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We analyze properties of bifurcation quantum detectors based on weakly nonlinear superconducting resonance circuits, in particular, with application to quantum readout. The developed quantitative description demonstrates strong influence of higher harmonics on their characteristics. While this effect is relevant for various circuits, including the conventional Josephson bifurcation amplifier and the parametrically driven circuit, we first focus on the period-doubling bifurcation under a force driving. This kind of bifurcation is due to nominally quadratic nonlinearity, which enables parametric down-conversion of the driving signal at nearly double resonance frequency to the basic mode. We analyze the effect of higher harmonics on the dynamics of the basic mode, inherent in a nonlinear circuit, which in our case is based on a Josephson junction with a sinusoidal current-phase relation as the origin of nonlinearity. We demonstrate that effects beyond the monochromatic approximation significantly modify the bare characteristics and evaluate their contribution. Due to high sensitivity of this circuit to small variations of parameters, it can serve as an efficient detector of the quantum state of superconducting qubits.

We analyze the effect of circuit parameter variation on the performance of Josephson traveling-wave parametric amplifiers (JTWPAs). Specifically, the JTWPA concept we investigate is using flux-biased nonhysteretic rf-SQUIDs in a transmission line configuration, which harnesses the three-wave mixing (3WM) regime. Dispersion engineering enables phasematching to achieve power gain of $\sim$20 dB, while suppressing the generation of unwanted mixing processes. Two dispersion engineering concepts using a 3WM-JTWPA circuit model, i.e., resonant phase-matching (RPM) and periodic capacitance modulation (PCM), are discussed, with results potentially also applicable to four-wave-mixing (4WM) JTWPAs. We propose suitable circuit parameter sets and evaluate amplifier performance with and without circuit parameter variance using transient circuit simulations. This approach inherently takes into account microwave reflections, unwanted mixing products, imperfect phasematching, pump depletion, etc. In the case of RPM the resonance frequency spread is critical, while PCM is much less sensitive to parameter spread. We discuss degrees of freedom to make the JTWPA circuits more tolerant to parameter spread. Finally, our analysis shows that the flux-bias point where rf-SQUIDs exhibit Kerr-free nonlinearity is close to the sweet spot regarding critical current spread., Comment: 6 pages, 3 figures

The recently proposed Josephson traveling-wave parametric amplifier (JTWPA) based on a ladder transmission line consisting of radio-frequency SQUIDs and exploiting three-wave mixing (3WM), has great potential in achieving both a gain of 20 dB and a flat bandwidth of at least 4 GHz. To realize this concept in practical amplifiers we model the advanced JTWPA circuit with periodic modulation of the circuit parameters (engineered dispersion loadings), which allow the basic mixing process, i.e., $\omega_s=\omega_p-\omega_i$, where $\omega_s$, $\omega_p$, and $\omega_i$ are the signal, the pump, and the idler frequencies, respectively, and efficiently suppress propagation of unwanted higher tones including $\omega_{2p}=2\omega_p$, $\omega_{p+s}=\omega_p +\omega_s$, $\omega_{p+i} = \omega_p + \omega_i$, etc. The engineered dispersion loadings allow achieving sufficiently wide $3$ dB-bandwidth from $3$ GHz to $9$ GHz combined with a reasonably small ripple ($\pm2$ dB) in the gain-versus-frequency dependence.

We investigated both theoretically and experimentally open-ended coplanar waveguide resonators with rf SQUIDs embedded in the central conductor at different positions. These rf SQUIDs can be tuned by an external magnetic field and thus may exhibit the non-centrosymmetric nonlinearity of $\chi^{(2)}$ type with suppressed Kerr nonlinearity. We demonstrated that this nonlinearity allows for efficient mixing of $\lambda/2$ and $\lambda$ modes in the cavity and thus enables various parametric effects with three wave mixing. These effects are the second harmonic generation, the half tone generation, the parametric amplification in both degenerate and non-degenerate regimes and deamplification in degenerate regime., Comment: 12 pages incl. 9 figures

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 SQUIDs whose nonlinearity is of $\chi^{(2)}$-type. QPM is achieved in the 3WM process, $\omega_p=\omega_s+\omega_i$ (where $\omega_p$, $\omega_s$, and $\omega_i$ 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 (ca. $0.4\omega_p$) and flat, while unwanted modes, including $\omega_{2p}=2\omega_p$, $\omega_+=\omega_p +\omega_s$, $\omega_- = 2\omega_p - \omega_s$, etc., are strongly suppressed with the help of engineered dispersion., Comment: 6 pages, 4 figures

We have developed a concept for a traveling-wave parametric amplifier driven by a magnetic flux wave. The circuit consists of a serial array of symmetric dc SQUIDs coupled inductively to a separate superconducting LC transmission line carrying the pump microwave; thereby the signal and pump are applied to different ports. The proposed three-wave-mixing amplifier includes, firstly, an adjustable phase velocity of the signal (idler) wave and hence good phase matching yielding large gain in a wide frequency range and, secondly, overcoming of the pump depletion problem. The experimental parameters and characteristics of this amplifier have been evaluated and show promise for applications in quantum-information single-photon circuits., Comment: 14 pages incl. 5 figures

We have developed a recently proposed Josephson traveling-wave parametric amplifier with three-wave mixing [A. B. Zorin, Phys. Rev. Applied 6, 034006, 2016]. The amplifier consists of a microwave transmission line formed by a serial array of nonhysteretic one-junction SQUIDs. These SQUIDs are flux-biased in a way that the phase drops across the Josephson junctions are equal to 90 degrees and the persistent currents in the SQUID loops are equal to the Josephson critical current values. Such a one-dimensional metamaterial possesses a maximal quadratic nonlinearity and zero cubic (Kerr) nonlinearity. This property allows phase matching and exponential power gain of traveling microwaves to take place over a wide frequency range. We report the proof-of-principle experiment performed at a temperature of T = 4.2 K on Nb trilayer samples, which has demonstrated that our concept of a practical broadband Josephson parametric amplifier is valid and very promising for achieving quantum-limited operation., Comment: Submitted for presentation at the 16th International Superconductive Electronics Conference, ISEC 2017, 12-16 June 2017, Sorrento, Italy

We develop a concept of the traveling-wave Josephson parametric amplifier exploiting quadratic nonlinearity of a serial array of one-junction SQUIDs embedded in a superconducting transmission line. The external magnetic flux applied to the SQUIDs makes it possible to efficiently control the shape of their current-phase relation and, hence, the balance between quadratic and cubic (Kerr-like) nonlinearities. This property allows us to operate in the favorable three-wave-mixing mode with minimal phase mismatch, an exponential dependence of the power gain on number of sections $N$, a large bandwidth, a high dynamic range, and substantially separated signal ($f_s$) and pump ($f_p$) frequencies obeying relation $f_s+f_i = f_p$, where $f_i$ is the idler frequency. An estimation of the amplifier characteristics with typical experimental parameters, a pump frequency of $12$ GHz, and $N = 300$ yields a flat gain of 20 dB in the bandwidth of 5.6 GHz.

Using a Josephson junction interferometer (DC SQUID) as a microwave source for irradiating a single-electron trap, both devices fabricated on the same chip, we study the process of photon-assisted tunneling as an effective mechanism of single photon detection. High sensitivity down to a very small oscillation amplitude $v_{\rm J} \sim$ 10 nV$\ll E_{\rm act} \lesssim hf_{\rm J}$ and down to low photon absorption rates $\Gamma_{\rm ph} \sim$ (1--50)Hz, as well as a clear threshold type of operation with an activation energy $E_{\rm act} \sim$ 400 $\mu$eV, are demonstrated for the trap with respect to the microwave photons of frequency $f_{\rm J} \sim$ (100--200)GHz. Tunable generation is demonstrated with respect to the power and frequency of the microwave signal produced by the SQUID source biased within the subgap voltage range. A much weaker effect is observed at the higher junction voltages along the quasiparticle branch of the $I-V$ curve; this response mostly appears due to the recombination phonons., Comment: 4 pages, 4 figures

We investigate the magnetization reversal mechanism in an individual permalloy (Py) nanotube (NT) using a hybrid magnetometer consisting of a nanometer-scale SQUID (nanoSQUID) and a cantilever torque sensor. The Py NT is affixed to the tip of a Si cantilever and positioned in order to optimally couple its stray flux into a Nb nanoSQUID. We are thus able to measure both the NT's volume magnetization by dynamic cantilever magnetometry and its stray flux using the nanoSQUID. We observe a training effect and temperature dependence in the magnetic hysteresis, suggesting an exchange bias. We find a low blocking temperature $T_B = 18 \pm 2$ K, indicating the presence of a thin antiferromagnetic native oxide, as confirmed by X-ray absorption spectroscopy on similar samples. Furthermore, we measure changes in the shape of the magnetic hysteresis as a function of temperature and increased training. These observations show that the presence of a thin exchange-coupled native oxide modifies the magnetization reversal process at low temperatures. Complementary information obtained via cantilever and nanoSQUID magnetometry allows us to conclude that, in the absence of exchange coupling, this reversal process is nucleated at the NT's ends and propagates along its length as predicted by theory., Comment: 8 pages, 4 figures