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Josephson transistors interacting with dissipative environment

Juha Leppäkangas

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

The quantum-mechanical effects typical for single atoms or molecules can be reproduced in micrometer-scale electric devices. In these systems the essential component is a small Josephson junction (JJ) consisting of two superconductors separated by a thin insulator. The quantum phenomena can be controlled in real time by external signals and have a great potential for novel applications. However, their fragility on uncontrolled disturbance caused by typical nearby environments is a drawback for quantum information science, but a virtue for detector technology. Motivated by this we have theoretically studied transistor kind of devices based on single-charge tunneling through small JJs. A common factor of the research is the analysis of the interplay between the coherent Cooperpair (charge carriers in the superconducting state) tunneling and incoherent environmental processes. In the first work we calculate the current due to incoherent Cooper-pair tunneling through a voltage-biased small JJ in series with large JJs and compare the results with recent experiments. We are able to reproduce the main experimental features and interpret these as traces of energy levels and energy bands of the mesoscopic device. In the second work we analyze a similar circuit (asymmetric single-Cooper-pair transistor) but under the assumption that the Cooper-pair tunneling is mainly coherent. This predicts new resonant transport voltages in the circuit due to higher-order processes. However, no clear traces of most of them are seen in the experiments, and similar discrepancy is present also in the case of the symmetric circuit. We continue to study this problem by modeling the interplay between the coherent and incoherent processes more accurately using a density-matrix approach. By this we are able to demonstrate that in typical conditions most of these resonances are indeed washed out by strong decoherence caused by the environment. We also analyze the contribution of three typical weakly interacting dissipative environments: electromagnetic environment, spurious charge fluctuators in the nearby insulating materials, and quasiparticles. In the last work we model the dynamics of a currentbiased JJ perturbed by a smaller JJ using a similar density-matrix approach. We demonstrate that the small JJ can be used also as a detector of the energy-band dynamics in a current biased JJ. The method is also used for modeling the charge transport in the Bloch-oscillating transistor.

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We have calculated the I — V characteristics of voltage biased asymmetric single‐Cooper‐pair transistors (SCPT), resulting from coherent Cooper pair tunneling across both the Josephson junctions (JJ), weak dissipation due the electromagnetic environment (EE) satisfying Re[Z(ω)] ≪ RQ, and quasiparticles. Due to the asymmetry, the smaller JJ is effectively probing the macroscopic quantum states of the island. A resonance occurs whenever the energy released in a tunneling of a single, or several, Cooper pair(s) across the smaller JJ matches to the energy needed to excite the island.

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Microwave Experiments and Noise in Mesoscopic Devices

Jayanta Sarkar

This thesis is a compilation of several works in the area of condensed matter physics, and with devices based on superconducting Josephson junctions (JJ) as the common denominator for the presented projects apart from the work on diffusive systems. Microwave measurements were conducted on a Superconducting Cooper pair transistor to explore its current-phase relationship. Measurements on a JJ-based qubit coupled to a LC resonator revealed the vibronic transitions obeying the Franck-Condon principle. The main body of the thesis is the work done on the Bloch Oscillating Transistor (BOT), an ultra low noise quantum amplifier. In the present work, we investigated the dynamics of the BOT near the bifurcation threshold as well as implemented differential BOTs to check its capability to reject common mode signals. To account for our studies of quantum features in mesoscopic systems other than JJs, we performed an experiment similar to the Hanbury-Brown and Twiss interferometry in optics. For this mesoscopic interference experiment we selected a multiterminal diffusive system. We developed a low temperature noise measurement scheme to study current-current correlations in the GHz frequency range. In our experiments we found a small positive HBT exchange correction factor in the non-interacting limit at low bias voltage in the presence of quantum interference. We found negative exchange correction factor in the hot electron case for similar structures, which agrees well with the theory. Altogether, our experiments demonstrated the theoretically predicted HBT exchange effects in non-interacting and interacting regime of electron transport in a diffusive mesoscopic system.

•Jan 1, 2015•1 citation
The quantum-mechanical effects typical for single atoms or molecules can be reproduced in micrometer-scale electric devices. In these systems the essential component is a small Josephson junction (JJ) consisting of two superconductors separated by a thin insulator. The quantum phenomena can be controlled in real time by external signals and have a great potential for novel applications. However, their fragility on uncontrolled disturbance caused by typical nearby environments is a drawback for quantum information science, but a virtue for detector technology. Motivated by this we have theoretically studied transistor kind of devices based on single-charge tunneling through small JJs. A common factor of the research is the analysis of the interplay between the coherent Cooperpair (charge carriers in the superconducting state) tunneling and incoherent environmental processes. In the first work we calculate the current due to incoherent Cooper-pair tunneling through a voltage-biased small JJ in series with large JJs and compare the results with recent experiments. We are able to reproduce the main experimental features and interpret these as traces of energy levels and energy bands of the mesoscopic device. In the second work we analyze a similar circuit (asymmetric single-Cooper-pair transistor) but under the assumption that the Cooper-pair tunneling is mainly coherent. This predicts new resonant transport voltages in the circuit due to higher-order processes. However, no clear traces of most of them are seen in the experiments, and similar discrepancy is present also in the case of the symmetric circuit. We continue to study this problem by modeling the interplay between the coherent and incoherent processes more accurately using a density-matrix approach. By this we are able to demonstrate that in typical conditions most of these resonances are indeed washed out by strong decoherence caused by the environment. We also analyze the contribution of three typical weakly interacting dissipative environments: electromagnetic environment, spurious charge fluctuators in the nearby insulating materials, and quasiparticles. In the last work we model the dynamics of a currentbiased JJ perturbed by a smaller JJ using a similar density-matrix approach. We demonstrate that the small JJ can be used also as a detector of the energy-band dynamics in a current biased JJ. The method is also used for modeling the charge transport in the Bloch-oscillating transistor.
We analyze how decoherence appears in the $I\text{\ensuremath{-}}V$ characteristics of a voltage-biased single-Cooper-pair transistor. Especially the effect on resonant single or several Cooper-pair tunneling is studied. We consider both a symmetric and an asymmetric transistor. As a decoherence source we use a small resistive impedance $(\text{Re}[Z(\ensuremath{\omega})]⪡{R}_{Q}=h/4{e}^{2})$ in series with the transistor, which provides both thermal and quantum fluctuations of the voltage. Additional decoherence sources are quasiparticle tunneling across the Josephson junctions and quantum fff noise caused by spurious charge fluctuators nearby the island. The analysis is based on a real-time diagrammatic technique which includes Zeno-type effects in the charge transport, where the tunneling is slowed down due to strong decoherence. As compared to the Pauli-master-equation treatment of the problem, the present results are more consistent with experiments where many of the predicted sharp resonant structures are missing or weakened due to decoherence.
We analyze tunneling of Cooper pairs across voltage biased asymmetric single-Cooper-pair transistors. Also tunneling of Cooper pairs across two capacitively coupled Cooper-pair boxes is considered, when the capacitive coupling and Cooper pair tunneling are provided by a small Josephson junction between the islands. The theoretical analysis is done at subgap voltages, where the current-voltage characteristics depend strongly on the macroscopic eigenstates of the island(s) and their coupling to the dissipative environment. As the environment we use an impedance which satisfies $\mathrm{Re}[Z(\ensuremath{\omega})]⪡{R}_{Q}$ and a few LCLCLC oscillators in series with $Z(\ensuremath{\omega})$. The numerically calculated $I\text{\ensuremath{-}}V$ curves are compared with experiments where the quantum states of mesoscopic SQUIDs are probed with inelastic Cooper pair tunneling. The main features of the observed $I\text{\ensuremath{-}}V$ data are reproduced. Especially, we find traces of band structure in the higher excited states of the Cooper-pair boxes as well as traces of multiphoton processes between two Cooper-pair boxes in the regime of large Josephson coupling EJ⪢EC{E}_{J}⪢{E}_{C}EJ​⪢EC​.
Properties of weak links between two superconductors, or Josephson junctions, make them interesting for fundamental physics research. Since their discovery over four decades ago, they have provided a unique way to study the behavior of the superconducting quantum phase. More recently, ultra small, or mesoscopic, Josephson junctions with substantial single Cooper pair charging energy have gained interest due to their behavior as macroscopic quantum objects. In addition to the theoretical interest, Josephson junctions can be used as active elements in circuit applications. Particularly, in this Thesis we study two different devices. We develop the required theoretical treatments, derive device properties, and compare the results with experimental data. The first application is a Josephson voltage standard based on externally damped Superconductor - Insulator - Superconductor junctions. It consists of an array of large Josephson junctions connected in series and irradiated with a 70 GHz microwave signal. Phase locking the Josephson dynamics into the signal leads to the quantization of the voltage. This is utilized in metrology. We introduce a new circuit solution based on frequency dependent damping of the junctions. Optimization and some designs for practical arrays are presented. The purpose is to find such a design that the array is fast, has low power consumption and is as stable as possible. Arrays able to generate DC voltages of order 1 volt with metrological accuracy are demonstrated experimentally and their applicability in AC voltage calibrations is analyzed. The second application is the Bloch Oscillating Transistor (BOT). The BOT is based on controlling the Cooper pair current in an ultra small Josephson junction by means of quasiparticles tunneling through a normal junction. As part of the thesis work, the principle of operation is first demonstrated computationally. The model is then refined to yield quantitative predictions of the characteristics. Finally, an analytic theory for the device is developed and the properties as an amplifier are derived.
We have calculated the I — V characteristics of voltage biased asymmetric single‐Cooper‐pair transistors (SCPT), resulting from coherent Cooper pair tunneling across both the Josephson junctions (JJ), weak dissipation due the electromagnetic environment (EE) satisfying Re[Z(ω)] ≪ RQ, and quasiparticles. Due to the asymmetry, the smaller JJ is effectively probing the macroscopic quantum states of the island. A resonance occurs whenever the energy released in a tunneling of a single, or several, Cooper pair(s) across the smaller JJ matches to the energy needed to excite the island.
We analyze how the dynamics in a current-biased mesoscopic Josephson junction can be probed by an additional smaller Josephson junction (probe). The probe is connected to a small island in between the Josephson junction and a resistor R >> R Q = h /4e 2 . The current through the resistor results in an effective current bias to the larger JJ. We model the steady state properties of the system under thermal and quantum fluctuations of the feed current. We use a density matrix approach based on the Born-Markov equations treating the current fluctuations perturbatively. The probe is also treated perturbatively assuming the regime of incoherent Cooper-pair tunneling. We find that the I - V characteristics across the probe shows traces of energy bands, Bloch oscillations and Zener tunneling in the current-biased Josephson junction.
This thesis is a compilation of several works in the area of condensed matter physics, and with devices based on superconducting Josephson junctions (JJ) as the common denominator for the presented projects apart from the work on diffusive systems. Microwave measurements were conducted on a Superconducting Cooper pair transistor to explore its current-phase relationship. Measurements on a JJ-based qubit coupled to a LC resonator revealed the vibronic transitions obeying the Franck-Condon principle. The main body of the thesis is the work done on the Bloch Oscillating Transistor (BOT), an ultra low noise quantum amplifier. In the present work, we investigated the dynamics of the BOT near the bifurcation threshold as well as implemented differential BOTs to check its capability to reject common mode signals. To account for our studies of quantum features in mesoscopic systems other than JJs, we performed an experiment similar to the Hanbury-Brown and Twiss interferometry in optics. For this mesoscopic interference experiment we selected a multiterminal diffusive system. We developed a low temperature noise measurement scheme to study current-current correlations in the GHz frequency range. In our experiments we found a small positive HBT exchange correction factor in the non-interacting limit at low bias voltage in the presence of quantum interference. We found negative exchange correction factor in the hot electron case for similar structures, which agrees well with the theory. Altogether, our experiments demonstrated the theoretically predicted HBT exchange effects in non-interacting and interacting regime of electron transport in a diffusive mesoscopic system.