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arXiv:cond-mat/0701144 · Physical Review B

Quasiparticle transitions in charge-phase qubits probed by rf oscillations

Jens Könemann, H. Zangerle, Brigitte Mackrodt, R. Dolata, Alexander B Zorin

Published Oct 10, 2007• 6 citations
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Abstract

We investigated transitions in an Al charge-phase qubit of superconducting quantum interference device configuration which was inductively coupled to an rf tank circuit that made it possible to read out the state by measuring the Josephson inductance of the qubit. Depending on the flux and charge bias and on the amplitude of the rf oscillations, we probed either the ground state or a dynamic change of the qubit states which we attributed to stochastic single quasiparticle tunneling onto and off the qubit island, involving an exchange of energy with the qubit. Within the scope of this model, a selection rule for quasiparticle-induced transitions in the qubit is discussed.

DOI
10.1103/physrevb.76.134507

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We investigated transitions in an Al charge-phase qubit of superconducting quantum interference device configuration which was inductively coupled to an rf tank circuit that made it possible to read out the state by measuring the Josephson inductance of the qubit. Depending on the flux and charge bias and on the amplitude of the rf oscillations, we probed either the ground state or a dynamic change of the qubit states which we attributed to stochastic single quasiparticle tunneling onto and off the qubit island, involving an exchange of energy with the qubit. Within the scope of this model, a selection rule for quasiparticle-induced transitions in the qubit is discussed.
We present investigations of Josephson charge-phase qubits of superconducting quantum interference device (SQUID) configuration, inductively coupled to a radio-frequency-driven tank circuit, enabling the readout of the states by measuring the Josephson inductance of the qubit. The circuits, including junctions with linear dimensions of $60\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\ifmmode\times\else\texttimes\fi{}60\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and $80\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\ifmmode\times\else\texttimes\fi{}80\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, are fabricated from Nb∕AlOx∕Nb\mathrm{Nb}∕\mathrm{Al}{\mathrm{O}}_{x}∕\mathrm{Nb}Nb∕AlOx​∕Nb trilayer and allow the determination of relevant sample parameters at liquid helium temperature. The observed partial suppression of the circulating supercurrent in the qubit loop at 4.2K4.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}4.2K is explained within the framework of a quantum-statistical model. We have probed the ground-state properties of qubit structures with different ratios of the Josephson coupling to Coulomb charging energy at 20mK20\phantom{\rule{0.3em}{0ex}}\mathrm{mK}20mK, demonstrating both the magnetic control of phase and the electrostatic control of charge of the qubit.
We have analyzed quasiparticle transitions in an Al charge-phase qubit inducing a dynamic change of the qubit states. The time-averaged mixed state is related to the strong coupling of the qubit to an ensemble of non-equilibrium quasiparticles in the leads. Such quasiparticles tunnel stochastically on and off the island and can excite the qubit. Continuous monitoring of the qubit impedance at a frequency of 80 MHz shows the admixture of the excited state. We present a numerical description of these cyclic transitions and compare it with our experimental data.
We implemented experimentally an interferometer-type charge qubit consisting of a single-Cooper-pair transistor closed by a superconducting loop that is in flip-chip configuration inductively coupled to a radio-frequency tank circuit. The tank permits us to readout the qubit state, acting as an inductance measuring apparatus. By applying continuous microwave power to the quantum device, we observed inductance alterations caused by redistributions of the energy-level populations. From the measured data we extracted the energy gap between ground and upper levels as a function of the transistor quasicharge as well as the Josephson phase across both junctions.
We investigate quasiparticle tunneling in a Cooper-pair box which is embedded in a superconducting ring to allow control of the total phase difference across the island. The phase affects the transition rate between different electron number parity states of the island, which can be observed in experiment by established means. The phase dependence also leads to what is known as the $\mathrm{cos}\ensuremath{\phi}$ term in the tunneling characteristics of classical Josephson junctions. This effect has remained controversial for decades; the proposed scheme opens an independent way to probe it.
Abstract The non-dissipative nonlinearity of Josephson junctions1 converts macroscopic superconducting circuits into artificial atoms2, enabling some of the best-controlled qubits today3, 4. Three fundamental types of superconducting qubit are known5, each reflecting a distinct behaviour of quantum fluctuations in a Cooper pair condensate: single-charge tunnelling (charge qubit6, 7), single-flux tunnelling (flux qubit8) and phase oscillations (phase qubit9 or transmon10). Yet, the dual nature of charge and flux suggests that circuit atoms must come in pairs. Here we introduce the missing superconducting qubit, ‘blochnium’, which exploits a coherent insulating response of a single Josephson junction that emerges from the extension of phase fluctuations beyond 2π (refs. 11–14). Evidence for such an effect has been found in out-of-equilibrium direct-current transport through junctions connected to high-impedance leads15–19, although a full consensus on the existence of extended phase fluctuations is so far absent20–22. We shunt a weak junction with an extremely high inductance—the key technological innovation in our experiment—and measure the radiofrequency excitation spectrum as a function of external magnetic flux through the resulting loop. The insulating character of the junction is manifested by the vanishing flux sensitivity of the qubit transition between the ground state and the first excited state, which recovers rapidly for transitions to higher-energy states. The spectrum agrees with a duality mapping of blochnium onto a transmon, which replaces the external flux by the offset charge and introduces a new collective quasicharge variable instead of the superconducting phase23, 24. Our findings may motivate the exploration of macroscopic quantum dynamics in ultrahigh-impedance circuits, with potential applications in quantum computing and metrology.
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.