boron-doped diamond SQUID above 2 K. We demonstrate that the step angle is a significant parameter for forming the Josephson junction and that the step angle can be controlled by adjusting the microwave plasma-enhanced chemical vapour deposition conditions of the regrowth layer. The fabricated junction exhibits superconductor-weak superconductor-superconductor-type behaviour without hysteresis and a high critical current density of 5800 A/cm2.

Engineering Electron-Phonon Coupling of Quantum Defects to a Semiconfocal Acoustic Resonator

Diamond-based microelectromechanical systems (MEMS) enable direct coupling between the quantum states of nitrogen-vacancy (NV) centers and the phonon modes of a mechanical resonator. One example, a diamond high-overtone bulk acoustic resonator (HBAR), features an integrated piezoelectric transducer and supports high-quality factor resonance modes into the gigahertz frequency range. The acoustic modes allow mechanical manipulation of deeply embedded NV centers with long spin and orbital coherence times. Unfortunately, the spin-phonon coupling rate is limited by the large resonator size, >100 μm, and thus strongly coupled NV electron-phonon interactions remain out of reach in current diamond BAR devices. Here, we report the design and fabrication of a semiconfocal HBAR (SCHBAR) device on diamond (silicon carbide) with f × Q > 10¹² (>10¹³). The semiconfocal geometry confines the phonon mode laterally below 10 μm. This drastic reduction in modal volume enhances defect center coupling to a mechanical mode by 1000 times compared to prior HBAR devices. For the native NV centers inside the diamond device, we demonstrate mechanically driven spin transitions and show a high strain-driving efficiency with a Rabi frequency of (2π)2.19(14) MHz/V_p, which is comparable to a typical microwave antenna at the same microwave power, making SCHBAR a power-efficient device useful for fast spin control, dressed state coherence protection, and quantum circuit integration.

Exchange-Enhanced Ultrastrong Magnon-Magnon Coupling in a Compensated Ferrimagnet

We experimentally study the spin dynamics in a gadolinium iron garnet single crystal using broadband ferromagnetic resonance. Close to the ferrimagnetic compensation temperature, we observe ultrastrong coupling of clockwise and counterclockwise magnon modes. The magnon-magnon coupling strength reaches almost 40% of the mode frequency and can be tuned by varying the direction of the external magnetic field. We theoretically explain the observed mode coupling as arising from the broken rotational symmetry due to a weak magnetocrystalline anisotropy. The effect of this anisotropy is exchange enhanced around the ferrimagnetic compensation point.

Strong Coupling between Magnons and Microwave Photons in On-Chip Ferromagnet-Superconductor Thin-Film Devices

We demonstrate strong magnon-photon coupling of a thin-film Permalloy device fabricated on a coplanar superconducting resonator. A coupling strength of 0.152 GHz and a cooperativity of 68 are found for a 30-nm-thick Permalloy stripe. The coupling strength is tunable by rotating the biasing magnetic field or changing the volume of Permalloy. We also observe an enhancement of magnon-photon coupling in the nonlinear regime of the superconducting resonator, which is attributed to the nucleation of dynamic flux vortices. Our results demonstrate a critical step towards future integrated hybrid systems for quantum magnonics and on-chip coherent information transfer.

Strong coupling of collective intermolecular vibrations in organic materials at terahertz frequencies

Several years ago, strong coupling between electronic molecular transitions and photonic structures was shown to modify the electronic landscape of the molecules and affect their chemical behavior. Since then, this concept has evolved into a new field known as polaritonic chemistry. An important ingredient in the progress of this field was the demonstration of strong coupling with intra-molecular vibrations, which enabled the modification of processes occurring at the electronic ground-state. Here we demonstrate strong coupling with collective, inter-molecular vibrations occurring in organic materials in the low-terahertz region (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lesssim$$\end{document}≲10¹² Hz). Using a cavity filled with α-lactose molecules, we measure the temporal evolution and observe coherent Rabi oscillations, corresponding to a splitting of 68 GHz. These results take strong coupling into a new class of materials and processes, including skeletal polymer motions, protein dynamics, metal organic frameworks and other materials, in which collective, spatially extended degrees of freedom participate in the dynamics.

Here, the authors demonstrate strong coupling between collective, terahertz inter-molecular vibrations of organic materials and a Fabry-Pérot cavity. These results extend the applicability of polaritonic chemistry to large-scale organic systems, such as biological macromolecules and polymer chains.

Many-Body Localization in the Presence of a Central Qudit

We consider a many-body localized system coupled globally to a central d-level system. Under an appropriate scaling of d and L, we find evidence that the localized phase survives. We argue for two possible thermalizing phases, depending on whether the qudit becomes fully ergodic. This system provides one of the first examples of many-body localization in the presence of long-range (nonconfining) interactions.

Imaging the Local Charge Environment of Nitrogen-Vacancy Centers in Diamond

Characterizing the local internal environment surrounding solid-state spin defects is crucial to harnessing them as nanoscale sensors of external fields. This is especially germane to the case of defect ensembles which can exhibit a complex interplay between interactions, internal fields, and lattice strain. Working with the nitrogen-vacancy (NV) center in diamond, we demonstrate that local electric fields dominate the magnetic resonance behavior of NV ensembles at a low magnetic field. We introduce a simple microscopic model that quantitatively captures the observed spectra for samples with NV concentrations spanning more than two orders of magnitude. Motivated by this understanding, we propose and implement a novel method for the nanoscale localization of individual charges within the diamond lattice; our approach relies upon the fact that the charge induces a NV dark state which depends on the electric field orientation.

Tunable Spin-Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules

Atomic-scale magnetic moments in contact with superconductors host rich physics based on the emergence of Yu-Shiba-Rusinov (YSR) magnetic bound states within the superconducting condensate. Here, we focus on a magnetic bound state induced into Pb nanoislands by individual vanadyl phthalocyanine (VOPc) molecules deposited on the Pb surface. The VOPc molecule is characterized by a spin magnitude of 1/2 arising from a well-isolated singly occupied d _xy-orbital and is a promising candidate for a molecular spin qubit with long coherence times. X-ray magnetic circular dichroism (XMCD) measurements show that the molecular spin remains unperturbed even for molecules directly deposited on the Pb surface. Scanning tunneling spectroscopy and density functional theory (DFT) calculations identify two adsorption geometries for this "asymmetric" molecule (i.e., absence of a horizontal symmetry plane): (a) oxygen pointing toward the vacuum with the Pc laying on the Pb, showing negligible spin-superconductor interaction, and (b) oxygen pointing toward the Pb, presenting an efficient interaction with the Pb and promoting a Yu-Shiba-Rusinov bound state. Additionally, we find that in the first case a YSR state can be induced smoothly by exerting mechanical force on the molecules with the scanning tunneling microscope (STM) tip. This allows the interaction strength to be tuned continuously from an isolated molecular spin case, through the quantum critical point (where the bound state energy is zero) and beyond. DFT indicates that a gradual bending of the VO bond relative to the Pc ligand plane promoted by the STM tip can modify the interaction in a continuously tunable manner. The ability to induce a tunable YSR state in the superconductor suggests the possibility of introducing coupled spins on superconductors with switchable interaction.

Strong light confinement in rod-connected diamond photonic crystals

We show that it is possible to confine light in a volume of order 10^-3 cubic wavelengths using only dielectric material. Low-index (air) cavities are simulated in high-index rod-connected diamond photonic crystals. These cavities show long storage times (Q-factors >10⁶) even at the lowest volumes. Fabrication of such structures could open a new field of photon-level interactions.

Dynamical coupling between a nuclear spin ensemble and electromechanical phonons

Dynamical coupling with high-quality factor resonators is essential in a wide variety of hybrid quantum systems such as circuit quantum electrodynamics and opto/electromechanical systems. Nuclear spins in solids have a long relaxation time and thus have the potential to be implemented into quantum memories and sensors. However, state manipulation of nuclear spins requires high-magnetic fields, which is incompatible with state-of-the-art quantum hybrid systems based on superconducting microwave resonators. Here we investigate an electromechanical resonator whose electrically tunable phonon state imparts a dynamically oscillating strain field to the nuclear spin ensemble located within it. As a consequence of the dynamical strain, we observe both nuclear magnetic resonance (NMR) frequency shifts and NMR sidebands generated by the electromechanical phonons. This prototype system potentially opens up quantum state engineering for nuclear spins, such as coherent coupling between sound and nuclei, and mechanical cooling of solid-state nuclei.

Nuclear spins in solids can be implemented into quantum devices but their manipulation usually requires microwave irradiation. Here instead the authors show that they can shift the NMR frequency and drive the nuclear spins into the resolved-sideband regime by using the tunable phonon states from an electromechanical resonator.

Witnessing quantum entanglement in ensembles of nitrogen-vacancy centers coupled to a superconducting resonator

A hybrid quantum device consisting of three ensembles of nitrogen-vacancy centers (NVEs) whose spins are collectively coupled to a superconducting coplanar waveguide resonator is shown to enable the generation of controllable tripartite macroscopic entangled states. The density matrix of such NVEs can be encoded to recast a three-qubit system state, which can be characterized in terms of the entanglement witnesses in relation to the Greenberger-Horne-Zeilinger (GHZ) states. We identify the parameter space within which the generated entangled states can have an arbitrarily large overlap with GHZ states, indicating an enhanced entanglement in the system.

Realizing a Circuit Analog of an Optomechanical System with Longitudinally Coupled Superconducting Resonators

We realize a superconducting circuit analog of the generic cavity-optomechanical Hamiltonian by longitudinally coupling two superconducting resonators, which are an order of magnitude different in frequency. We achieve longitudinal coupling by embedding a superconducting quantum interference device into a high frequency resonator, making its resonance frequency depend on the zero point current fluctuations of a nearby low frequency LC resonator. By applying sideband drive fields we enhance the intrinsic coupling strength of about 15 kHz up to 280 kHz by controlling the amplitude of the drive field. Our results pave the way towards the exploration of optomechanical effects in a fully superconducting platform and could enable quantum optics experiments with photons in the yet unexplored radio frequency band.

Enhancing Cavity Quantum Electrodynamics via Antisqueezing: Synthetic Ultrastrong Coupling

We present and analyze a method where parametric (two-photon) driving of a cavity is used to exponentially enhance the light-matter coupling in a generic cavity QED setup, with time-dependent control. Our method allows one to enhance weak-coupling systems, such that they enter the strong coupling regime (where the coupling exceeds dissipative rates) and even the ultrastrong coupling regime (where the coupling is comparable to the cavity frequency). As an example, we show how the scheme allows one to use a weak-coupling system to adiabatically prepare the highly entangled ground state of the ultrastrong coupling system. The resulting state could be used for remote entanglement applications.

Tunable coupling of spin ensembles

Spin ensembles are promising candidates for quantum memory units because they have long coherence time. Controlling the coupling between spin ensembles is necessary and important in quantum information processing. In this Letter, we propose a method to realize tunable coupling between spin ensembles by a superconducting flux qubit acting as a coupler. The resulting coupling can be used to high-fidelity speed up the adiabatic transfer of quantum information.

Storing quantum information in spins and high-sensitivity ESR

Quantum information, encoded within the states of quantum systems, represents a novel and rich form of information which has inspired new types of computers and communications systems. Many diverse electron spin systems have been studied with a view to storing quantum information, including molecular radicals, point defects and impurities in inorganic systems, and quantum dots in semiconductor devices. In these systems, spin coherence times can exceed seconds, single spins can be addressed through electrical and optical methods, and new spin systems with advantageous properties continue to be identified. Spin ensembles strongly coupled to microwave resonators can, in principle, be used to store the coherent states of single microwave photons, enabling so-called microwave quantum memories. We discuss key requirements in realising such memories, including considerations for superconducting resonators whose frequency can be tuned onto resonance with the spins. Finally, progress towards microwave quantum memories and other developments in the field of superconducting quantum devices are being used to push the limits of sensitivity of inductively-detected electron spin resonance. The state-of-the-art currently stands at around 65 spins per Hz, with prospects to scale down to even fewer spins.

Coupling ultracold atoms to a superconducting coplanar waveguide resonator

Ensembles of trapped atoms interacting with on-chip microwave resonators are considered as promising systems for the realization of quantum memories, novel quantum gates, and interfaces between the microwave and optical regime. Here, we demonstrate coupling of magnetically trapped ultracold Rb ground-state atoms to a coherently driven superconducting coplanar resonator on an integrated atom chip. When the cavity is driven off-resonance from the atomic transition, the microwave field strength in the cavity can be measured through observation of the AC shift of the atomic hyperfine transition frequency. When driving the cavity in resonance with the atoms, we observe Rabi oscillations between hyperfine states, demonstrating coherent control of the atomic states through the cavity field. These observations enable the preparation of coherent atomic superposition states, which are required for the implementation of an atomic quantum memory.

Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena

Circuit QED techniques have been instrumental in manipulating and probing with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices in which the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments uses cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.

Coherent coupling between Vanadyl Phthalocyanine spin ensemble and microwave photons: towards integration of molecular spin qubits into quantum circuits

Electron spins are ideal two-level systems that may couple with microwave photons so that, under specific conditions, coherent spin-photon states can be realized. This represents a fundamental step for the transfer and the manipulation of quantum information. Along with spin impurities in solids, molecular spins in concentrated phases have recently shown coherent dynamics under microwave stimuli. Here we show that it is possible to obtain high cooperativity regime between a molecular Vanadyl Phthalocyanine (VOPc) spin ensemble and a high quality factor superconducting YBa₂Cu₃O₇ (YBCO) coplanar resonator at 0.5 K. This demonstrates that molecular spin centers can be successfully integrated in hybrid quantum devices.

Strong Coupling of Microwave Photons to Antiferromagnetic Fluctuations in an Organic Magnet

Coupling between a crystal of di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium radicals and a superconducting microwave resonator is investigated in a circuit quantum electrodynamics (circuit QED) architecture. The crystal exhibits paramagnetic behavior above 4 K, with antiferromagnetic correlations appearing below this temperature, and we demonstrate strong coupling at base temperature. The magnetic resonance acquires a field angle dependence as the crystal is cooled down, indicating anisotropy of the exchange interactions. These results show that multispin modes in organic crystals are suitable for circuit QED, offering a platform for their coherent manipulation. They also utilize the circuit QED architecture as a way to probe spin correlations at low temperature.