Josephson Phase Research Articles

Junction fabrication by shadow evaporation without a suspended bridge

We present a novel shadow evaporation technique for the realization of junctionsand capacitors. The design by e-beam lithography of strongly asymmetricundercuts on a bilayer resist enables in situ fabrication of junctions and capacitorswithout the use of the well-known suspended bridge (Dolan 1977 Appl. Phys.Lett. 31 337–9). The absence of bridges increases the mechanical robustnessof the resist mask as well as the accessible range of the junction size, from10 − 2 µm2 to more than104 µm2. We havefabricated Al/AlOx/Al Josephson junctions, phase qubit and capacitors using a 100 kV e-beam writer. Althoughthis high voltage enables a precise control of the undercut, implementation using aconventional 20 kV e-beam is also discussed. The phase qubit coherence times, extractedfrom spectroscopy resonance width, Rabi and Ramsey oscillation decays and energyrelaxation measurements, are longer than the ones obtained in our previous samplesrealized by standard techniques. These results demonstrate the high quality of the junctionobtained by this bridge-free technique.

Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit

Analytical descriptions of the geometric phases (GPs) for the total system and subsystems are studied for a current biased Josephson phase qubit strongly coupled to a lossy LC circuit in the dispersive limit. It is found that, the GP and purity depend on the damping parameter which leads to the phenomenon of GP death. Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP. The asymptotic behavior of the GP and the purity for the qubit-LC resonator state closely follow that for the qubit state, but however, for the LC circuit these asymptotic values are equal to zero.

Terahertz electromagnetic radiation from intrinsic Josephson junctions at zero magnetic field via breather-type self-oscillations

I propose a new mechanism of intense high-frequency electromagnetic wave generation by spatially uniform stacked Josephson junctions at zero magnetic field. The ac-Josephson effect converts the dc-bias voltage into ac-supercurrent, however, in the absence of spatial variation of Josephson phase difference, does not provide dc-to-ac power conversion, needed for emission of electromagnetic waves. Here I demonstrate that at geometrical resonance conditions, the spatial homogeneity of phase can be spontaneously broken by appearance of breathers (bound fluxon-antifluxon pairs), facilitating effective dc-to-ac power conversion. The proposed mechanism explains all major features of recently observed THz radiation from large area Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ mesa structures.

Microwave-induced supercurrent in a ferromagnetic Josephson junction

We study the supercurrent resulting from coupling of the Josephson phase and the spinwave excited by microwave radiation in a ferromagnetic Josephson junction, in which twosuperconductors are separated by a ferromagnet. To explore how the spin-wave excitationaffects the current–voltage curve, the resistively shunted junction model, which is anequation of motion for the Josephson phase, is extended by considering the gaugeinvariance including magnetization. When the magnetization is driven by the microwaveadjusted to the ferromagnetic resonance frequency, the dc supercurrent is induced in thejunction and the current–voltage curve shows step structures as a function of appliedvoltage. The position of each step in voltage is proportional to the microwave frequencymultiplied by an even number. This means that the even number of magnons is necessaryfor the singlet Cooper pair to go through the ferromagnetic layer. The magnitudes ofstep height can be controlled by tuning the shape of the interface. Our resultspresent a new route to observe the spin-wave excitation by the Josephson effect.

Microwave readout scheme for a Josephson phase qubit

We present experimental results on a microwave scheme for reading out a Josephson phase qubit. A capacitively shunted superconducting quantum interference device (SQUID) is used as a nonlinear resonator which is inductively coupled to the qubit. The flux state of the qubit is detected by measuring the amplitude and phase of a microwave pulse reflected from the SQUID resonator. By this low-dissipative method, the qubit state measurement time is reduced to 25 μs, which is much faster than the conventional readout performed by switching the SQUID to its nonzero dc voltage state. The readout scheme presented here allows for reading out multiple qubits using a single microwave line by employing frequency-division multiplexing.

Fluctuations of the Josephson current and electron-electron interactions in superconducting weak links

We derive a microscopic effective action for superconducting contacts with arbitrary transmission distribution of conducting channels. Provided fluctuations of the Josephson phase remain sufficiently small our formalism allows to fully describe fluctuation and interaction effects in such systems. As compared to the well-studied tunneling limit our analysis yields a number of qualitatively distinct features which occur due to the presence of subgap Andreev bound states in the system. We investigate the equilibrium supercurrent noise and evaluate the electron-electron interaction correction to the Josephson current across superconducting contacts. At $T=0$ this correction is found to vanish for fully transparent contacts indicating the absence of Coulomb effects in this limit.

Josephson junctions with nonsinusoidal current-phase relations based on heterostructures with a ferromagnetic spacer and their applications

A detailed review of theories describing the current-phase relations in Josephson junctions based on heterostructures with ferromagnetic layers is presented. The particular attention has been focused on the possibilities of making the so-called ϕ-junctions in which the ground state in the absence of the current is realized when the Josephson phase ϕ is nonzero. The recently popular speculations concerning the possibility of applying the Josephson π- and ϕ-junctions, which are made on the basis of heterostructures with ferromagnetic layers, to the formation of quantum bits (qubits) have been illustrated. An attempt to formulate the requirements for the characteristics of the Josephson heterostructures based on the first principles of the quantum-mechanical description of superconducting interferometers with a low inductance has been made.

Quantum phase measurement and Gauss sum factorization of large integers in a superconducting circuit

We study the implementation of quantum phase measurement in a superconducting circuit, where two Josephson phase qubits are coupled to the photon field inside a resonator. We show that the relative phase of the superposition of two Fock states can be imprinted in one of the qubits. The qubit can thus be used to probe and store the quantum coherence of two distinguishable Fock states of the single-mode photon field inside the resonator. The effects of dissipation of the photon field on the phase detection are investigated. We find that the visibilities can be greatly enhanced if the Kerr nonlinearity is exploited. We also show that the phase measurement method can be used to perform the Gauss sum factorization of numbers (${\geq} 10^4$) into a product of prime integers, as well as to precisely measure both the resonator's frequency and the nonlinear interaction strength. The largest factorizable number is mainly limited by the coherence time. If the relaxation time of the resonator were to be ${\sim} 10$ $\mu$s (${\sim} 1$ ms), then the largest factorizable number can be ${\geq} 10^4N$ (${\geq} 10^{7}N$), where $N$ is the number of photons in the resonator.

Lifetime and Coherence of Two-Level Defects in a Josephson Junction

We measure the lifetime (T₁) and coherence (T₂) of two-level defect states (TLSs) in the insulating barrier of a Josephson phase qubit and compare to the interaction strength between the two systems. We find for the average decay times a power-law dependence on the corresponding interaction strengths, whereas for the average coherence times we find an optimum at intermediate coupling strengths. We explain both the lifetime and the coherence results using the standard TLS model, including dipole radiation by phonons and anticorrelated dependence of the energy parameters on environmental fluctuations.

Self-resonant modes in Josephson junctions with a phase discontinuity

We extend the theory of self-resonances in short Josephson junctions to the case of a piecewise constant critical current density and a κ discontinuity in the Josephson phase. We calculate the amplitude of the self-resonances as a function of applied magnetic field by using an extension of the approach introduced by Kulik for conventional Josephson junctions (I. O. Kulik, JETP Lett. 2, 84 (1965)). The theory given here agrees with existing experiments on superconducting–insulator–ferromagnet–superconductor 0–π Josephson junctions. The results are relevant to the characterization of all modern 0–π junctions as well as 0–κ junctions with artificially created phase discontinuities: high-temperature grain boundary junctions, junctions with a ferromagnetic barrier, and junctions with current injectors.

Incoherent microwave-induced resistive states of small Josephson junctions

We report an experimental and theoretical study of low-voltage resistive states observed in small tunnel Josephson junctions subject to microwave radiation. The observed features result from Shapiro steps in the current–voltage characteristics and appear when both thermal fluctuations and high frequency dissipation are strong. Without microwave radiation, Josephson junctions have a phase diffusion supercurrent branch characterized by a finite small resistance and hysteretic switching to a higher voltage range under these conditions. When microwave radiation is applied, three different types of resistive states are observed in the current-voltage characteristics. First, a phase diffusion branch steadily evolves and its maximum voltage Vm increases with the microwave power. Another interesting observed feature is a zero-crossing resistive state characterized by a negative resistance. Finally, we find that the low-voltage resistive state can split into numerous hysteretic fine branches resembling incoherent Shapiro-like steps. The appearance of a particular resistive state depends on the interrelations among the Josephson energy EJ, the energy kBT of thermal fluctuations, and the microwave frequency ω. A theoretical analysis based on incoherent multi-photon absorption by a junction biased in the Josephson phase diffusion regime is in good agreement with the experimental observations.

Quantum state engineering with flux-biased Josephson phase qubits by rapid adiabatic passages

In this article, the scheme of quantum computing based on the Stark-chirped rapid adiabatic passage (SCRAP) technique [L. F. Wei, J. R. Johansson, L. X. Cen, S. Ashhab, and F. Nori, Phys. Rev. Lett. 100, 113601 (2008)] is extensively applied to implement quantum state manipulations in flux-biased Josephson phase qubits. The broken-parity symmetries of bound states in flux-biased Josephson junctions are utilized to conveniently generate the desirable Stark shifts. Then, assisted by various transition pulses, universal quantum logic gates as well as arbitrary quantum state preparations can be implemented. Compared with the usual $\ensuremath{\pi}$-pulse operations widely used in experiments, the adiabatic population passages proposed here are insensitive to the details of the applied pulses and thus the desirable population transfers can be satisfyingly implemented. The experimental feasibility of the proposal is also discussed.

Spontaneous symmetry breaking and collapse in bosonic Josephson junctions

We investigate an attractive atomic Bose-Einstein condensate (BEC) trapped by a double-well potential in the axial direction and by a harmonic potential in the transverse directions. We obtain numerically, for the first time, a quantum phase diagram which includes all the three relevant phases of the system: Josephson, spontaneous symmetry breaking (SSB), and collapse. We consider also the coherent dynamics of the BEC and calculate the frequency of population-imbalance mode in the Josephson phase and in the SSB phase up to the collapse. We show that these phases can be observed by using ultracold vapors of 7Li atoms in a magneto-optical trap.

Detection of the Phase Shift from a Single Abrikosov Vortex

We probe a quantum mechanical phase rotation induced by a single Abrikosov vortex in a superconducting lead, using a Josephson junction, made at the edge of the lead, as a phase-sensitive detector. We observe that the vortex induces a Josephson phase shift equal to the polar angle of the vortex within the junction length. When the vortex is close to the junction it induces a π step in the Josephson phase difference, leading to a controllable and reversible switching of the junction into the 0-π state. This in turn results in an unusual Φ(0)/2 quantization of the flux in the junction. The vortex may hence act as a tunable "phase battery" for quantum electronics.

Quantum process tomography of a universal entangling gate implemented with Josephson phase qubits

Quantum gates must perform reliably when operating on standard input basis states and on complex superpositions thereof. Experiments using superconducting qubits have validated truth tables for particular implementations of, for example, the controlled-NOT gate1,2, but have not fully characterized gate operation for arbitrary superpositions of input states. Here we demonstrate the use of quantum process tomography3,4 (QPT) to fully characterize the performance of a universal entangling gate between two superconducting qubits. Process tomography permits complete gate analysis, but requires precise preparation of arbitrary input states, control over the subsequent qubit interaction and ideally simultaneous single-shot measurement of output states. In recent work, it has been proposed to use QPT to probe noise properties5 and time dynamics6 of qubit systems and to apply techniques from control theory to create scalable qubit benchmarking protocols7,8. We use QPT to measure the fidelity and noise properties5 of an entangling gate. In addition to demonstrating a promising fidelity, our entangling gate has an on-to-off ratio of 300, a level of adjustable coupling that will become a requirement for future high-fidelity devices. This is the first solid-state demonstration of QPT in a two-qubit system, as QPT has previously been demonstrated only with single solid-state qubits9,10,11.

Josephson phase qubit with an optimal point

Current fluctuations in a Josephson phase qubit are considered to be a source of decoherence, especially for pure dephasing. One possible way of evading such decoherence is to employ an optimal operation point as used in flux and charge qubits, where the qubit is insensitive to the bias fluctuations. However, there is no optimal point in a phase qubit since qubit energy splitting becomes monotonically smaller with increasing the bias current. Here we propose a phase qubit with an optimal point by introducing qubit energy splitting that depends nonmonotonically on the current bias realized in capacitively coupled Josephson junctions. The effect of junction asymmetry on the optimal point is also investigated.

Current fluctuations in rough superconducting tunnel junctions

Intrinsic noise is known to be ubiquitous in Josephson junctions. We investigate a voltage biased superconducting tunnel junction including a very small number of pinholes - transport channels possessing a transmission coefficient close to unity. Although few of these pinholes contribute very little to the conductance, they can dominate current fluctuations in the low-voltage regime. We show that even fully transparent transport channels between superconductors contribute to shot noise due to the uncertainty in the number of Andreev cycles. We discuss shot noise enhancement by Multiple Andreev Reflection in such a junction and investigate whether pinholes might contribute as a microscopic mechanism of two-level current fluctuators. We discuss the connection of these results to the junction resonators observed in Josephson phase qubits.

Scaling of the superfluid density in strongly underdopedYBa2Cu3O6+y: Evidence for a Josephson phase

Recent measurements on extremely underdoped ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{6+y}$ [Phys. Rev. Lett. 99, 237003 (2007)] have allowed the critical temperature ${T}_{c}$, superfluid density ${\ensuremath{\rho}}_{s0}\ensuremath{\equiv}{\ensuremath{\rho}}_{s}(T⪡{T}_{c})$, and dc conductivity ${\ensuremath{\sigma}}_{\text{dc}}(T\ensuremath{\gtrsim}{T}_{c})$ to be determined for a series of electronic dopings for ${T}_{c}\ensuremath{\simeq}3--17\text{ }\text{K}$. The general scaling relation ${\ensuremath{\rho}}_{s0}/8\ensuremath{\simeq}4.4{\ensuremath{\sigma}}_{\text{dc}}{T}_{c}$ is observed, extending the validity of both the $ab$-plane and $c$-axis scaling an order of magnitude and creating a region of overlap. This suggests that strongly underdoped materials may constitute a Josephson phase; as the electronic doping is increased a more uniform superconducting state emerges.

Autler-Townes Effect in a Superconducting Three-Level System

When a three-level quantum system is irradiated by an intense coupling field resonant with one of the three possible transitions, the absorption peak of an additional probe field involving the remaining level is split. This process is known in quantum optics as the Autler-Townes effect. We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an "artificial atom" with a multilevel quantum structure. The spectroscopy peaks can be explained reasonably well by a simple three-level Hamiltonian model. Simulation of a more complete model (including dissipation, higher levels, and cross coupling) provides excellent agreement with all of the experimental data.

Theory of fractional vortex escape in a long Josephson junction

We consider a fractional Josephson vortex in an infinitely long $0\text{\ensuremath{-}}\ensuremath{\kappa}$ Josephson junction. A uniform bias current applied to the junction exerts a Lorentz force acting on a vortex. When the bias current becomes equal to the critical (or depinning) current, the Lorentz force tears away an integer fluxon and the junction switches to the resistive state. In the presence of thermal and quantum fluctuations this escape process takes place with finite probability already at subcritical values of the bias current. We analyze the escape of a fractional vortex by mapping the Josephson phase dynamics to the dynamics of a single particle in a metastable potential and derive the effective parameters of this potential. This allows us to predict the behavior of the escape rate as a function of the topological charge of the vortex.