Radio-frequency Superconducting Quantum Interference Device Research Articles

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.

Wideband Power-Dependent Power Limiter Based on Distributed Low-Temperature Superconductor rf-SQUIDs for Cryogenic RF Receivers

A novel design of a radio-frequency (RF) power limiter for protecting sensitive superconductor receiver components from high-power microwave signals is presented. In this approach, two low- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T} _{c}$ </tex-math></inline-formula> superconductor microstrip lines, one of which is coupled with an array of RF superconducting quantum interference devices (rf-SQUIDs), are combined with a pair of hybrid couplers to provide the power limiting operation at very low RF power levels. The key concept is built on the fact that a microstrip line coupled to an array of rf-SQUIDs behaves as a power-dependent phase shifter and its phase can be controlled by the input RF power. This phenomenon is exploited to achieve the desired RF power-limiting operation. The device is fabricated using an eight-layer niobium-based superconducting process node SFQ5ee by MIT Lincoln Laboratory (MIT-LL). A monolithically integrated wideband hybrid coupler is used in this design as it dictates the bandwidth of the overall device. The operating frequency of the power limiter is 10 GHz with a 2-GHz bandwidth. The performance of the device is measured for input RF power levels ranging from −30 to +10 dBm, as well as arising intermodulation products are experimentally investigated. The output power increases linearly with the input power up to −15 dBm, and for higher power levels, the device offers an increasing attenuation to limit the output RF power starting above −15 dBm.

Observation of SQUID‐Like Behavior in Fiber Laser with Intra‐Cavity Epsilon‐Near‐Zero Effect

AbstractEstablishing relations between fundamental effects in far‐flung areas of physics is a subject of great interest in the current research. Realization of a novel photonic system akin to the radio‐frequency superconducting quantum interference device (RF‐SQUID), in a fiber laser cavity with epsilon‐near‐zero (ENZ) nanolayers as intra‐cavity components is reported here. Emulating the RF‐SQUID scheme, the photonic counterpart of the supercurrent, represented by the optical wave, circulates in the cavity, passing through effective optical potential barriers. Different ENZ wavelengths translate into distinct spectral outputs through the variation of cavity resonances, emulating the situation with a frequency‐varying tank circuit in the RF‐SQUID. Due to the presence of the ENZ element, the optical potential barrier is far lower for selected frequency components, granting them advantage in the gain‐resource competition. The findings reported in this work provide a deeper insight into the ultrafast ENZ photonics, revealing a new path toward the design of nanophotonic on‐chip devices with various operational functions, and offer a new approach to study superconducting and quantum‐mechanical systems.

Consideration of Magnetic Dipole Orientation in Liquid Detected by Metallic Contaminants Detection System Using High-Tc SQUID

The market for high-performance lithium-ion (Li-ion) batteries is growing rapidly as automobiles become electrified. The presence of small metallic particles of the order of 10 m in a battery is likely to cause failure; therefore, it is important to eliminate them. We have developed a prototype system for detecting metallic foreign matter in liquid components for Li-ion batteries using a high-temperature superconducting radio-frequency superconducting quantum interference device, which is a highly sensitive magnetic sensor. Signal waveforms of a magnetized metallic piece passing through a trench located below the SQUID were measured. We found that the waveform depended on the direction of the magnetic dipole at the time of detection and could be roughly divided into six categories to explain all the experimental results. The maximum magnitude obtained for each sample was plotted against the equivalent spherical diameter of the sample. Our results indicate that the signal intensity was proportional to the cube of the sample diameter and that particles larger than 20 m 30 m (equivalent spherical diameter 23 m) were detected with signal-to-noise ratio 3.

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.

Characterization of energy potential in tunable rf-SQUIDs with the classical regime toward precise design of superconducting flux qubit

The detailed characteristics of classical states in a radio-frequency superconducting quantum interference device (rf-SQUID) with well-designed energy-potential shape are investigated at 4.2 K. Using Nb/AlO x standard process which enables precise circuit-parameter implementation, the rf-SQUID is designed in its energy potential. Directions of persistent current can be distinguished in the rf-SQUID we have fabricated. Analyses in circuit simulations indicate the device design based on enough high critical current provides available parameters to construct the device for 10 mK measurement by circuit-parameter scaling. This knowledge may contribute to the precise design of the rf-SQUID for superconducting qubit through device process with lower critical current density.

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.

Magnetotactic bacteria diversity of and magnetism contribution to sediment in Wudalianchi volcanic barrier lakes, NE China

Magnetotactic bacteria (MTB), the members of sediment microorganisms, play an important role in geochemical iron-cycling and sediment magnetism. This study aimed to investigate the diversity and magnetism contribution of MTB in three volcanic barrier lakes with different waterbody types (open waterbody, YC; semi-enclosed waterbody, WB; and enclosed waterbody, YYP). High-throughput sequencing results showed that MTB affiliated to Alphaproteobacteria, Betaproteobacteria and Nitrospira distributed widely in these lakes. The genera of Magnetococcus (98.10%) and Candidatus Magnetoovum (1.47%) were endemic to YC and WB, respectively. The changes in frequency-dependent susceptibility (χfd) values before and after magnetic collection in YC, WB and YYP samples were − 0.28%, 0.05% and − 0.22%, respectively. The magnetic susceptibility was significantly associated with Chao1 (R2 = 0.637 to 0.763, p < .01) and Shannon index (R2 = 0.803 to 0.998, p < .01). The room- and low-temperature magnetic characteristics of sediment samples were analyzed by vibrating sample magnetometer (VSM) and radio-frequency superconducting quantum interference device (SQUID). Results indicated that the presence or absence of MTB could lead to the changes in the room- and low-temperature magnetism of volcanic lake sediments, which would extend our knowledge of MTB magnetism contribution to volcanic ecosystems.

Working principle and demonstrator of microwave-multiplexing for the HOLMES experiment microcalorimeters

The determination of the neutrino mass is an open issue in modern particle physics and astrophysics. The direct mass measurement is the only theory-unrelated experimental tool capable to probe such quantity. The HOLMES experiment aims to measure the end-point energy of the electron capture (EC) decay of 163Ho with a statistical sensitivity on the neutrino mass as low as ∼ 1 eV/c2. In order to acquire the large needed statistics, by keeping the pile-up contribution as low as possible, 1024 transition edge sensors (TESs) with high energy and time resolutions will be employed. Microcalorimeter and bolometer arrays based on transition edge sensor with thousands of pixels are under development for several space-based and ground-based applications, including astrophysics, nuclear and particle physics, and materials science. The common necessary challenge is to develop pratical multiplexing techniques in order to simplify the cryogenics and readout systems. Despite the various multiplexing variants which are being developed have been successful, new approaches are needed to enable scaling to larger pixel counts and faster sensors, as requested for HOLMES, reducing also the cost and complexity of readout. A very novel technique that meets all of these requirements is based on superconducting microwave resonators coupled to radio-frequency Superconducting Quantum Interference Devices, in which the changes in the TES input current is tranduced to a change in phase of a microwave signal. In this work we introduce the basics of this technique, the design and development of the first two-channel read out system and its performances with the first TES detectors specifically designed for HOLMES. In the last part we explain how to extend this approach scaling to 1024 pixels.

Tunable Superconducting Cavity using Superconducting Quantum Interference Device Metamaterials

Here we consider a tunable superconducting cavity that can be used either as a tunable coupler to a qubit inside the cavity or as a tunable low noise, low temperature, RF filter. Our design consists of an array of radio-frequency superconducting quantum interference devices (rf SQUIDs) inside a superconducting cavity. This forms a tunable metamaterial structure which couples to the cavity through its magnetic plasma frequency. By tuning the resonant frequency of the metamaterial through an applied magnetic flux, one can tune the cavity mode profile. This allows us to detune the cavity initially centered at 5.593 GHz by over 200 MHz. The maximum quality factor approaches that of the empty cavity, which is 4.5 × 106. The metamaterial electromagnetic response is controlled via a low-frequency or dc magnetic flux bias, and we present a control line architecture that is capable of applying sufficient magnetic flux bias with minimal parasitic coupling. Together this design allows for an in-situ tunable cavity which enables low-temperature quantum control applications.

Imaging collective behavior in an rf-SQUID metamaterial tuned by DC and RF magnetic fields

We examine the collective behavior of two-dimensional nonlinear superconducting metamaterials using a non-contact spatially resolved imaging technique. The metamaterial is made up of sub-wavelength nonlinear microwave oscillators in a strongly coupled 27 × 27 planar array of radio-frequency Superconducting QUantum Interference Devices (rf-SQUIDs). By using low-temperature laser scanning microscopy, we image microwave currents in the driven SQUIDs while in non-radiating dark modes and identify the clustering and uniformity of like-oscillating meta-atoms. We follow the rearrangement of coherent patterns due to meta-atom resonant frequency tuning as a function of external dc and rf magnetic flux bias. We find that the rf current distribution across the SQUID array at zero dc flux and small rf flux reveals a low degree of coherence. By contrast, the spatial coherence improves dramatically upon increasing the rf flux amplitude, in agreement with simulation.

Intrinsic Dissipation in Superconducting Junctions Probed by Qubit Spectroscopy

The study of frequency‐dependent intrinsic dissipation in a highly transparent Josephson junction by means of quantum‐bit (qubit) spectroscopy is proposed. The spectral density of the effective dissipative bath may contain significant contributions from Andreev bound states coupled to fluctuations of the Josephson phase. Varying either the bias current applied to the junction or magnetic flux through a superconducting ring in the radiofrequency superconducting quantum interference device (rf‐SQUID) setup, one can tune the level splitting value close to the bottom of the Josephson potential well. Monitoring the qubit energy relaxation time one can probe the spectral density of the effective dissipative bath and unambiguously identify the contribution emerging from Andreev levels.

Harmonic Analysis for Finding the Optimum Working Point of High-Tc RF SQUID

High-Tc radio-frequency (RF) superconducting quantum interference devices (SQUIDs) are well understood and have been adequately expounded in theory, but in practice, it is not so easy to find the optimum working points for their low-noise operations. Starting from the basic equations describing the RF SQUID in nonhysteretic mode, a polynomial expression for its flux-to-voltage characteristic was deduced. For simplicity, the expansion was truncated to the first three harmonics in the flux quantum. The optimum working point is determined as the location of the maximum gradient of its transfer function. The analysis was compared with experimental flux-to-voltage characteristics of the RF SQUIDs with a step-edge junction, measured at 77 K for different settings of the readout electronics. Six typical kinds of the measured flux-to-voltage curves were fitted and analyzed with respect to their harmonics in the magnetic flux. The findings can be of referential value for automatically setting the working points of high-Tc RF SQUIDs in the practical applications.

A simplified HTc rf SQUID to analyze the human cardiac magnetic field

We have developed a four-channel high temperature radio-frequency superconducting quantum interference device (HTc rf SQUID) in a simple magnetically shielded room (MSR) that can be used to analyze the cardiac magnetic field. It is more robust and compact than existing systems. To achieve the high-quality magnetocardiographic signal, we explored new adaptive software gradiometry technology constructed by the first-order axial gradiometer with a baseline of 80mm, which can adjust its performance timely with the surrounding conditions. The magnetic field sensitivity of each channel was less than 100fT/√Hz in the white noise region. Especially, in the analysis of MCG signal data, we proposed the total transient mapping (TTM) technique to visualize current density map (CDM), then we focused to observe the time-varying behavior of excitation propagation and estimated the underlying currents at T wave. According to the clear 3D imaging, isomagnetic field and CDM, the position and distribution of a current source in the heart can be visualized. It is believed that our four-channel HTc rf SQUID magnetometer based on biomagnetic system is available to detect MCG signals with sufficient signal-to-noise (SNR) ratio. In addition, the CDM showed the macroscopic current activation pattern, in a way, it has established strong underpinnings for researching the cardiac microscopic movement mechanism and opening the way for its use in clinical diagnosis.

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.

History matters for a stirred superfluid

The observation of path dependence in the response of a superfluid to stirring promises potential applications in precision rotation sensing, and provides a test bed for microscopic theories of ultracold atomic gases. See Letter p.200 Hysteresis, a phenomenon by which the physical properties of a system depend strongly on the history of the applied perturbation, is widely exploited in electronic circuits including hard disk drives and flux-gate magnetometers and is essential to the function of radio-frequency SQUIDs (superconducting quantum interference devices). Hysteresis is also fundamental to superfluidity and has been predicted to occur in superfluid atomic-gases, such as Bose–Einstein condensates (BECs). Gretchen Campbell and colleagues now report the first direct detection of hysteresis between quantized circulation states in a circuit formed from a ring of superfluid BEC obstructed by a rotating weak link. The presence of hysteresis in this system is of importance in the emerging field of 'atomtronics', in which ultracold atoms have a role analogous to that of the electrons in electronics. Controlled hysteresis in atomtronic circuits may prove to be a crucial feature for the development of practical devices.

Entanglement-assisted electron microscopy based on a flux qubit

A notorious problem in high-resolution biological electron microscopy is radiation damage caused by probe electrons. Hence, acquisition of data with minimal number of electrons is of critical importance. Quantum approaches may represent the only way to improve the resolution in this context, but all proposed schemes to date demand delicate control of the electron beam in highly unconventional electron optics. Here we propose a scheme that involves a flux qubit based on a radio-frequency superconducting quantum interference device, inserted in a transmission electron microscope. The scheme significantly improves the prospect of realizing a quantum-enhanced electron microscope for radiation-sensitive specimens.

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.

Electrodynamics of a split-ring Josephson resonator in a microwave line

We consider the coupling of an electromagnetic wave to a split-ring Josephson oscillator or radio-frequency superconducting quantum interference device in the hysteretic regime. This device is similar to an atomic system in that it has a number of steady states. We show that one can switch between these with a suitable short external microwave pulse. The steady states can be characterized by their resonant lines which are of the Fano type. Using a static magnetic field, we can shift these spectral lines and lift their degeneracy.