Superconducting coplanar waveguide resonators for low temperature pulsed electron spin resonance spectroscopy

Microwave Fluorescence Detection of Spin Echoes

Counting the microwave photons emitted by an ensemble of electron spins when they relax radiatively has recently been proposed as a sensitive method for electron paramagnetic resonance spectroscopy, enabled by the development of operational single microwave photon detectors at millikelvin temperature. Here, we report the detection of spin echoes in the spin fluorescence signal. The echo manifests itself as a coherent modulation of the number of photons spontaneously emitted after a π/2_{X}-τ-π_{Y}-τ-π/2_{Φ} sequence, dependent on the relative phase Φ. We demonstrate experimentally this detection method using an ensemble of Er^{3+} ion spins in a scheelite crystal of CaWO_{4}. We use fluorescence-detected echoes to measure the erbium spin coherence time, as well as the echo envelope modulation due to the coupling to the ^{183}W nuclear spins surrounding each ion. We finally compare the signal-to-noise ratio of inductively detected and fluorescence-detected echoes, and show that it is larger with the fluorescence method.

Pulsed Electron-Nuclear Double Resonance in the Fourier Regime

Nuclear magnetic resonance (NMR) spectroscopy provides atomic-level molecular structural information. However, in molecules containing unpaired electron spins, NMR signals are difficult to measure directly. In such cases, data is obtained using the electron-nuclear double resonance (ENDOR) method, where nuclei are detected through their interaction with nearby unpaired electron spins. Unfortunately, electron spins spread the ENDOR signals, which challenges current acquisition techniques, often resulting in low spectral resolution that provides limited structural details. Here, we show that by using miniature microwave resonators to detect a small number of electron spins, integrated with miniature NMR coils, one can excite and detect a wide bandwidth of ENDOR data in a single pulse. This facilitates the measurement of ENDOR spectra with narrow lines spread over a large frequency range at much better spectral resolution than conventional approaches, which helps reveal details of the paramagnetic molecules' chemical structure that were not accessible before.

Recent advances in microresonators and supporting instrumentation for electron paramagnetic resonance spectroscopy

Electron paramagnetic resonance (EPR) spectroscopy characterizes the magnetic properties of paramagnetic materials at the atomic and molecular levels. Resonators are an enabling technology of EPR spectroscopy. Microresonators, which are miniaturized versions of resonators, have advanced inductive-detection EPR spectroscopy of mass-limited samples. Here, we provide our perspective of the benefits and challenges associated with microresonator use for EPR spectroscopy. To begin, we classify the application space for microresonators and present the conceptual foundation for analysis of resonator sensitivity. We summarize previous work and provide insight into the design and fabrication of microresonators as well as detail the requirements and challenges that arise in incorporating microresonators into EPR spectrometer systems. Finally, we provide our perspective on current challenges and prospective fruitful directions.

Milliwatt three- and four-pulse double electron electron resonance for protein structure determination

Electron paramagnetic resonance (EPR) experiments for protein structure determination using double electron-electron resonance (DEER) spectroscopy rely on high-power microwave amplifiers (>300 W) to create the short pulse lengths needed to excite a sizable portion of the spectrum. The recently introduced self-resonant microhelix combines a high B₁ conversion efficiency with an intrinsically large bandwidth (low Q-value) and a high absolute sensitivity. We report dead times in 3-pulse DEER experiments as low as 14 ± 2 ns achieved using less than 1 W of power at X-band (nominally 9.5 GHz) for experiments on a molecular ruler and a T4 lysozyme sample for concentrations down to 100 μM. These low-power experiments were performed using an active volume 120 times smaller than that of a standard pulse EPR resonator, while only a 11-fold decrease in the signal-to-noise ratio was observed. Small build sizes, as realized with the microhelix, give access to volume-limited samples, while shorter dead times allow the investigation of fast relaxing spin species. With the significantly reduced dead times, the 3-pulse DEER experiment can be revisited. Here, we show experimentally that 3-pulse DEER offers superior sensitivity over 4-pulse DEER. We assert that the microhelix paves the road for low-cost benchtop X-band pulse EPR spectrometers by eliminating the need for high-power amplifiers, accelerating the adoption of pulse EPR to a broader community.

Superconducting micro-resonators for electron spin resonance - the good, the bad, and the future

The field of electron spin resonance (ESR) is in constant need of improving its capabilities. Among other things, this means having better resonators to reach improved spin sensitivity and enable larger microwave-power-to-microwave-magnetic-field conversion factors. Surface micro-resonators, made of small metallic patches on a dielectric substrate, provide very good absolute spin sensitivity and high conversion factors due to their very small mode volume. However, such resonators suffer from relatively low spin concentration sensitivity and a low-quality factor, a fact that offsets some of their significant potential advantages. The use of superconducting patches to replace the metallic layer seems a reasonable and straightforward solution to the quality factor issue, at least for measurements carried out at cryogenic temperatures. Nevertheless, superconducting materials, especially those that can operate at moderate cryogenic temperatures, are not easily incorporated into setups requiring high magnetic fields due to the electric current vortices generated in the latter's surface. This makes the transition from normal conducting materials to superconductors highly nontrivial. Here we present the design, fabrication, and testing results of surface micro-resonators made of yttrium barium copper oxide (YBCO), a superconducting material that operates also at high magnetic fields and makes it possible to pursue ESR at moderate cryogenic temperatures (up to ∼ 80 K). We show that with a unique experimental setup, these resonators can be made to operate well even at high fields of ∼ 1.2 T. Furthermore, we analyze the effect of current vortices on the ESR signal and the spins' coherence times. Finally, we provide a head-to-head comparison of YBCO vs copper resonators of the same dimensions, which clearly shows their pros and cons and directs us to future potential developments and improvements in this field.

Plasmonic Metasurface Resonators to Enhance Terahertz Magnetic Fields for High-Frequency Electron Paramagnetic Resonance

Nanoscale magnetic systems play a decisive role in areas ranging from biology to spintronics. Although, in principle, THz electron paramagnetic resonance (EPR) provides high-resolution access to their properties, lack of sensitivity has precluded realizing this potential. To resolve this issue, the principle of plasmonic enhancement of electromagnetic fields that is used in electric dipole spectroscopies with great success is exploited, and a new type of resonators for the enhancement of THz magnetic fields in a microscopic volume is proposed. A resonator composed of an array of diabolo antennas with a back-reflecting mirror is designed and fabricated. Simulations and THz EPR measurements demonstrate a 30-fold signal increase for thin film samples. This enhancement factor increases to a theoretical value of 7500 for samples confined to the active region of the antennas. These findings open the door to the elucidation of fundamental processes in nanoscale samples, including junctions in spintronic devices or biological membranes.

S-band electron spin resonance spectroscopy using a short-circuited coplanar waveguide resonator

In this work, we study the development of a coplanar waveguide (CPW) resonator and its use in an electron spin resonance (ESR) spectrometer. The CPW resonator is designed to operate in S-band (2-4 GHz), with a short circuit configuration leading to miniaturization. It is so constructed such that it has a characteristic impedance of 50 ohms. The resonator supports quasi-TEM mode of propagation owing to its uniplanar nature, demanding detailed electromagnetic simulation. The design parameters and the electromagnetic field distribution are obtained from the simulation. The resonator is fabricated using optical lithography with a rapid prototyping technique. The characteristic response of the resonator is measured by coupling it to a Vector Network Analyzer (VNA). The ESR absorption spectrum of free radical 2,2-diphenyl-1-picrylhydrazyl (DPPH) is captured by using this resonator in reflection geometry. The microwave magnetic field distribution at the sample position is investigated. The ascertained value of Lande g-factor is consistent with that reported in the literature. Spin sensitivity of the order of 1015 spins/gauss is achieved upon using this resonator at room temperature. The quality factor of this resonator is found to be low and this makes it suitable for use in a Pulsed ESR spectrometer.

Scalable microresonators for room-temperature detection of electron spin resonance from dilute, sub-nanoliter volume solids

We report a microresonator platform that allows room temperature detection of electron spins in volumes on the order of 100 pl, and demonstrate its utility to study low levels of dopants in perovskite oxides. We exploit the toroidal moment in a planar anapole, using a single unit of an anapole metamaterial architecture to produce a microwave resonance exhibiting a spatially confined magnetic field hotspot and simultaneously high quality-factor (Q-factor). To demonstrate the broad implementability of this design and its scalability to higher frequencies, we deploy the microresonators in a commercial electron paramagnetic resonance (EPR) spectrometer operating at 10 GHz and a NIST-built EPR spectrometer operating at 35 GHz. We report continuous-wave (CW) EPR spectra for various samples, including a dilute Mn²⁺-doped perovskite oxide, CaTiO₃, and a transition metal complex, CuCl₂2H₂O. The anapole microresonator presented here is expected to enable multifrequency EPR characterization of dopants and defects in perovskite oxide microcrystals and other volume-limited materials of technological importance.

Cryogenic frequency-domain electron spin resonance spectrometer based on coplanar waveguides and field modulation

We present an instrument to perform frequency-domain electron spin resonance experiments that is based on coplanar waveguides and field modulation. A large parameter space in frequency (up to 25 GHz), magnetic field (up to 8 T), and temperature (down to 1.6 K) is accessible. We performed experiments on DPPH (2,2-diphenyl-1-picrylhydrazyl) as a standard to calibrate the field modulation as well as on a carbon fiber sample to estimate the overall sensitivity of the instruments. Spectra of a ruby sample in a broad frequency and field range at cryogenic temperatures are recorded with and without field modulation. The comparison reveals the improved signal-to-noise ratio achieved by field modulation.

Adjustable coupling and in situ variable frequency electron paramagnetic resonance probe with loop-gap resonators for spectroscopy up to X-band

In standard electron paramagnetic resonance (EPR) spectroscopy, the frequency of an experiment is set and the spectrum is acquired using the magnetic field as the independent variable. There are cases in which it is desirable instead to fix the field and tune the frequency such as when studying avoided level crossings. We have designed and tested an adjustable frequency and variable coupling EPR probe with loop-gap resonators (LGRs) that works at a temperature as low as 1.8 K. The frequency is tuned by adjusting the height of a dielectric piece of sapphire inserted into the gap of an LGR; coupling of the microwave antenna is varied with the height of the antenna above the LGR. Both coupling antenna and dielectric are located within the cryogenic sample chamber, but their motion is controlled with external micrometers located outside the cryostat. The frequency of the LGR (∼4 GHz) can be adjusted by more than 1 GHz (>25%). To cover a wide range of frequencies, different LGRs can be designed to cover frequencies up to X-band. We demonstrate the operation of our probe by mapping out avoided crossings for the Ni₄ molecular nanomagnet to determine the tunnel splittings with high precision.

Detection of L-band electron paramagnetic resonance in the DPPH molecule using impedance measurements

(a) Schematic diagram of our experimental set up. (b) Resistance and reactance of the DPPH molecule for 2 GHz current in the strip coil.

Advanced surface resonators for electron spin resonance of single microcrystals

Electron spin resonance (ESR) spectroscopy of paramagnetic species in single crystals is a powerful tool for characterizing the latter's magnetic interaction parameters in detail. Conventional ESR systems are optimized for millimeter-size samples and make use of cavities and resonators that accommodate tubes and capillaries in the range 1-5 mm. Unfortunately, in the case of many interesting materials such as enzymes and inorganic catalytic materials (e.g., zeolites), single crystals can only be obtained in micron-scale sizes (1-200 µm). To boost ESR sensitivity and to enable experiments on microcrystals, the ESR resonator needs to be adapted to the size and shape of these specific samples. Here, we present a unique family of miniature surface resonators, known as "ParPar" resonators, whose mode volume and shape are optimized for such micron-scale single crystals. This approach significantly improves upon the samples' filling factor and thus enables the measurement of much smaller crystals than was previously possible. We present here the design of such resonators with a typical mode dimension of 20-50 µm, as well as details about their fabrication and testing methods. The devices' resonant mode(s) are characterized by ESR microimaging and compared to the theoretical calculations. Moreover, experimental ESR spectra of single microcrystals with typical sizes of ∼25-50 µm are presented. The measured spin sensitivity for the 50-µm resonator at cryogenic temperatures of 50 K is found to be ∼1.8 × 10⁶ spins/G √Hz for a Cu-doped single crystal sample that is representative of many biological samples of relevance.

A single chip electron spin resonance detector based on a single high electron mobility transistor

Single-chip microwave oscillators are promising devices for inductive electron spin resonance spectroscopy (ESR) experiments on nanoliter and subnanoliter samples. Two major problems of the previously reported designs were the large minimum microwave magnetic field (0.1-0.7 mT) and large power consumption (0.5-200 mW), severely limiting their use for the investigation of samples having long relaxation times and for operation at low temperatures. Here we report on the design and characterization of a single-chip ESR detector operating with a microwave magnetic field and a power consumption orders of magnitude lower compared with previous designs. These significant improvements are mainly due to the use of a high electron mobility transistor (HEMT) technology instead of a complementary metal-oxide semiconductor (CMOS) technology. The realized single-chip ESR detector, which operates at 11.2 GHz, consists of an LC Colpitts oscillator realized with a single high-electron mobility transistor and a co-integrated single turn planar coil having a diameter of 440 μm. The realized detector operates from 300 K down to 1.4 K, at least. Its minimum microwave magnetic field is 0.4 μT at 300 K and 0.06 μT at 1.4 K, whereas its power consumption is 90 μW at 300 K and 4 μW at 1.4 K, respectively. The experimental spin sensitivity on a sensitive volume of about 30 nL, as measured with a single crystal of α,γ-bisdiphenylene-β-phenylallyl (BDPA)/benzene complex, is of 8 × 10¹⁰ spins/Hz^1/2 at 300 K and 2 × 10⁹ spins/Hz^1/2 at 10 K, respectively. In a volume of about 100 pL, located in proximity to the coil wire, the spin sensitivity improves by two orders of magnitude.

All-electric control of donor nuclear spin qubits in silicon

The electronic and nuclear spin degrees of freedom of donor impurities in silicon form ultra-coherent two-level systems that are potentially useful for applications in quantum information and are intrinsically compatible with industrial semiconductor processing. However, because of their smaller gyromagnetic ratios, nuclear spins are more difficult to manipulate than electron spins and are often considered too slow for quantum information processing. Moreover, although alternating current magnetic fields are the most natural choice to drive spin transitions and implement quantum gates, they are difficult to confine spatially to the level of a single donor, thus requiring alternative approaches. In recent years, schemes for all-electrical control of donor spin qubits have been proposed but no experimental demonstrations have been reported yet. Here, we demonstrate a scalable all-electric method for controlling neutral ³¹P and ⁷⁵As donor nuclear spins in silicon. Using coplanar photonic bandgap resonators, we drive Rabi oscillations on nuclear spins exclusively using electric fields by employing the donor-bound electron as a quantum transducer, much in the spirit of recent works with single-molecule magnets. The electric field confinement leads to major advantages such as low power requirements, higher qubit densities and faster gate times. Additionally, this approach makes it possible to drive nuclear spin qubits either at their resonance frequency or at its first subharmonic, thus reducing device bandwidth requirements. Double quantum transitions can be driven as well, providing easy access to the full computational manifold of our system and making it convenient to implement nuclear spin-based qudits using ⁷⁵As donors.

Recent trends in high spin sensitivity magnetic resonance

Magnetic resonance is a very powerful methodology that has been employed successfully in many applications for about 70years now, resulting in a wealth of scientific, technological, and diagnostic data. Despite its many advantages, one major drawback of magnetic resonance is its relatively poor sensitivity and, as a consequence, its bad spatial resolution when examining heterogeneous samples. Contemporary science and technology often make use of very small amounts of material and examine heterogeneity on a very small length scale, both of which are well beyond the current capabilities of conventional magnetic resonance. It is therefore very important to significantly improve both the sensitivity and the spatial resolution of magnetic resonance techniques. The quest for higher sensitivity led in recent years to the development of many alternative detection techniques that seem to rival and challenge the conventional "old-fashioned" induction-detection approach. The aim of this manuscript is to briefly review recent advances in the field, and to provide a quantitative as well as qualitative comparison between various detection methods with an eye to future potential advances and developments. We first offer a common definition of sensitivity in magnetic resonance to enable proper quantitative comparisons between various detection methods. Following that, up-to-date information about the sensitivity capabilities of the leading recently-developed detection approaches in magnetic resonance is provided, accompanied by a critical comparison between them and induction detection. Our conclusion from this comparison is that induction detection is still indispensable, and as such, it is very important to look for ways to significantly improve it. To do so, we provide expressions for the sensitivity of induction-detection, derived from both classical and quantum mechanics, that identify its main limiting factors. Examples from current literature, as well as a description of new ideas, show how these limiting factors can be mitigated to significantly improve the sensitivity of induction detection. Finally, we outline some directions for the possible applications of high-sensitivity induction detection in the field of electron spin resonance.

Single-chip electron spin resonance detectors operating at 50GHz, 92GHz, and 146GHz

We report on the design and characterization of single-chip electron spin resonance (ESR) detectors operating at 50GHz, 92GHz, and 146GHz. The core of the single-chip ESR detectors is an integrated LC-oscillator, formed by a single turn aluminum planar coil, a metal-oxide-metal capacitor, and two metal-oxide semiconductor field effect transistors used as negative resistance network. On the same chip, a second, nominally identical, LC-oscillator together with a mixer and an output buffer are also integrated. Thanks to the slightly asymmetric capacitance of the mixer inputs, a signal at a few hundreds of MHz is obtained at the output of the mixer. The mixer is used for frequency down-conversion, with the aim to obtain an output signal at a frequency easily manageable off-chip. The coil diameters are 120μm, 70μm, and 45μm for the U-band, W-band, and the D-band oscillators, respectively. The experimental frequency noises at 100kHz offset from the carrier are 90Hz/Hz^1/2, 300Hz/Hz^1/2, and 700Hz/Hz^1/2 at 300K, respectively. The ESR spectra are obtained by measuring the frequency variations of the single-chip oscillators as a function of the applied magnetic field. The experimental spin sensitivities, as measured with a sample of α,γ-bisdiphenylene-β-phenylallyl (BDPA)/benzene complex, are 1×10⁸spins/Hz^1/2, 4×10⁷spins/Hz^1/2, 2×10⁷spins/Hz^1/2 at 300K, respectively. We also show the possibility to perform experiments up to 360GHz by means of the higher harmonics in the microwave field produced by the integrated single-chip LC-oscillators.

Coupling molecular spin centers to microwave planar resonators: towards integration of molecular qubits in quantum circuits

Strong coupling meets coordination chemistry: hints in the design of molecular qubits in hybrid quantum circuits.

Anisotropic stark effect and electric-field noise suppression for phosphorus donor qubits in silicon

We report the use of novel, capacitively terminated coplanar waveguide resonators to measure the quadratic Stark shift of phosphorus donor qubits in Si. We confirm that valley repopulation leads to an anisotropic spin-orbit Stark shift depending on electric and magnetic field orientations relative to the Si crystal. By measuring the linear Stark effect, we estimate the effective electric field due to strain in our samples. We show that in the presence of this strain, electric-field sources of decoherence can be non-negligible. Using our measured values for the Stark shift, we predict magnetic fields for which the spin-orbit Stark effect cancels the hyperfine Stark effect, suppressing decoherence from electric-field noise. We discuss the limitations of these noise-suppression points due to random distributions of strain and propose a method for overcoming them.

Instrument for in-situ orientation of superconducting thin-film resonators used for electron-spin resonance experiments

When used in electron-spin resonance measurements, superconducting thin-film resonators must be precisely oriented relative to the external magnetic field in order to prevent the trapping of magnetic flux and the associated degradation of resonator performance. We present a compact design solution for this problem that allows in-situ control of the orientation of the resonator at cryogenic temperatures. Tests of the apparatus show that when proper alignment is achieved, there is almost no hysteresis in the field dependence of the resonant frequency.

Cryogenic single-chip electron spin resonance detector

We report on the design and characterization of a single-chip electron spin resonance detector, operating at a frequency of about 20 GHz and in a temperature range extending at least from 300 K down to 4 K. The detector consists of an LC oscillator formed by a 200 μm diameter single turn aluminum planar coil, a metal-oxide-metal capacitor, and two metal-oxide-semiconductor field effect transistors used as negative resistance network. At 300 K, the oscillator has a frequency noise of 20 Hz/Hz(1/2) at 100 kHz offset from the 20 GHz carrier. At 4 K, the frequency noise is about 1 Hz/Hz(1/2) at 10 kHz offset. The spin sensitivity measured with a sample of DPPH is 10(8)spins/Hz(1/2) at 300 K and down to 10(6)spins/Hz(1/2) at 4 K.

Cavity cooling of an ensemble spin system

We describe how sideband cooling techniques may be applied to large spin ensembles in magnetic resonance. Using the Tavis-Cummings model in the presence of a Rabi drive, we solve a Markovian master equation describing the joint spin-cavity dynamics to derive cooling rates as a function of ensemble size. Our calculations indicate that the coupled angular momentum subspaces of a spin ensemble containing roughly 10(11) electron spins may be polarized in a time many orders of magnitude shorter than the typical thermal relaxation time. The described techniques should permit efficient removal of entropy for spin-based quantum information processors and fast polarization of spin samples. The proposed application of a standard technique in quantum optics to magnetic resonance also serves to reinforce the connection between the two fields, which has recently begun to be explored in further detail due to the development of hybrid designs for manufacturing noise-resilient quantum devices.

A cryogenic receiver for EPR

Cryogenic probes have significantly increased the sensitivity of NMR. Here, we present a compact EPR receiver design capable of cryogenic operation. Compared to room temperature operation, it reduces the noise by a factor of ≈2.5. We discuss in detail the design and analyze the resulting noise performance. At low microwave power, the input noise density closely follows the emission of a cooled 50Ω resistor over the whole measurement range from 20K up to room temperature. To minimize the influence of the microwave source noise, we use high microwave efficiency (≈1.1-1.7mTW(-1/2)) planar microresonators. Their efficient conversion of microwave power to magnetic field permits EPR measurements with very low power levels, typically ranging from a few μW down to fractions of nW.

Towards realizing a quantum memory for a superconducting qubit: storage and retrieval of quantum states

We have built a hybrid system composed of a superconducting flux qubit (the processor) and an ensemble of nitrogen-vacancy centers in diamond (the memory) that can be directly coupled to one another, and demonstrated how information can be transferred from the flux qubit to the memory, stored, and subsequently retrieved. We have established the coherence properties of the memory and succeeded in creating an entangled state between the processor and memory, demonstrating how the entangled state's coherence is preserved. Our results are a significant step towards using an electron spin ensemble as a quantum memory for superconducting qubits.