We investigate the distribution of the switching current of a current-biased Josephson junction (CBJJ) and its dependence on the microwave frequency using two theoretical methods, one of which is the quantum trajectory method and the other is the master equation method. Both the methods show that the distribution of the switching current of CBJJ will exhibit double peaks in a certain range of microwave frequency if proper microwave power is given, and the gap between the two peaks will increase with the microwave frequency. The obtained results can be used to identify the energy difference of the ground and first excited states in a Josephson junction for any bias current.
We investigate the distribution of the switching current of a current-biased Josephson junction (CBJJ) and its dependence on the microwave frequency using two theoretical methods, one of which is the quantum trajectory method and the other is the master equation method. Both the methods show that the distribution of the switching current of CBJJ will exhibit double peaks in a certain range of microwave frequency if proper microwave power is given, and the gap between the two peaks will increase with the microwave frequency. The obtained results can be used to identify the energy difference of the ground and first excited states in a Josephson junction for any bias current.
We perform both theoretical and experimental investigations on the phase escape of a current-biased Josephson tunnel junction under microwave irradiation. The switching current distributions exhibit abundant nonlinear behaviors depending on the power and frequency of the applied microwave. We present a model to describe the behavior of the primary peak in the switching current distribution, which is confirmed by our experimental results. The obtained features can be used to characterize the damping parameter of Josephson junctions.
A quantum-mechanical analysis of the Josephson phase escape in the presence of both dc and ac bias currents is presented. We find that the potential barrier for the escape of the phase is effectively suppressed as the resonant condition occurs, i.e., when the frequency $\ensuremath{\omega}$ of the ac bias matches the Josephson-junction energy-level separation. This effect manifests itself by a pronounced drop in the dependence of the switching current Is on the power W of the applied microwave radiation and by a peculiar double-peak structure in the switching current distribution P(Is). The developed theory is in a good accord with an experiment which we also report in this paper. The obtained features can be used to characterize certain aspects of the quantum-mechanical behavior of the Josephson phase, such as the energy level quantization, the Rabi frequency of coherent oscillations, and the effect of damping.
The switching current distributions P(I) with different sweep rates are obtained in microwave-driven current-biased Josephson tunnel junctions. We observe the resonant peak caused by microwave-assisted tunneling in P(I). By measuring the magnitude of the microwave resonant peak as a function of the sweep rate, we develop a novel method of extracting the energy relaxation time T1 of the junction. With this simple method, it is determined that T1 of a Nb/AlOx/Nb Josephson junction is approximately 0.5 µs.
Josepshon junction has its switching current distribution, from which one could get not only the escape rate but also other quantum information like the energy level quantization, Rabi oscillation with proper microwave. The measurements on the switching current distribution of a Josephson junction is very helpful to the development of supercondutor qubit including phase qubit, chage qubit, flux qubit and their combinations. We present three measurement techniques and perform a measurement (10+4 times) on the switching current distribution of a homemade NbN/AlN-x/NbN Josephson junction at certain temperature. According to the disadvantages of the presently used technique and the result we get, more advices are given to the next measurements on the switching current distribution at the ultra low temperature (mK).
It is well known that the current-biased Josephson junction (CBJJ) can serve as a Josephson threshold detector (JTD) for the sensitive detection of weak microwave signals. Based on the recent work (PRB {\bf 111}, 024501 (2025)) on the detection sensitive limit of the usual equilibrium JTD, here we numerically demonstrate that a non-equilibrium JTD can be alternatively utilized to implement the higher sensitive detection of a weak microwave signal, arriving at its energy quantum limit. In the presence of thermal noise, we numerically simulate the phase dynamics for the CBJJ in the JTD with the different sweep rates of the biased currents, and find that the SCDs of the JTD with and without the microwave signal input show different behaviors. It is demonstrated that, depending on how high the sweep rate of the biased current being applied, the JTD can be operated in either the equilibrium- or the non-equilibrium state. Specifically, under the rapidly non-adiabatic driving, the SCDs of the JTD are obviously insensitive to the thermal noises, which means that the non-equilibrium JTD can possess a higher achievable detection sensitivity, compared with its equilibrium state counterpart. Consequently, the non-equilibrium JTD can be utilized to implement the desired single microwave-photon detection. Also, some of the achievable performance indexes, such as the dynamic range, detection bandwidth, and the photon-number resolvability, etc., of the non-equilibrium JTD have been estimated, when it serves as a wideband microwave single-photon detector.
We present a simple model to describe multiphoton transitions between the quasi-bound states of a current-driven Josephson junction. The transitions are induced by applying an ac voltage with controllable frequency and amplitude across the junction. The voltage induces transitions across the junction when the frequency $\ensuremath{\omega}$ satisfies $n\ensuremath{\hbar}\ensuremath{\omega}=\ensuremath{\Delta}{E}_{10}$, where $\ensuremath{\Delta}{E}_{10}$ is the splitting between the ground and first excited quasi-bound state of the junction. We calculate the matrix elements of the transitions as a function of the dc bias current I, and the frequency $\ensuremath{\omega}$ and amplitude Vac of the microwave voltage, for representative junction parameters. We also calculate the frequency-dependent absorption coefficient by solving the relevant Bloch equations when the ac voltage is sufficiently weak. In this regime, the absorption coefficient is a sum of Lorentzian lines centered at the n-photon absorption frequency, of strength proportional to the squared matrix elements. For fixed Vac, the transition rate for an n-photon process usually decreases with increasing n. We also find a characteristic even-odd effect: The absorption coefficient typically increases with I for n even but decreases for n odd. Our results agree qualitatively with recent experiments.