Frequency Superconducting Quantum Interference Device Research Articles

Magnetic Flux Sensor Based on Spiking Neurons with Josephson Junctions.

Josephson junctions (JJs) are superconductor-based devices used to build highly sensitive magnetic flux sensors called superconducting quantum interference devices (SQUIDs). These sensors may vary in design, being the radio frequency (RF) SQUID, direct current (DC) SQUID, and hybrid, such as D-SQUID. In addition, recently many of JJ's applications were found in spiking models of neurons exhibiting nearly biological behavior. In this study, we propose and investigate a new circuit model of a sensory neuron based on DC SQUID as part of the circuit. The dependence of the dynamics of the designed model on the external magnetic flux is demonstrated. The design of the circuit and derivation of the corresponding differential equations that describe the dynamics of the system are given. Numerical simulation is used for experimental evaluation. The experimental results confirm the applicability and good performance of the proposed magnetic-flux-sensitive neuron concept: the considered device can encode the magnetic flux in the form of neuronal dynamics with the linear section. Furthermore, some complex behavior was discovered in the model, namely the intermittent chaotic spiking and plateau bursting. The proposed design can be efficiently applied to developing the interfaces between circuitry and spiking neural networks. However, it should be noted that the proposed neuron design shares the main limitation of all the superconductor-based technologies, i.e., the need for a cryogenic and shielding system.

Variation of the performance of YBa[formula omitted]Cu[formula omitted]O[formula omitted] radio frequency superconducting quantum interference device with bicrystal grain boundary angle

High transition temperature (high-Tc) superconducting quantum interference devices (SQUIDs) based on bicrystal grain boundary junctions have been utilized in a wide range of applications. To explore the effect of the bicrystal grain boundary angle on the property of the high-Tc SQUID, we fabricated and characterized YBa2Cu3O7−δ (YBCO) radio frequency (rf) SQUIDs using [001]-tilt grain boundary junctions on SrTiO3 (STO) bicrystal substrates with three different misorientation angles of θ=18∘, 24°, and 30°. Unlike the device of θ=18∘ showing only the triangular waveform of the voltage–flux (V−Φ) characteristics, for device of θ=24∘ and 30°, the shape of the V−Φ curve can be tuned from approximately triangular into nearly rectangular by adjusting the working point of the device. It suggests that, as θ increases from 18° to 30°, the operation of the device may change from the hysteretic mode into the nonhysteretic mode. This is backed by electrical transport measurements of YBCO bicrystal junctions on separate STO substrates, which help to reveal that lying behind the indicated changeover of the SQUID operation mode is the exponential decrease of the junction critical current density Jc as θ increases. The white noise of the device, which decreases with increasing flux-to-voltage transfer coefficient ∂V/∂Φ, shows a large drop as θ increases to 24°. For both 24° and 30° devices, the white field noise at 77 K is about 90 fT/Hz1/2 at respective optimum working points. For device of 30° with nearly rectangular V−Φ characteristics showing the largest ∂V/∂Φ among the fabricated samples, the white noise region extends below 10 Hz and a field noise of 145 fT/Hz1/2 at 1 Hz is shown, demonstrating the potential of obtaining high-performance bicrystal YBCO rf SQUIDs with this grain boundary angle.

Dynamical behavior of two locally coupled asymmetric RF-SQUIDs

An asymmetric system consisting of two coupled radio frequency superconducting quantum interference devices (RF-SQUIDs) with general geometry as nonlinear macroscopic system with mutual inductance under the influence of a time-dependent external field has been investigated numerically. Due to the importance of mutual induction in the construction of such nonlinear asymmetric systems, the dependence of coupling coefficient on the frequency changes, the primary and secondary resonance amplitudes and also the anti-resonances in both squids have been investigated. By changing the geometry of the arrangement of squids, the dynamic behavior parameters of the system have been studied. The eigenvalues of this system have been found and by changing frequency, the stable and unstable states have been studied.

Cryogenic Analog Microwave Variable Attenuator Using rf-SQUIDs for Quantum Systems

We present the design, fabrication and testing of a low-temperature superconducting (LTS) analog microwave variable attenuator. The two-port circuit includes two <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$90^{\circ }$</tex-math></inline-formula> hybrid couplers and a phase shifter to realize a variable attenuation at the output port. The wideband analog phase shifter is implemented using LTS microstrip transmission line (TL) coupled to an array of radio frequency superconducting quantum interference devices (rf-SQUIDs). The phase shift is achieved by passing a dc current through a TL adjacent to the SQUID-loaded microstrip line which controls the flux through the rf-SQUIDs. The proposed variable attenuator shows more than 30 dB of precise analog flat attenuation tuning range over 8 GHz to 12 GHz with a dc control current ranging from 0 mA to 4.5 mA. The device exhibits a wideband operation with variable attenuation seen not only in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X-</i> band but also in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ku-</i> band. The device is fabricated using a multilayer niobium-based superconducting process SFQ5ee by MIT Lincoln Laboratory, and has a compact footprint of 1.3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{mm}^{2}$</tex-math></inline-formula> . To the best of our knowledge, this is the first implementation of a variable attenuator using distributed rf-SQUIDs. This device has implications in a variety of applications such as cryogenic receivers and qubit circuit measurements.

Low-Temperature Superconductor rf-SQUIDs-Based Fully Integrated Reflective-Type Analog Phase Shifter for Quantum Applications

This article presents a low-temperature superconductor (LTS)-based microwave phase shifter. The device utilizes a superconducting hybrid coupler monolithically integrated with two tunable reflective loads. An array of radio frequency superconducting quantum interference devices (rf-SQUIDs) is used to achieve inductive tuning in reflective loads, resulting in a broadband true time delay phase shift. The rf-SQUIDs are current controlled using an on-chip dc bias circuitry. The proof-of-concept fabricated device provides excellent RF performance in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${X}$ </tex-math></inline-formula> - and Ku -band with a phase shift of 49° at 10 GHz and 67° at 15 GHz. The insertion loss is < 1.5 dB for the entire range from 8 to 18 GHz. The methods to further improve the obtained phase shift are discussed. The overall device has a chip footprint of 0.6 mm2 and is fabricated using MIT-Lincoln Lab (MIT-LL) SFQ5ee eight-layer Niobium (Nb)-based superconducting fabrication process.

Metallic Contaminant Detection in Liquids using a High-Tc RF-SQUID

We have developed a system using high-temperature radio frequency superconducting quantum interference device (RF-SQUID) for detecting metallic contaminants in the liquid component of a lithium-ion battery. Although we have executed detection experiments using a simulated system without liquid in the past[1], we have developed a new system to inspect real liquid components. Small cylindrical metallic contaminant samples were fabricated using a gallium-focused ion beam to evaluate the detection performance. Tap water containing the metallic contaminant sample was poured into the tube using a pump, and the magnetic signal of the contaminant matter was detected using the RF-SQUID. Among the tested small metallic contaminant samples, the volume of a minimum detectable metallic contaminant was evaluated to be 2 × 104 μm3, which corresponded to that of a spherical sample with a diameter of 33 μm and a sensitivity of a signal-to-noise ratio of more than three. Moreover, the dependence of the detected signal strength on the volume of the metallic contaminant samples is discussed here.

Quasi-phasematching in a poled Josephson traveling-wave parametric amplifier with three-wave mixing

We develop the concept of quasi-phasematching (QPM) by implementing it in the recently proposed Josephson traveling-wave parametric amplifier (JTWPA) with three-wave mixing (3WM). The amplifier is based on a ladder transmission line consisting of flux-biased radio frequency superconducting quantum interference devices (SQUIDs) whose nonlinearity is of χ(2)-type. QPM is achieved in the 3WM process, ωp=ωs+ωi (where ωp, ωs, and ωi are the pump, signal, and idler frequencies, respectively) due to designing the JTWPA to include periodically inverted groups of these SQUIDs that reverse the sign of the nonlinearity. Modeling shows that the JTWPA bandwidth is relatively large (∼ 0.4ωp) and flat, while unwanted modes, including ω2p=2ωp, ω+=ωp+ωs, and ω−=2ωp−ωs, are strongly suppressed with the help of engineered dispersion.

Fabrication and characterization of YBa&lt;sub&gt;2&lt;/sub&gt;Cu&lt;sub&gt;3&lt;/sub&gt;O&lt;sub&gt;7–&lt;/sub&gt;&lt;inline-formula&gt;&lt;tex-math id="Z-20210129174424"&gt;\begin{document}$_{ \delta}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201291_Z-20210129174424.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201291_Z-20210129174424.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; step-edge Josephson junctions on MgO substrate for high-temperature superconducting quantum interference devices

The YBa&lt;sub&gt;2&lt;/sub&gt;Cu&lt;sub&gt;3&lt;/sub&gt;O&lt;sub&gt;7–&lt;i&gt;δ&lt;/i&gt;&lt;/sub&gt; (YBCO) step-edge Josephson junction on MgO substrate has recently been shown to have important applications in making advanced high-transition temperature (high-&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt;) superconducting devices such as high-sensitivity superconducting quantum interference device (SQUID), superconducting quantum interference filter, and THz detector. In this paper, we investigate the fabrication and transport properties of YBCO step-edge junction on MgO substrate. By optimizing the two-stage ion beam etching process, steps on MgO (100) substrates are prepared with an edge angle &lt;i&gt;θ&lt;/i&gt; of about 34°. The YBCO step-edge junctions are then fabricated by growing the YBCO thin films with a pulsed laser deposition technique and subsequent traditional photolithography. The resistive transition of the junction shows typical foot structure which is well described by the Ambegaokar-Halperin theory of thermally-activated phase slippage for overdamped Josephson junctions. The voltage-current curves with temperature dropping down to 77 K exhibit resistively shunted junction behavior, and the Josephson critical current density &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; is shown to follow the &lt;inline-formula&gt;&lt;tex-math id="Z-20210127094830-1"&gt;\begin{document}$(T_{\rm C}-T)^2$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201291_Z-20210127094830-1.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201291_Z-20210127094830-1.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; dependence. At 77 K, the &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; of the junction reaches 1.4 × 10&lt;sup&gt;5&lt;/sup&gt; A/cm&lt;sup&gt;2&lt;/sup&gt;, significantly higher than the range of 10&lt;sup&gt;3&lt;/sup&gt;–10&lt;sup&gt;4&lt;/sup&gt; A/cm&lt;sup&gt;2&lt;/sup&gt; as presented by other investigators for YBCO step-edge junctions on MgO substrate with comparable &lt;i&gt;θ&lt;/i&gt; of 35°–45°. This indicates a rather strong Josephson coupling of the junction, and by invoking the results of YBCO bicrystal junctions showing similar values of &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt;, it is tentatively proposed that the presently fabricated junction might be described as an S-s′-S junction with s′ denoting the superconducting region of depressed &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; in the vicinity of the step edge or as an S-N-S junction with N denoting a very thin non-superconducting layer. By incorporating the MgO-based YBCO step-edge junction, high-&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; radio frequency (RF) SQUID is made. The device shows decent voltage-flux curve and magnetic flux sensitivity of 250 &lt;inline-formula&gt;&lt;tex-math id="Z-20210128093740-1"&gt;\begin{document}$ \text{μ}\Phi_0/{\rm Hz}^{1/2} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201291_Z-20210128093740-1.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201291_Z-20210128093740-1.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; at 1 kHz and 77 K, comparable to the values reported in the literature. To further improve the RF SQUID performance, efforts could be devoted to optimizing the junction parameters such as the junction &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt;. By using the YBCO step-edge junction on MgO substrate, high-&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; direct current SQUID could also be developed, as reported recently by other investigators, to demonstrate the potential of MgO-based step-edge junction in making such a kind of device with superior magnetic flux sensitivity.

Analytical and numerical analysis of linear and nonlinear properties of an rf-SQUID based metasurface

We derive a model to describe the interaction of an rf-SQUID (radio frequency superconducting quantum interference device) based metasurface with free space electromagnetic waves. The electromagnetic fields are described on the base of Maxwell's equations. For the rf-SQUID metasurface we rely on an equivalent circuit model. After a detailed derivation, we show that the problem that is described by a system of coupled differential equations is wellposed and, therefore, has a unique solution. In the small amplitude limit, we provide analytical expressions for reflection, transmission, and absorption depending on the frequency. To investigate the nonlinear regime, we numerically solve the system of coupled differential equations using a finite element scheme with transparent boundary conditions and the Crank-Nicolson method. We also provide a rigorous error analysis that shows convergence of the scheme at the expected rates. The simulation results for the adiabatic increase of either the field's amplitude or its frequency show that the metasurface's response in the nonlinear interaction regime exhibits bistable behavior both in transmission and reflection.

Coherent oscillations of driven rf SQUID metamaterials.

Through experiments and numerical simulations we explore the behavior of rf SQUID (radio frequency superconducting quantum interference device) metamaterials, which show extreme tunability and nonlinearity. The emergent electromagnetic properties of this metamaterial are sensitive to the degree of coherent response of the driven interacting SQUIDs. Coherence suffers in the presence of disorder, which is experimentally found to be mainly due to a dc flux gradient. We demonstrate methods to recover the coherence, specifically by varying the coupling between the SQUID meta-atoms and increasing the temperature or the amplitude of the applied rf flux.

Macroscopic resonant tunneling in an rf-SQUID flux qubit under a single-cycle sinusoidal driving**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474154, 61371036, 61571219, 11227904, and 61501222) and the Natural Science Fund for Distinguished Young Scholars of Jiangsu Province, China (Grant No. BK2012013) and PAPD.

We experimentally demonstrate the observation of macroscopic resonant tunneling (MRT) phenomenon of the macroscopic distinct flux states in a radio frequency superconducting quantum interference device (rf-SQUID) under a single-cycle sinusoidal driving. The population of the qubit exhibits interference patterns corresponding to resonant tunneling peaks between states in the adjacent potential wells. The dynamics of the qubit depends significantly on the amplitude, frequency, and initial phase of the driving signal. We do the numerical simulations considering the intra-well and inter-well relaxation mechanism, which agree well with the experimental results. This approach provides an effective way to manipulate the qubit population by adjusting the parameters of the external driving field.

Intermodulation in nonlinear SQUID metamaterials: Experiment and theory

The response of nonlinear metamaterials and superconducting electronics to two-tone excitation is critical for understanding their use as low-noise amplifiers and tunable filters. A new setting for such studies is that of metamaterials made of radio frequency superconducting quantum interference devices (rf-SQUIDs). The two-tone response of self-resonant rf-SQUID meta-atoms and metamaterials is studied here via intermodulation (IM) measurement over a broad range of tone frequencies and tone powers. A sharp onset followed by a surprising strongly suppressed IM region near the resonance is observed. Using a two time scale analysis technique, we present an analytical theory that successfully explains our experimental observations. The theory predicts that the IM can be manipulated with tone power, center frequency, frequency difference between the two tones, and temperature. This quantitative understanding potentially allows for the design of rf-SQUID metamaterials with either very low or very high IM response.

Detection of small single-cycle signals by stochastic resonance using a bistable superconducting quantum interference device

We propose and experimentally demonstrate detecting small single-cycle and few-cycle signals by using the symmetric double-well potential of a radio frequency superconducting quantum interference device (rf-SQUID). We show that the response of this bistable system to single- and few-cycle signals has a non-monotonic dependence on the noise strength. The response, measured by the probability of transition from initial potential well to the opposite one, becomes maximum when the noise-induced transition rate between the two stable states of the rf-SQUID is comparable to the signal frequency. Comparison to numerical simulations shows that the phenomenon is a manifestation of stochastic resonance.

Fabrication and properties of high performance YBa2Cu3O7−δ radio frequency SQUIDs with step-edge Josephson junctions

We describe the fabrication of high performance Yba2Cu3O7−δ (YBCO) radio frequency (RF) superconducting quantum interference devices (SQUIDs), which were prepared on 5 mm × 5 mm LaAlO3 (LAO) substrates by employing step-edge junctions (SEJs) and in flip-chip configuration with 12 mm × 12 mm resonators. The step in the substrate was produced by Ar ion etching with step angles ranging from 47° to 61°, which is steep enough to ensure the formation of grain boundaries (GBs) at the step edges. The YBCO film was deposited using the pulsed laser deposition (PLD) technique with a film thickness half of the height of the substrate step. The inductance of the SQUID washer was designed to be about 157 pH. Under these circumstances, high performance YBCO RF SQUIDs were successfully fabricated with a typical flux-voltage transfer ratio of 83 mV/Φ0, a white flux noise of 29 μΦ0/√Hz, and the magnetic field sensitivity as high as 80 fT/√Hz. These devices have been applied in magnetocardiography and geological surveys.

White noise of Nb-based microwave superconducting quantum interference device multiplexers with NbN coplanar resonators for readout of transition edge sensors

White noise of dissipationless microwave radio frequency superconducting quantum interference device (RF-SQUID) multiplexers has been experimentally studied to evaluate their readout performance for transition edge sensor (TES) photon counters ranging from near infrared to gamma ray. The characterization has been carried out at 4 K, first to avoid the low-frequency fluctuations present at around 0.1 K, and second, for a feasibility study of readout operation at 4 K for extended applications. To increase the resonant Q at 4 K and maintain low noise SQUID operation, multiplexer chips consisting of niobium nitride (NbN)-based coplanar-waveguide resonators and niobium (Nb)-based RF-SQUIDs have been developed. This hybrid multiplexer exhibited 1 × 104 ≤ Q ≤ 2 × 104 and the square root of spectral density of current noise referred to the SQUID input √SI = 31 pA/√Hz. The former and the latter are factor-of-five and seven improvements from our previous results on Nb-based resonators, respectively. Two-directional readout on the complex plane of the transmission component of scattering matrix S21 enables us to distinguish the flux noise from noise originating from other sources, such as the cryogenic high electron mobility transistor (HEMT) amplifier. Systematic noise measurements with various microwave readout powers PMR make it possible to distinguish the contribution of noise sources within the system as follows: (1) The achieved √SI is dominated by the Nyquist noise from a resistor at 4 K in parallel to the SQUID input coil which is present to prevent microwave leakage to the TES. (2) The next dominant source is either the HEMT-amplifier noise (for small values of PMR) or the quantization noise due to the resolution of 300-K electronics (for large values of PMR). By a decrease of these noise levels to a degree that is achievable by current technology, we predict that the microwave RF-SQUID multiplexer can exhibit √SI ≤ 5 pA/√Hz, i.e., close to √SI of state-of-the-art DC-SQUID-based multiplexers.

Tunable resonant and nonresonant interactions between a phase qubit and LC resonator.

We use a flux-biased radio frequency superconducting quantum interference device (rf SQUID) with an embedded flux-biased direct current SQUID to generate strong resonant and nonresonant tunable interactions between a phase qubit and a lumped-element resonator. The rf SQUID creates a tunable magnetic susceptibility between the qubit and resonator providing resonant coupling strengths from zero to near the ultrastrong coupling regime. By modulating the magnetic susceptibility, nonresonant parametric coupling achieves rates >100 MHz. Nonlinearity of the magnetic susceptibility also leads to parametric coupling at the subharmonics of the qubit-resonator detuning.

Realization and Modeling of Metamaterials Made of rf Superconducting Quantum-Interference Devices

We have prepared meta-atoms based on radio frequency superconducting quantum interference devices (RF SQUIDs) and examined their tunability with dc magnetic field, rf current, and temperature. RF SQUIDs are superconducting split ring resonators in which the usual capacitance is supplemented with a Josephson junction, which introduces strong nonlinearity in the rf properties. We find excellent agreement between the data and a model which regards the Josephson junction as the resistively and capacitively-shunted junction. A magnetic field tunability of 80 THz/Gauss at 12 GHz is observed, a total tunability of 56$%$ is achieved, and a unique electromagnetically-induced transparency feature at intermediate excitation powers is demonstrated for the first time. An RF SQUID metamaterial is shown to have qualitatively the same behavior as a single RF SQUID with regards to DC flux and temperature tuning.

Increasing the Flux Measurement Range of an RF-SQUID Resonant Detection Circuit Using the Robust Symmetrical Number System

The design and simulation of a new low temperature Niobium radio frequency superconducting quantum interference devices (RF-SQUID) flux measurement architecture concept that uses N = 3 RF-SQUID rings (or channels) to significantly extend the range of the flux measurement capability beyond ±Φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> /4 is presented. A resonant detection method based on a robust symmetrical number system (RSNS) preprocessing technique is shown to provide a large increase in the flux measurement range while producing a high-resolution representation of the input magnetic field. The RSNS preprocessing is a modular scheme in which a modulus number of comparators is used at the output of each RF SQUID. The number of comparators with logic 1 in each channel represents the integer values within each RSNS modulus sequence. When considered together, the integers within each sequence change one at a time at the next code position, resulting in an integer Gray code property. We show that the RSNS preprocessing has the feature that the maximum nonlinearity is less than a least significant bit.

Novel flux concentrator with a single CSRR surrounded by a resonator for radio frequency superconducting quantum interference device

A novel flux concentrator surrounded by a resonator is proposed in this paper. A complementary single split ring resonator (single CSRR) is introduced for the flux concentrator, while the resonator surrounding the flux concentrator employs a third-order stepped-impedance hairpin resonator (SIR). High frequency structure simulation software ANSYS HFSSv.11 is used to simulate the proposed flux concentrator and resonator. Moreover, the single CSRR is analyzed theoretically. Simulation and theoretical results shows that the novel flux concentrator surrounded by a resonator introduces a single CSRR, which improves the flux focus effect of the concentrator significantly, and so enhances the performance of coupling between the RF SQUID and the flux concentrator (the coupling coefficient ksc is improved 2 times) and increases the effective area to 1.227 mm2.

Nanohertz frequency determination for the gravity probe B high frequency superconducting quantum interference device signal

In this paper, we present a method to measure the frequency and the frequency change rate of a digital signal. This method consists of three consecutive algorithms: frequency interpolation, phase differencing, and a third algorithm specifically designed and tested by the authors. The succession of these three algorithms allowed a 5 parts in 10(10) resolution in frequency determination. The algorithm developed by the authors can be applied to a sampled scalar signal such that a model linking the harmonics of its main frequency to the underlying physical phenomenon is available. This method was developed in the framework of the gravity probe B (GP-B) mission. It was applied to the high frequency (HF) component of GP-B's superconducting quantum interference device signal, whose main frequency f(z) is close to the spin frequency of the gyroscopes used in the experiment. A 30 nHz resolution in signal frequency and a 0.1 pHz/s resolution in its decay rate were achieved out of a succession of 1.86 s-long stretches of signal sampled at 2200 Hz. This paper describes the underlying theory of the frequency measurement method as well as its application to GP-B's HF science signal.