The phase of the microwave on a Josephson transmission line

Nicholas Grabon, Roman Kuzmin, Yen‐Hsiang Lin +3 more

T. Yu. Karminskaya, Victor K. Kornev

Alexander S. Averkin, A. A. Kopasov, I. Pologov +5 more

We present experimental and theoretical studies of the off-resonant and strongly nonlinear regime of Josephson transmission lines (JTLs) with galvanically-coupled nonlinear elements. The transition from the weakly to the strongly nonlinear regime of a JTL induced by increasing the input power of the pump is probed via two-tone spectroscopy. Measurements of the phase of the transmission coefficient for a weak probe signal reveal a large increase and pronounced oscillations in the phase length variation as a function of the microwave power of the pump. Experimental observations are explained on the basis of the developed theoretical approach suitable for the description of the nonlinear response of strongly driven JTLs. Using the derived nonlinear wave equation, we show that the behavior of the phase length variation is associated with the oscillatory dependence of the Josephson inductances on the microwave power. It is demonstrated that the dissipation-induced propagation losses increase in the strongly nonlinear regime and also lead to smearing out the phase length oscillations. The developed theoretical analysis is in good agreement with experimental observations.

Igor A. Devyatov, Alexander Brinkman, Alexandr Golubov +1 more

P. H. Ouyang, Jiangang Ma, Suirong He +5 more

As a typical nonlinear device, Josephson junction (JJ) can be either served as a microwave device to scatter the traveling microwave or embedded in a transmission line (TL) resonator to modify the mode structure. However, two mutually exclusive circuit models have been proposed to describe the JJ embedded in a TL: one is the series embed model [see, e.g., Zueco et al., Phys. Rev. B 86, 024503 (2012)] and another is the parallel embedded one [see, e.g., Yamamoto et al., Appl. Phys. Lett. 93, 042510 (2008)]. Here, beginning with the comparison of the theoretical predictions of these two models, we fabricate the JJ-embedded TL device and measure its microwave scattering parameters at 50-mK low temperature. The experimental results support the parallel embedded model, thus rule out the series embedded one. The present work might lay the physical foundation for the designs of various microwave JJ devices, such as the microwave photonic crystals, superconducting qubits, also the Josephson parameter amplifiers, etc., by embedding the JJs into the superconducting TLs.

Juha Leppäkangas, Göran Johansson, Michael Marthaler +1 more

We study microwave radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. An input-output formalism for the radiation field is established, using a perturbation expansion in the junction's critical current. Using output field operators solved up to the second order, we estimate the spectral density and the second-order coherence of the emitted field. For typical transmission line impedances and at frequencies below the main emission peak at the Josephson frequency, radiation occurs predominantly due to two-photon emission. This emission is characterized by a high degree of photon bunching if detected symmetrically around half of the Josephson frequency. Strong phase fluctuations in the transmission line make related nonclassical phase-dependent amplitude correlations short lived, and there is no steady-state two-mode squeezing. However, the radiation is shown to violate the classical Cauchy-Schwarz inequality of intensity cross-correlations, demonstrating the nonclassicality of the photon pair production in this region.