Putting mechanics into circuit quantum electrodynamics

We review the use of mechanical oscillators in circuit quantum electrodynamics. The capacitive coupling of nano-electromechanical systems with quantum bits and superconducting microwave resonators gives rise to a rich quantum physics involving electrons, photons and phonons. We focus in particular on the linear coupling between a mechanical oscillator and a microwave resonator and present the quantum dynamics that stems from the phonotonic Josephson junction. The microwave cavity turns out to be a powerful device to detect quantum phonon states and manipulate entangled states between phonons and photons.     

Classical analogs for Rabi-oscillations,Ramsey-fringes,and spin-echo in Josephson junctions

We investigate the results of recently published experiments on the quantum behavior of Josephson circuits in terms of the classical modeling based on the resistively and capacitively-shunted (RCSJ) junction model. Our analysis shows evidence for a close analogy between the nonlinear behavior of a pulsed microwave-driven Josephson junction at low temperature and low dissipation and the experimental observations reported for the Josephson circuits. Specifically, we demonstrate that Rabi-oscillations, Ramsey-fringes, and spin-echo observations are not phenomena with a unique quantum interpretation. In fact, they are natural consequences of transients to phase-locking in classical nonlinear dynamics and can be observed in a purely classical model of a Josephson junction when the experimental recipe for the application of microwaves is followed and the experimental detection scheme followed. We therefore conclude that classical nonlinear dynamics can contribute to the understanding of relevant experimental observations of Josephson response to various microwave perturbations at very low temperature and low dissipation.     

The microwave circuit model of Josephson junction at liquid nitrogen temperature

We have measured the microwave characteristics of Josephson junction at liquid nitrogen temperature by using microwave network analyser. Based upon these experimental results we present a microwave circuit model of Josephson junction at liquid nitrogen temperature and calculate the parameters of microwave circuit model of Josephson junction.     

微波场中Josephson结的微波发射与吸收研究

采用数值仿真方法,研究微波场中约瑟夫森结微波感应台阶处的功率特性。发现微波场中约瑟夫森结不止吸收辐射,也发射辐射的情况。得到微波辐照和结电阻对功率吸收和发射的影响规律。结果表明,处于发射功率的状态对应的偏置电流范围占整个台阶总电流范围的比例可以趋于50%。这一发现对约瑟夫森结理论和应用研究具有重要的意义。     

超导弱连接中的Josephson电流在一个磁通量子内的振荡(Ⅰ)——Josephson结

本文指出如果Josephson结处在Q值足够高的谐振腔内,当Josephson频率ω=(2eV₀)/h与谐振腔的本征频率ω_r发生谐振时,谐振的电磁场对Josephson结自身的反馈作用将导致超流电流在一个磁通量子内随磁场的小周期振荡。 关键词：     

Decoherence in josephson phase qubits from junction resonators

Although Josephson junction qubits show great promise for quantum computing, the origin of dominant decoherence mechanisms remains unknown. Improving the operation of a Josephson junction based phase qubit has revealed microscopic two-level systems or resonators within the tunnel barrier that cause decoherence. We report spectroscopic data that show a level splitting characteristic of coupling between a two-state qubit and a two-level system. Furthermore, we show Rabi oscillations whose "coherence amplitude" is significantly degraded by the presence of these spurious microwave resonators. The discovery of these resonators impacts the future of Josephson qubits as well as existing Josephson technologies.     

Nature of the microwave response of a YBaCuO Josephson junction on a bicrystalline substrate

The response of YBaCuO Josephson junctions on a bicrystalline substrate to the action of microwave radiation is found to contain, besides the Josephson response, a contribution associated with the tunneling of quasiparticles through channels formed by localized states in the region of the Josephson junction. It is shown that this contribution is associated with an increase in the conduction through these channels under the action of the radiation on the junction. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 416–420 (25 September 1996)     

SrTiO3基片上Tl-2212双晶约瑟夫森结的动态特性及噪声影响研究

在SrTiO₃（STO）基片上制作了Tl-2212双晶约瑟夫森结,并对其进行了微波辐照下的I-V特性测试,观察到了夏皮罗台阶,符合约瑟夫森电压-频率关系.利用数值仿真对约瑟夫森结建立了RCSJ模型,仿真结果与实验数据符合较好,利用此模型深入研究了噪声对结动态特性的影响,解释了噪声影响下结的微波感应台阶幅度减小和极小值展宽现象,提出了有效噪声温度为工作温度和外部噪声的等效温度之和. 关键词： RCSJ模型 噪声 Tl-2212双晶约瑟夫森结     

On Effectiveness of Protocol Creating Maximum Entanglement of Two Charge-Phase Qubits by Cavity Field

We revisit the protocols to create maximally entangled states between two Josephson junction （33） charge phase qubits coupled to a microwave field in a cavity as a quantum data bus. We analyze a novel mechanism of quantum decoherence due to the adiabatic entanglement between qubits and the data bus, the off-resonance microwave field. We show that even if the variable of the data bus can be adiabatically eliminated, the entanglement between the qubits and data bus remains and can decohere the superposition of two-particle state. Fortunately we can construct a decoherencefree subspace of two-dimension to against this adiabatic decoherence. To carry out the analytic study for this decoherence problem, we develop Frohlich transformation to re-derive the effective Hamiltonian of these systems, which is equivalent to that obtained from the adiabatic elimination approach.     

Spectrum of Andreev bound states in a molecule embedded inside a microwave-excited superconducting junction

Nondissipative Josephson current through nanoscale superconducting constrictions is carried by spectroscopically sharp energy states, the so-called Andreev states. Although theoretically predicted almost 40 years ago, no direct spectroscopic evidence of these Andreev bound states exists to date. We propose a novel type of spectroscopy based on embedding a superconducting constriction, formed by a single-level molecule junction, in a microwave QED cavity environment. In the electron-dressed cavity spectrum we find a polariton excitation at twice the Andreev bound state energy, and a superconducting-phase-dependent ac Stark shift of the cavity frequency. Dispersive measurement of this frequency shift can be used for Andreev bound state spectroscopy.     

Magnetic flux control of chiral Majorana edge modes in topological superconductor

We study the transport of chiral Majorana edge modes (CMEMs) in a hybrid quantum anomalous Hall insulator-topological superconductor (QAHI-TSC) system in which the TSC region contains a Josephson junction and a cavity. The Josephson junction undergoes a topological transition when the magnetic flux through the cavity passes through half-integer multiples of magnetic flux quantum. For the trivial phase, the CMEMs transmit along the QAHI-TSC interface as without magnetic flux. However, for the nontrivial phase, a zero-energy Majorana state appears in the cavity, leading to that a CMEM can resonantly tunnel through the Majorana state to a different CMEM. These findings may provide a feasible scheme to control the transport of CMEMs by using the magnetic flux and the transport pattern can be customized by setting the size of the TSC.     

Microwave absorption in high-Tc superconductors studied by the EPR method

Dependences of the microwave absorption on temperature, magnetic field and microwave power obtained for the high-T _c superconductors are presented. Shape of the magnetically modulated microwave absorption, low-field phase diagram and overheating of the Josephson junction system induced by microwave irradiation are discussed. The model of the Josephson junction system interacting with microwaves has been used to explain the behavior of the high-T _c superconductors in low magnetic field.     

嵌入Fabry-Perot谐振腔的高温超导双晶约瑟夫森结的毫米波辐照特性研究

采用嵌入Fabry-Perot谐振腔的方式,研究了Tl2Ba2CaCu2O8(Tl-2212)高温超导薄膜双晶约瑟夫森结的毫米波辐照特性.重点研究了双晶约瑟夫森结与Fabry-Perot谐振腔的耦合特性,发现放置在谐振腔中的结的位置、角度、结的图形以及Fabry-Perot谐振腔中两镜面间的距离等对耦合都有很大的影响.通过精细调节这些参数,可使双晶约瑟夫森结与外加毫米波达到最佳耦合.在最佳耦合情况下,能观察到9级明显的夏皮罗台阶.利用Fabry-Perot谐振腔技术,解决了约瑟夫森结与毫米波的耦合问题,为高温超导约瑟夫森结的毫米波及太赫兹波的辐射和检测研究奠定了基础.     

Stability analysis of nonlinear microwave circuits in time domain

Frequency-domain based methods are not valid to analyze a nonlinear microwave circuit with general, arbitrary nonlinearities. Therefore, analysis of nonlinear microwave circuits in time-domain is presented. Subharmonics and instabilities can be predicted. As examples, Josephson junction and the Schottkybarrier mixer diode are discussed.     

Equivalent Josephson junctions

The magnetic field dependences of critical current are numerically constructed for a long Josephson junction with a shunt-or resistor-type microscopic inhomogeneities and compared to the critical curve of a junction with exponentially varying width. The numerical results show that it is adequate to replace the distributed inhomogeneity of a long Josephson junction by an inhomogeneity localized at one of its ends, which has certain technological advantages. It is also shown that the critical curves of junctions with exponentially varying width and inhomogeneities localized at the ends are unaffected by the mixed fluxon-antifluxon distributions of the magnetic flow. This fact may explain the improvement of the spectra of microwave radiation noted in the literature.     

Microwave photon counter based on Josephson junctions

We describe a microwave photon counter based on the current-biased Josephson junction. The junction is tuned to absorb single microwave photons from the incident field, after which it tunnels into a classically observable voltage state. Using two such detectors, we have performed a microwave version of the Hanbury Brown-Twiss experiment at 4 GHz and demonstrated a clear signature of photon bunching for a thermal source. The design is readily scalable to tens of parallelized junctions, a configuration that would allow number-resolved counting of microwave photons.     

A microwave photon detector

The possibility of the implementation of a single-photon detector in the microwave range has been discussed. It has been shown that, for these purposes, it is possible to use an unshunted Josephson junction, which is switched from the superconducting state into a finite-voltage state at the presence of an external signal. The sensitivity of this detector is determined by the distribution of switchings in the absence of an external signal. It has been demonstrated that there is a Josephson junction with a noise temperature below 60 mK at a nominal external temperature of 10 mK. A specific detector intended for the measurement of external microwave signals has been proposed, designed, and fabricated. The first experimental results have been presented.     

Tunneling spectroscopy of two-level systems inside a Josephson junction

We consider a two-level system (TLS) with energy level separation plankvOmega0 inside a Josephson junction. The junction is shunted by a resistor R and is voltage V biased. If the TLS modulates the Josephson energy and/or is optically active, it is Rabi driven by the Josephson oscillations in the running phase regime near the resonance 2eV=plankvOmega0. The Rabi oscillations, in turn, translate into oscillations of current and voltage that can be detected in noise measurements. This effect provides an option to fully characterize the TLS inside Josephson junction and to find the TLS's contribution to the decoherence when the junction is used as a qubit.     

Cavity-Induced Self-Trapping of a Bose Josephson Junction

We investigate the self-trapping of a Bose Josephson junction, which is dispersively coupled to a driven optical cavity. The cavity-induced nonlinearity is presented analytically, and its effect results in the appearance of the self-trapping for the Bose-Einstein condensates in the Josephson oscillation regime. In addition, there exists competition between the nonlinearitiesinduced by the interatomic interaction and by the driven cavity for the emergences of self-trapping. Our results show that the driven cavity can be utilized as a possible tool to produce the self-trapping for the condensates with weak interatomic interaction.     

约瑟夫森结跳变电流在微波辐照下的分布

在16 mK的极低温下,我们对电流偏置的Nb/AlOx/Nb结进行了跳变电流统计分布的测量.在没有外加微波的辐照时,分布曲线只有一个峰;在有外加微波的辐照时,其跳变电流的统计分布除了基峰外,会出现谐振峰,形成双峰结构.该谐振峰的位置和结的量子化的能级相关,其高度随外加微波功率的改变而改变.研究约瑟夫森结跳变电流在微波辐照下的分布,对于研究超导量子比特的能级量子化、Rabi振荡等具有重要的意义.