No Arabic abstract
A superconducting quantum interference device with differential output or DSQUID was proposed earlier for operation in the presence of large common-mode signals. The DSQUID is the differential connection of two identical SQUIDs. Here we show that besides suppression of electromagnetic interference this device provides effective linearization of DC SQUID voltage response. In the frame of the resistive shunted junction model with zero capacitance, we demonstrate that Spur-Free Dynamic Range (SFDR) of DSQUID magnetic flux-to-voltage transfer function is higher than SFDR > 100 dB while Total Harmonic Distortion (THD) of a signal is less than THD < $10^{-3}%$ with a peak-to-peak amplitude of a signal being a quarter of half flux quantum, $2Phi_a = Phi_0/8$. Analysis of DSQUID voltage response stability to a variation of the circuit parameters shows that DSQUID implementation allows doing highly linear magnetic flux-to-voltage transformation at the cost of a high identity of Josephson junctions and high-precision current supply.
We report measurements of transfer functions and flux shifts of 20 on-chip high T$_C$ DC SQUIDs half of which were made purposely geometrically asymmetric. All of these SQUIDs were fabricated using standard high T$_C$ thin film technology and they were single layer ones, having 140 nm thickness of YBa$_2$Cu$_3$O$_{7-x}$ film deposited by laser ablation onto MgO bicrystal substrates with 24$^0$ misorientation angle. For every SQUID the parameters of its intrinsic asymmetry, i. e., the density of critical current and resistivity of every junction, were measured directly and independently. We showed that the main reason for the on-chip spreading of SQUIDs voltage-current and voltage-flux characteristics was the intrinsic asymmetry. We found that for SQUIDs with a relative large inductance ($L>120 $ pH) both the voltage modulation and the transfer function were not very sensitive to the junctions asymmetry, whereas SQUIDs with smaller inductance ($Lsimeq 65-75 $ pH) were more sensitive. The results obtained in the paper are important for the implementation in the sensitive instruments based on high T$_C$ SQUID arrays and gratings.
We consider voltage and current responses formation in DC SQUID with overdamped Josephson junctions in resistive and superconducting state in the frame of resistively shunted junction (RSJ) model. For simplicity we neglect the junction capacitance and the noise effect. Explicit expressions for the responses in resistive state were obtained for a SQUID which is symmetrical with respect to bias current injection point. Normalized SQUID inductance $l = 2 e I_c L/hbar$ (where $I_c$ is the critical current of Josephson junction, $L$ is the SQUID inductance, $e$ is the electron charge and $hbar$ is the Planck constant) was assumed to be within the range $l leq 1$, subsequently expanded up to $l approx 7$ using two fitting parameters. SQUID current response in superconducting state was considered for arbitrary value of the inductance. Impact of small technological spread of parameters relevant for low-temperature superconductor (LTS) technology was studied with generalization of the developed analytical approach for a case of small difference of critical currents and shunt resistances of the Josephson junctions, and inequality of SQUID inductive shoulders for both resistive and superconducting states. Comparison with numerical calculation results shows that developed analytical expressions can be used in practical LTS SQUIDs and SQUID-based circuits design, e.g. large serial SQIF, drastically decreasing the time of simulation.
We report measurements of Rabi oscillations and spectroscopic coherence times in an Al/AlOx/Al and three Nb/AlOx/Nb dc SQUID phase qubits. One junction of the SQUID acts as a phase qubit and the other junction acts as a current-controlled nonlinear isolating inductor, allowing us to change the coupling to the current bias leads in situ by an order of magnitude. We found that for the Al qubit a spectroscopic coherence time T2* varied from 3 to 7 ns and the decay envelope of Rabi oscillations had a time constant T = 25 ns on average at 80 mK. The three Nb devices also showed T2* in the range of 4 to 6 ns, but T was 9 to 15 ns, just about 1/2 the value we found in the Al device. For all the devices, the time constants were roughly independent of the isolation from the bias lines, implying that noise and dissipation from the bias leads were not the principal sources of dephasing and inhomogeneous broadening.
We investigate the quantum dynamics of a quadratic-quartic anharmonic oscillator formed by a potential well between two potential barriers. We realize this novel potential shape with a superconducting circuit comprised of a loop interrupted by two Josephson junctions, with near-zero current bias and flux bias near half a flux quantum. We investigate escape out of the central well, which can occur via tunneling through either of the two barriers, and find good agreement with a generalized double-path macroscopic quantum tunneling theory. We also demonstrate that this system exhibits an optimal line in current and flux bias space along which the oscillator, which can be operated as a phase qubit, is insensitive to decoherence due to low-frequency current fluctuations.
We report spectroscopic measurements of discrete two-level systems (TLSs) coupled to a dc SQUID phase qubit with a 16 mum2 area Al/AlOx/Al junction. Applying microwaves in the 10 GHz to 11 GHz range, we found eight avoided level crossings with splitting sizes from 10 MHz to 200 MHz and spectroscopic lifetimes from 4 ns to 160 ns. Assuming the transitions are from the ground state of the composite system to an excited state of the qubit or an excited state of one of the TLS states, we fit the location and spectral width to get the energy levels, splitting sizes and spectroscopic coherence times of the phase qubit and TLSs. The distribution of splittings is consistent with non-interacting individual charged ions tunneling between random locations in the tunnel barrier and the distribution of lifetimes is consistent with the AlOx in the junction barrier having a frequency-independent loss tangent. To check that the charge of each TLS couples independently to the voltage across the junction, we also measured the spectrum in the 20-22 GHz range and found tilted avoided level crossings due to the second excited state of the junction and states in which both the junction and a TLS were excited.