Superconducting Quantum Interference Device (SQUID) is the most sensitive detector of magnetic field (F. Wellstood, et al., “Integrated DC SQUID magnetometer with a high slew rate,” Rev. Sci. Instr. 55, 952, 1984) which energy resolution approaches quantum limit. The interfering paths in DC SQUID are formed by two Josephson junctions connected in parallel.
Specifically, as shown in FIG. 1, a SQUID 10 is composed of two Josephson tunnel junctions 12 that are connected together in a superconducting loop. Each Josephson junction is formed by two superconducting regions that are separated by thin insulating barrier. Current exists in the Josephson junction without any voltage drop, up to a maximum value of the critical current Ic. When the SQUID is biased with a constant current Ib that exceeds the critical current of the Josephson junction, the changes in the magnetic flux Φ surrounding the SQUID loop produce changes in the voltage drop VSQUID across the SQUID.
The produced SQUID voltage VSQUID is a periodic non-linear function of magnetic flux (V-Φ function) threading the SQUID loop:VSQUID=0.5R√{square root over (Ib2−4Ic2 cos2(πΦ/Φ0))}  (Eq. 1)where R is the normal resistance of Josephson junction, Ib is the SQUID bias current, Ic is the Josephson critical current, Φ is the SQUID magnetic flux, and Φ0=πh/e˜2.07×10−15 Wb is the magnetic flux quantum with the reduced Planck constant h and the electron charge e.
In order to linearize the non-linear SQUID response and increase its dynamic range, SQUID magnetometers are typically operated in a flux-locked loop (FLL) regime (D. Drung, Supercond Sci. Technology, 16, 1320, 2003). Specifically, in order to convert the nonlinear response to a linear signal, a negative feedback circuit 14 is used to apply an “error” feedback flux to the SQUID in order to maintain a constant total flux through the SQUID. Where the SQUID is “locked” at nΦ0 by means of flux locked loop (FLL), the magnitude of the “error” feedback flux is proportional to the external magnetic field applied to the SQUID.
In order to obtain an optimum feedback system, a modulation technique usually is employed. An oscillator operating at the modulation frequency ωm, and a coil responsive thereto cooperate to modulate the flux threading the SQUID loop. A magnetic flux oscillating at ωm with amplitude on the order of Φ0 is inductively coupled to the SQUID circuit by means of the modulation coil. When static flux equals nΦ0, n=0, 1, 2, . . . , the SQUID produces only even harmonics of the modulation flux 2ωm. This is demodulated by a lock-in amplifier in the FLL circuit referenced to ωm, which yields a zero output. If the static flux becomes greater or less than nΦ0, the lock-in amplifier outputs a positive or negative voltage, respectively, due to existence of a fundamental harmonic in the SQUID voltage. Output of the lock-in amplifier is integrated and fed back into the SQUID via the modulation coil. Thus, the SQUID performs as a null detector with the feedback signal (“error” signal) serving as a measure of magnetic field.
Because of delay in transmission lines connecting the SQUID to room temperature electronics, the closed loop bandwidth of SQUID magnetometers is fundamentally limited to 20 MHz (D. Drung, et al., IEEE Trans. Appl. Supercond. 15, 777, 2005), although state of the art schemes allow increasing it up to 50-100 MHz (D. Drung, Supercond. Sci. Technology, 16, 1320, 2003).
To overcome this limitation, a technique for sensing radio-frequency (RF) and microwave magnetic fields was designed where nonlinearity of the V-Φ function of the SQUID is used for rectification of the RF field (R. C. Black, et al. “Imaging radio-frequency fields using a scanning SQUID microscope,” Appl. Phys. Lett, 66, 1267, 1995).
Recently, a scanning SQUID microscope was demonstrated which is capable of measuring GHz magnetic fields by using a hysteretic DC SQUID and a pulsed sampling technique (J. Matthews, et al. “Sampling method to extend bandwidth of scanning SQUID microscopes,” IEEE Trans Appl. Supercond., 15, 688, 2005). Major disadvantage of above schemes is the open loop operation.
Another issue often hampering RF applications of SQUIDs is capacitive and/or inductive near-field coupling (i.e., “cross-talk”, “coherent pick-up”) between various parts of the measurement setup. Since the size of the measurement system and the length of cables connecting SQUID and electronics are about λ˜1 m, they both behave like antennas. Unlike the condition at low (below 10 MHz) or microwave (above >3 GHz) frequencies, where the system size is much greater or much less than λ, respectively, there are created spurious RF signals, which may overshadow a low level SQUID signal. Additionally, an impedance mismatch between the SQUID dynamic resistance (˜1Ω) and RF electronics input (50Ω) may affect the signal integrity and detectability as well.
An RF magnetometer based on DC SQUID which is capable of detecting coherent magnetic fields up to and higher than 200 MHz is a long-lasting need in the field of SQUID magnetometry.