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arXiv:1712.07605 · Physical review. B./Physical review. B

Tunable ohmic environment using Josephson junction chains

Gianluca Rastelli, Ioan M. Pop

Published May 17, 2018• 15 citations
arXivHTMLPDF

Abstract

We propose a scheme to implement a tunable, wide frequency-band dissipative environment using a double chain of Josephson junctions. The two parallel chains consist of identical superconducting quantum interference devices (SQUIDs), with magnetic-flux tunable inductance, coupled to each other at each node via a capacitance much larger than the junction capacitance. Thanks to this capacitive coupling, the system sustains electromagnetic modes with a wide frequency dispersion. The internal quality factor of the modes is maintained as high as possible, and the damping is introduced by a uniform coupling of the modes to a transmission line, itself connected to an amplification and readout circuit. For sufficiently long chains, containing several thousands of junctions, the resulting admittance is a smooth function versus frequency in the microwave domain, and its effective dissipation can be continuously monitored by recording the emitted radiation in the transmission line. We show that by varying in situ the SQUIDs' inductance, the double chain can operate as a tunable ohmic resistor in a frequency band spanning up to 1 GHz, with a resistance that can be swept through values comparable to the resistance quantum ${R}_{q}=h/(4{e}^{2})\ensuremath{\simeq}6.5\phantom{\rule{4pt}{0ex}}\text{k}\mathrm{\ensuremath{\Omega}}$. We argue that the circuit complexity is within reach using current Josephson junction technology.

DOI
10.1103/physrevb.97.205429

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We propose a scheme to implement a tunable, wide frequency-band dissipative environment using a double chain of Josephson junctions. The two parallel chains consist of identical superconducting quantum interference devices (SQUIDs), with magnetic-flux tunable inductance, coupled to each other at each node via a capacitance much larger than the junction capacitance. Thanks to this capacitive coupling, the system sustains electromagnetic modes with a wide frequency dispersion. The internal quality factor of the modes is maintained as high as possible, and the damping is introduced by a uniform coupling of the modes to a transmission line, itself connected to an amplification and readout circuit. For sufficiently long chains, containing several thousands of junctions, the resulting admittance is a smooth function versus frequency in the microwave domain, and its effective dissipation can be continuously monitored by recording the emitted radiation in the transmission line. We show that by varying in situ the SQUIDs' inductance, the double chain can operate as a tunable ohmic resistor in a frequency band spanning up to 1 GHz, with a resistance that can be swept through values comparable to the resistance quantum Rq=h/(4e2)\ensuremath≃6.5k\ensuremathΩ{R}_{q}=h/(4{e}^{2})\ensuremath{\simeq}6.5\phantom{\rule{4pt}{0ex}}\text{k}\mathrm{\ensuremath{\Omega}}Rq​=h/(4e2)\ensuremath≃6.5k\ensuremathΩ. We argue that the circuit complexity is within reach using current Josephson junction technology.
We study the microwave properties of a superconducting tunable coplanar waveguide (CPW). Pairs of Josephson junctions are forming superconducting quantum interference devices (SQUIDs), which shunt the central conductor of the CPW. The Josephson inductance of the SQUIDs is varied in the range of 0.08–0.5 nH by applying a dc magnetic field. The central conductor of the CPW contains Josephson junctions connected in series that provide extra inductances; the magnetic field controlling the SQUIDs is weak enough not to influence the inductance of the chain of the single junctions. The circuit is designed to have left- and right-handed transmission properties separated by a variable rejection band; the band edges can be tuned by the magnetic field. We present transmission measurements on CPWs based on up to 120 Nb–AlO x –Nb Josephson junctions. At zero magnetic field, we observed no rejection band in the frequency range of 8–11 GHz. When applying the magnetic field, a rejection band between 7 GHz and 9 GHz appears. The experimental data are compared with numerical simulations.
We introduce a setup which realises a tunable engineered environment for experiments in circuit quantum electrodynamics. We illustrate this concept with the specific example of a quantum bit, qubit, in a high-quality-factor cavity which is capacitively coupled to another cavity including a resistor. The temperature of the resistor, which acts as the dissipative environment, can be controlled in a well defined manner in order to provide a hot or cold environment for the qubit, as desired. Furthermore, introducing superconducting quantum interference devices (SQUIDs) into the cavity containing the resistor, provides control of the coupling strength between this artificial environment and the qubit. We demonstrate that our scheme allows us to couple strongly to the environment enabling rapid initialization of the system, and by subsequent tuning of the magnetic flux of the SQUIDs we may greatly reduce the resistor-qubit coupling, allowing the qubit to evolve unhindered.
A Josephson junction subject to an ohmic dissipative environment undergoes a zero-temperature quantum phase transition called Schmid-Bulgadaev transition form an insulating state to a superconducting state upon increasing the impedance of the environment above the resistance quantum. Superconducting qubits based on Josephson junction chains represent a system where it is possible to dynamically explore both sides of this transition by probing the scattering of individual plasma modes of the junction chain on a SQUID at the boundary which was achieved in recent experiments. Here, we provide a theoretical analysis of the scattering in the system paying special attention to the non-perturbative superconducting regime. We find that in this regime, a specific diagrammatic resummation must be performed in order to correctly account for fluctuation renormalization of the SQUID's potential. We find analytic expressions for the modes' frequency shifts and quality factors which together provide a full description of scattering. We argue that the non-perturbative nature of the superconducting phase manifests itself through a power-law dependence of the frequency shifts on the SQUID flux and through non-monotonous dependence of the quality factors on the mode frequency. Our predictions may be readily verified in modern low-temperature experiments.
We have measured the current-voltage characteristics of a Josephson junction with tunable Josephson energy EJ{E}_{J}EJ​ embedded in an inductive environment provided by a chain of SQUIDs. Such an environment induces localization of the charge on the junction, which results in an enhancement of the zero-bias resistance of the circuit. We explain this result quantitatively in terms of the Bloch band dynamics of the localized charge. This dynamics is governed by charge diffusion in the lowest Bloch band of the Josephson junction as well as by Landau-Zener transitions out of the lowest band into the higher bands. In addition, the frequencies corresponding to the self-resonant modes of the SQUID array exceed the Josephson energy EJ{E}_{J}EJ​ of the tunable junction, which results in a renormalization of EJ{E}_{J}EJ​, and, as a consequence, an increase of the effective bandwidth of the lowest Bloch band.
Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance Cs{C}_{s}Cs​ and resistance Rs{R}_{s}Rs​ in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.
Gate-tunable Josephson junctions embedded in a microwave environment provide a promising platform to in situ engineer and optimize novel superconducting quantum circuits. The key quantity for the circuit design is the phase-dependent complex admittance of the junction, which can be probed by sensing a radio frequency SQUID with a tank circuit. Here, we investigate a graphene-based Josephson junction as a prototype gate-tunable element enclosed in a SQUID loop that is inductively coupled to a superconducting resonator operating at 3 GHz. With a concise circuit model that describes the dispersive and dissipative response of the coupled system, we extract the phase-dependent junction admittance corrected for self-screening of the SQUID loop. We decompose the admittance into the current-phase relation and the phase-dependent loss, and as these quantities are dictated by the spectrum and population dynamics of the supercurrent-carrying Andreev bound states, we gain insight to the underlying microscopic transport mechanisms in the junction. We theoretically reproduce the experimental results by considering a short, diffusive junction model that takes into account the interaction between the Andreev spectrum and the electromagnetic environment, from which we estimate lifetimes on the order of $\ensuremath{\sim}10$ ps for nonequilibrium populations.