Current-biased Josephson junctions are prime candidates for the realization of quantum bits; however, a present limitation is their coherence time. In this paper it is shown qualitatively that quasiparticles create decoherence. We can decrease the number of quasiparticles present in the junctions by two methods - reducing the creation rate with current shunts and increasing the depletion rate with normal-metal traps. Experimental data demonstrate that both methods are required to significantly reduce the number of quasiparticles and increase the system's coherence. We conclude that these methods are effective and that the design of Josephson-junction qubits must consider the role of quasiparticles.
Current-biased Josephson junctions are prime candidates for the realization of quantum bits; however, a present limitation is their coherence time. In this paper it is shown qualitatively that quasiparticles create decoherence. We can decrease the number of quasiparticles present in the junctions by two methods - reducing the creation rate with current shunts and increasing the depletion rate with normal-metal traps. Experimental data demonstrate that both methods are required to significantly reduce the number of quasiparticles and increase the system's coherence. We conclude that these methods are effective and that the design of Josephson-junction qubits must consider the role of quasiparticles.
We investigated decoherence of a Josephson vortex quantum bit (qubit) in dissipative and noisy environment. As the Josephson vortex qubit (JVQ) is fabricated by using a long Josephson junction (LJJ), we use the perturbed sine-Gordon equation to describe the phase dynamics representing a two-state system and estimate the effects of quasiparticle dissipation and weakly fluctuating critical and bias currents on the relaxation time T1 and on the dephasing time ${T}_{\ensuremath{\phi}}$. We show that the critical current fluctuation does not contribute to dephasing of the qubit in the lowest order approximation. Modeling the weak current variation from magnetic field fluctuations in the LJJ by using the Gaussian colored noise with long correlation time, we show that the coherence time T2 is limited by the low frequency current noise at very low temperatures. Also, we show that a ultra-long coherence time may be obtained from the JVQ by using experimentally accessible value of physical parameters.
I studied the Josephson junction system in the context of its usability for quan-tum computation. The zero-voltage state of a Josephson junction biased with constant current has a set of metastable quantum energy levels. In principle, it should be possible to use the two lowest states as a qubit for a quantum computer, provided both the dissipation time and coherence time of this qubit can be made long enough. I describe two methods for isolating a Josephson junction to increase its dissipation time. The rst is a resistive isolation scheme, for which I fabricated and measured a prototype system. I discuss the results of these measurements and show that the constraints of heating in conjunction with high-frequency design require-ments make it unlikely that this isolation method will lead to the coherence times required for quantum computation. I then discuss a resonant isolation method that I used to successfully increase the dissipation time of a Josephson junction qubit. I performed spectroscopic mea-surements at low temperatures to nd the coherence time of resonantly isolated 100 m2 Al/AlOx/Al and Nb/AlOx/Nb junctions with critical currents of roughly 10 A. The results of these measurements reveal two mechanisms beyond spontaneous emission for decoherence: low-frequency current noise and tunneling to the voltage state. To explain these results on decoherence, I present a model based on the Bloch equations. Going beyond a single qubit, I designed a capacitively coupled two-qubit system. Using spectroscopy, I showed that the energy level spacings between the ground state and the excited entangled states of the system agree with those calculated from the Schrodinger equation.
In superconducting qubits, the interaction of the qubit degree of freedom with quasiparticles defines a fundamental limitation for the qubit coherence. We develop a theory of the pure dephasing rate ${\ensuremath{\Gamma}}_{\ensuremath{\phi}}$ caused by quasiparticles tunneling through a Josephson junction and of the inhomogeneous broadening due to changes in the occupations of Andreev states in the junction. To estimate ${\ensuremath{\Gamma}}_{\ensuremath{\phi}}$, we derive a master equation for the qubit dynamics. The tunneling rate of free quasiparticles is enhanced by their large density of states at energies close to the superconducting gap. Nevertheless, we find that ${\ensuremath{\Gamma}}_{\ensuremath{\phi}}$ is small compared to the rates determined by extrinsic factors in most of the current qubit designs (phase and flux qubits, transmon, fluxonium). The split transmon, in which a single junction is replaced by a SQUID loop, represents an exception that could make possible the measurement of ${\ensuremath{\Gamma}}_{\ensuremath{\phi}}$. Fluctuations of the qubit frequency leading to inhomogeneous broadening may be caused by the fluctuations in the occupation numbers of the Andreev states associated with a phase-biased Josephson junction. This mechanism may be revealed in qubits with small-area junctions, since the smallest relative change in frequency it causes is of the order of the inverse number of transmission channels in the junction.
Bogoliubov quasiparticle excitations are detrimental for the operation of many superconducting devices. In superconducting qubits, quasiparticles interact with the qubit degree of freedom when tunneling through a Josephson junction, and this interaction can lead to qubit relaxation. At millikelvin temperatures, there is substantial evidence of nonequilibrium quasi- particles. While there is no agreed upon explanation for the origin of these excess quasiparticles, it is nevertheless possible to limit the quasiparticle-induced relaxation by steering quasiparticles away from qubit active elements. In this thesis, we study quasiparticle traps that are formed by a normal-metal in tunnel contact with the superconducting electrode of a qubit. We develop a model to explain how a trap can influence the dynamics of the excess quasiparticles injected in a transmontype qubit. This model makes it possible to find the time it takes to evacuate the injected quasiparticles from the transmon as a function of trap parameters. We show when the trap size is increased, the evacuation time decreases monotonically and saturates at a level that depends on the quasiparticles diffusion constant and the qubit geometry. We find the characteristic trap size needed for the evacuation time to approach the saturation value. It turns out that the bottleneck limiting the trapping rate is the slow quasiparticle energy relaxation inside the normal-metal trap, a quantity that is very hard to control. In order to optimize normal-metal quasiparticle trapping, we study the effects of trap size, number, and placement. These factors become important when the trap size increases beyond the characteristic length. We discuss for some experimentally relevant examples how to shorten the evacuation time of the excess quasiparticle density. Moreover, we show that a trap in the vicinity of a Josephson junction can significantly suppress the steady-state quasiparticle density near that junction and reduce the impact of fluctuations in the generation rate of quasiparticles. When such normal-metal elements are connected to a superconducting material, Cooper- pairs can leak into the normal-metal trap. This modifies the superconductor properties and, in turn, affects the qubit coherence. Using the Usadel formalism, we first revisit the proximity effect in uniform NS bilayers; despite the long history of this problem, we present novel findings for the density of states. We then extend our results to describe a non-uniform system in the vicinity of a trap edge. Using these results together with the previously developed model for the suppression of the quasiparticle density due to the trap, we find in a transmon qubit an optimum trap-junction distance at which the qubit relaxation rate is minimized. This optimum distance, of the order of 4 to 20 coherence lengths, originates from the competition between proximity effect and quasiparticle density suppression. We conclude that the harmful influence of the proximity effect can be avoided so long as the trap is farther away from the junction than this optimum.
The fluxonium qubit has arisen as one of the most promising candidate devices for implementing quantum information in superconducting devices, since it is both insensitive to charge noise (like flux qubits) and insensitive to flux noise (like charge qubits). Here, we investigate the stability of the quantum information to quasiparticle tunneling through a Josephson junction. Microscopically, this dephasing is due to the dependence of the quasiparticle transmission probability on the qubit state. We argue that on a phenomenological level the dephasing mechanism can be understood as originating from heat currents, which are flowing in the device due to possible effective temperature gradients, and their sensitivity to the qubit state. The emerging dephasing time is found to be insensitive to the number of junctions with which the superinductance of the fluxonium qubit is realized. Furthermore, we find that the dephasing time increases quadratically with the shunt-inductance of the circuit which highlights the stability of the device to this dephasing mechanism.
The zero-voltage state of a Josephson junction biased with constant current consists of a set of metastable quantum energy levels. We probe the spacings of these levels by using microwaves to induce transitions and thereby enhance the escape rate to the voltage state. The widths of the resonances give a measurement of the spectroscopic coherence time of the two metastable states involved in the transitions. We observe a decoherence time shorter than that expected from dissipation alone in resonantly isolated $20\ifmmode\times\else\texttimes\fi{}5\ensuremath{\mu}{\mathrm{m}}^{2}$ area Al/AlOx/Al junctions at 60 mK. The data are well fit by a model that includes the dephasing effects of both low-frequency current noise and the escape rate to the voltage state. We discuss implications for quantum computation using current-biased Josephson-junction qubits, including limits on the minimum number of levels needed in the well.