Quantization of the superconducting energy gap in an intense microwave field

Abstract

We study photon assisted tunneling in Nb/AlOx/Nb Josephson junctions. A quantitative calibration of the microwave field in the junction allowed direct verification of the quantum efficiency of microwave photon detection by the junctions. We observe that voltages of photon assisted tunneling steps vary both with the microwave power and the tunneling current. However, this variation is not monotonous, but staircase-like. The phenomenon is caused by mutual locking of positive and negative step series. A similar locking is observed with Shapiro steps. As a result the superconducting gap assumes quantized values equal to multiples of the quarter of the photon energy. The quantization is a manifestation of nonequilibrium tuning (suppression or enhancement) of superconductivity by the microwave field.Superconducting Josephson junctions are used as sensitive detectors of microwave (MW) and terahertz signals [1][2][3][4][5][6][7][8]. Application of MW radiation leads to appearance of Shapiro and photon assisted tunneling (PAT) steps in the current-voltage (I-V ) characteristics of a junction at eV = ±nhf /2 and eV = ±2∆ ± nhf , respectively. Here f is the MW frequency and ∆ is the superconducting energy gap. Shapiro and PAT steps originate from Cooper pair and quasiparticle (QP) currents, correspondingly (for details see e.g. Ref.[9]). A response of junctions to weak MW signals is well understood [1][2][3]. For example, the differential conductivity due to PAT is described by the Tien-Gordon theory:where J n are Bessel functions of integer order n, V M W is the MW voltage amplitude in the junction and I 0 (V ) is a dc-current without MW. Positive/negative n terms in this expression describe contributions from PAT with absorbtion/emission of n photons. However, such a textbook description works only for weak MW signals that do not affect superconducting properties of junction electrodes. Strong electromagnetic fields may disturb a thermal equilibrium state. This may either suppress [10,11] or enhance [12][13][14][15] superconducting properties, such as ∆ and the critical current I c . Current flow through the junctions also leads to disruption of the equilibrium. Analysis of such nonequilibrium effects at low temperatures is complicated by essentially nonlinear response of the junction to perturbations [16]. Detailed understanding of nonequilibrium effects in Josephson junctions is lacking and is important both for optimization of operation of superconducting quantum devices [17][18][19][20][21][22] and for fundamental studies of the pairing mechanism in unconventional superconductors [23]. To investigate the influence of nonequilibrium effects in intense MW fields V M V > 2∆/e on detection characteristics of Josephson junctions is the main objective of our work.In this work we study photon assisted tunneling steps in Nb/AlOx/Nb Josephson junctions. Using an absolute calibration of the MW field inside the junction we demonstrate quantum efficiency of microwave photon detection by our junctions. We observe that contrary to...

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

“…Both sets of resonances were observed experimentally and described theoretically in (Boris and Krasnov, 2015). In that study, it was demonstrated that the Shapiro steps and PAT states originate from Cooper-pair and quasiparticle currents; and if a JJ is subjected to an intense microwave signal, both sets of resonances can be observed in the current, changing both the voltage and microwave power (Boris and Krasnov, 2015;Snyder et al, 2018).…”

“…The former relates to the tunneling of electrons (quasiparticles) and results in the steps on the current-voltage curve as displaced in voltage by k ω/e; the latter assumes the supercurrent response, which occurs as the Shapiro steps at voltages k ω/2e (Nakamura et al, 2001). Both sets of resonances were observed experimentally and described theoretically in (Boris and Krasnov, 2015). In that study, it was demonstrated that the Shapiro steps and PAT states originate from Cooper-pair and quasiparticle currents; and if a JJ is subjected to an intense microwave signal, both sets of resonances can be observed in the current, changing both the voltage and microwave power (Boris and Krasnov, 2015;Snyder et al, 2018).…”

Dynamics of dissipative Landau-Zener transitions in an anisotropic three-level system

“…To visualize the effects of the periodic driving field [74], in Fig. 3, a contour plot of P -1 (t = 5/ω) is displayed as a function of (D, A z ), where the x-axis is the anisotropy D and the y-axis is the z-direction driving field amplitude A z .…”