Superconducting Single-electron Transistor Research Articles

Bipolar thermoelectric superconducting single-electron transistor

Bipolar thermoelectric superconducting single-electron transistor

Single charge transport in a fully superconducting SQUISET locally tuned by self-inductance effects

We present a single-electron device for the manipulation of charge states via quantum interference in nanostructured electrodes. Via self-inductance effects, we induce two independent magnetic fluxes in the electrodes and we demonstrate sensitivity to single charge states and magnetic field at variable temperature. Moreover, our approach allows us to demonstrate local and independent control of the single-particle conductance between nano-engineered tunnel junctions in a fully superconducting quantum interference single-electron transistor, thereby increasing the flexibility of our single-electron transistors. Our devices show a robust modulation of the current-to-flux transfer function via control currents while exploiting the single-electron filling of a mesoscopic superconducting island. Further applications of the device concept to single charge manipulation and magnetic-flux sensing are also discussed.

Phase-dependent transport in thermally driven superconducting single-electron transistors

We investigate thermally driven transport of heat and charge in a superconducting single-electron transistor by means of a real-time diagrammatic transport theory. Our theoretical approach allows us to account for strong Coulomb interactions and arbitrary nonequilibrium conditions while performing a systematic expansion in the tunnel coupling. We find that a temperature bias across the system gives rise to finite heat and charge currents close to the particle-hole symmetric point which depend both on the gate voltage as well as on the phase difference between the superconducting reservoirs. The finite thermoelectric effect arises due to level renormalization from virtual tunneling processes. Furthermore, we find that the phase bias can give rise to finite charge currents even in the presence of an inversion-symmetric temperature bias.

Ab Initio Study of the Electron–Phonon Coupling in Ultrathin Al Layers

The impact of film thickness to the electron–phonon coupling and the critical temperature of the superconducting transition, as well as to the structural, phonon and electronic properties of Al films in the ultrathin regime, was studied by means of ab initio calculations. The presence of the inevitable quantum fluctuations in the regime of 5 to 9 atomic layers was found not to be detrimental for the transition critical temperature, as quantum confinement was found to have a monotonically positive impact. As calculations were performed on perfect crystalline films, results of this work give further indirect evidence of the impact of the experimentally observed defects on the superconducting transition. The reduction of the dimensions of materials in the critically low regime of quantum effects can unlock new prospects for high Tc superconducting devices, such as cryogenic light detectors and superconducting single-electron transistors; hence, the understanding of the underlying mechanisms is required for the deterministic tailoring of their properties.

DC measurement of dressed states in a coupled 100 GHz resonator system using a single quasiparticle transistor as a sensitive microwave detector

We report on the on-chip detection of microwaves in the frequency range around 100 GHz. For the purpose of detection, we employ a discrete transport channel triggered in a superconducting single-electron transistor by photon-assisted tunneling of quasiparticles. The technique is applied to observe the spectrum of the dressed states of a model circuit quantum electrodynamics system consisting of a superconducting coplanar resonator coupled to a Josephson oscillator. The dressed states appear as typical resonance anticrossing exhibiting, in our case, an expectedly wide frequency splitting corresponding to the Jaynes–Cummings coupling strength, g/π∼ 10 GHz. Due to the high decay rate, γ∼ 20–40 GHz, in the very transparent Josephson junctions used, the strong coupling limit, g≫γ, which is required for qubit operation, is not achieved, and the photon population in the resonator is low, ⟨n⟩< 1. Remarkably, the continuous readout of the low population states demonstrates the high microwave sensitivity of the detector.

Reversible thermal diode and energy harvester with a superconducting quantum interference single-electron transistor

The density of states of proximitized normal nanowires interrupting superconducting rings can be tuned by the magnetic flux piercing the loop. Using these as the contacts of a single-electron transistor allows us to control the energetic mirror asymmetry of the conductor, thus introducing rectification properties. In particular, we show that the system works as a diode that rectifies both charge and heat currents and whose polarity can be reversed by the magnetic field and a gate voltage. We emphasize the role of dissipation at the island. The coupling to substrate phonons enhances the effect and furthermore introduces a channel for phase tunable conversion of heat exchanged with the environment into electrical current.

Temperature Effects on Singularity Matching and Parity in a Superconducting Single-Electron Transistor

In this paper, we present results demonstrating the effect of temperature on singularity matching (SM) tunneling down to 300 mK in superconducting single-electron transistors (SSETs). The studied SSETs have charging energies significantly larger than the Josephson energy, which makes it possible to study the SM condition without other sub-superconducting gap conduction mechanisms obscuring the SM signatures at low biases. The presence of parity in one such device has also allowed us to explore the effect of temperature on the effect of parity on SM features.

Correlation-induced refrigeration with superconducting single-electron transistors

A model of a superconducting tunnel junction which refrigerates a nearby metallic island without any particle exchange is presented. Heat extraction is mediated by charge fluctuations in the coupling capacitance of the two systems. The interplay of the Coulomb interaction and the superconducting gap reduces the power consumption of the refrigerator. The island is predicted to be cooled from lattice temperatures of 200 mK down to close to 50 mK for realistic parameters. The results emphasize the role of non-equilibrium correlations in bipartite mesoscopic conductors. This mechanism can be applied to create local temperature gradients in tunnel junction arrays or explore the role of interactions in the thermalization of non-equilibrium systems.

Characterization of superconducting single-electron transistors with small Al/AlO/V Josephson junctions

Superconducting single-electron transistors (SSETs) composed of small Al/AlO/V junctions were fabricated, and their transport properties were investigated. The device with an Al island exhibited a supercurrent that was 2e-periodic in the gate charge while that with a V island showed a periodicity of e, where e is an elementary charge. The Josephson-quasiparticle (JQP)-cycle current appeared at the bias voltage V in the range , where is the superconducting gap of Al and is the charging energy of an elementary charge. This is different from the commonly accepted range for the JQP current such as that in the case of an all Al SSET. There also appeared a large leakage current at , where is the superconducting gap of V. All these properties are accounted for by considering the finite subgap quasiparticle density of states in the V electrode.

Stochastic Bloch-Redfield theory: Quantum jumps in a solid-state environment

We discuss mapping the Bloch-Redfield master-equation to Lindblad form and then unravelling the resulting evolution into a stochastic Schr\"odinger equation according to the quantum-jump method. We give two approximations under which this mapping is valid. This approach enables us to study solid-state-systems of much larger sizes than is possible with the standard Bloch-Redfield master-equation, while still providing a systematic method for obtaining the jump operators and corresponding rates. We also show how the stochastic unravelling of the Bloch-Redfield equations becomes the kinetic Monte Carlo (KMC) algorithm in the secular approximation when the system-bath-coupling operators are given by tunnelling-operators between system-eigenstates. The stochastic unravelling is compared to the conventional Bloch-Redfield approach with the superconducting single electron transistor (SSET) as an example.

Charge sensing in a Si/SiGe quantum dot with a radio frequency superconducting single-electron transistor

We report the operation of a radio frequency superconducting single-electron transistor (rf-SSET) as a charge sensor for single and double Si/SiGe quantum dots (QDs). Real-time electron tunneling events are observed from the reflected signal of the rf-SSET with a charge sensitivity of 4×10−6 e/Hz, which demonstrates a fast charge detection time of a few tens of microseconds. Measurements of the reflected power are used to map out the stability diagram of the double quantum dot.

Quantum current noise from a Born-Markov master equation

Quantum coherent oscillations in the electric charge passing through a mesoscopic conductor can give rise to a current noise spectrum which is strongly asymmetric in frequency. The asymmetry reveals the fundamental difference between quantum and classical fluctuations in the current. We show how the quantum current noise can be obtained starting from a Born-Markov master equation, an approach which is applicable to a wide class of systems. Our method enables us to analyze the rich behavior of the current noise associated with the double Josephson quasiparticle resonance in a superconducting single-electron transistor (SSET). The asymmetric part of the noise is found to be strongly dependent on the choice of operating point for the SSET and can be either positive or negative. Our results are in good agreement with recent measurements.

Leggett-Garg inequalities for the statistics of electron transport

We derive a set of Leggett-Garg inequalities (temporal Bell's inequalities) for the moment generating function of charge transferred through a conductor. Violation of these inequalities demonstrates the absence of a macroscopic-real description of the transport process. We show how these inequalities can be violated by quantum-mechanical systems and consider transport through normal and superconducting single-electron transistors as examples.

Phase transitions in trajectories of a superconducting single-electron transistor coupled to a resonator

Recent progress in the study of dynamical phase transitions has been made with a large-deviation approach to study trajectories of stochastic jumps using a thermodynamic formalism. We study this method applied to an open quantum system consisting of a superconducting single-electron transistor, near the Josephson quasiparticle resonance, coupled to a resonator. We find that the dynamical behavior shown in rare trajectories can be rich even when the mean dynamical activity is small, and thus the formalism gives insights into the form of fluctuations. The structure of the dynamical phase diagram found from the quantum-jump trajectories of the resonator is studied, and we see that sharp transitions in the dynamical activity may be related to the appearance and disappearance of bistabilities in the state of the resonator as system parameters are changed. We also demonstrate that for a fast resonator, the trajectories of quasiparticles are similar to the resonator trajectories.

Lasing, trapping states, and multistability in a circuit quantum electrodynamical analog of a single-atom injection maser

We study a superconducting single-electron transistor (SSET) which is coupled to a LC-oscillator via the phase difference across one of the Josephson junctions. This leads to a strongly anharmonic coupling between the SSET and the oscillator. The coupling can oscillate with the number of photons which makes this system very similar to the single-atom injection maser. However, the advantage of a design based on superconducting circuits is the strong coupling and existence of standard methods to measure the radiation field in the oscillator. This makes it possible to study many effects that have been predicted for the single-atom injection maser in a circuit quantum electrodynamics setup.

Si/SiGe quantum dot with superconducting single-electron transistor charge sensor

We report a robust process for fabrication of surface-gated Si/SiGe quantum dots (QDs) with an integrated superconducting single-electron transistor (SSET) charge sensor. A combination of a deep mesa etch and AlOx backfill is used to reduce gate leakage. After the leakage current is suppressed, Coulomb oscillations of the QD and the current-voltage characteristics of the SSET are observed at a temperature of 0.3 K. Coupling of the SSET to the QD is confirmed by using the SSET to perform sensing of the QD charge state.

Charge noise at Cooper-pair resonances

We analyze the charge dynamics of a superconducting single-electron transistor (SSET) in the regime where charge transport occurs via Cooper-pair resonances. Using an approximate description of the system Hamiltonian, in terms of a series of resonant doublets, we derive a Born-Markov master equation describing the dynamics of the SSET. The average current displays sharp peaks at the Cooper-pair resonances and we find that the charge noise spectrum has a characteristic structure which consists of a series of asymmetric triplets of peaks. The strongest feature in the charge noise spectrum is the triplet of peaks centered at zero frequency which has a peak spacing equal to the level separation within the doublets and is similar to the triplet in the spectrum of a driven, damped, two-level system. We also explore the back-action that the SSET charge noise would have on an oscillator coupled to the island charge, measurement of which provides a way of probing the charge noise spectrum.

Sensing individual terahertz photons

One of the promising ways to perform single-photon counting of terahertz radiationconsists in sensitive probing of plasma excitation in the electron gas upon photonabsorption. We demonstrate the ultimate sensor operating on this principle. It isassembled from a GaAs/AlGaAs quantum dot, electron reservoir and superconductingsingle-electron transistor. The quantum dot is isolated from the surrounding electronreservoir in such a way that when the excited plasma wave decays, an electroncould tunnel off the dot to the reservoir. The resulting charge polarization ofthe dot is detected with the single-electron transistor. Such a system forms aneasy-to-use sensor enabling single-photon counting in a very obscure wavelength region.

Spectral properties of a resonator driven by a superconducting single-electron transistor

We analyze the spectral properties of a resonator coupled to a superconducting single electron transistor (SSET) close to the Josephson quasiparticle resonance. Focussing on the regime where the resonator is driven into a limit-cycle state by the SSET, we investigate the behavior of the resonator linewidth and the energy relaxation rate which control the widths of the main features in the resonator spectra. We find that the linewidth becomes very narrow in the limit-cycle regime, where it is dominated by a slow phase diffusion process, as in a laser. The overall phase diffusion rate is determined by a combination of direct phase diffusion and the effect of amplitude fluctuations which affect the phase because the resonator frequency is amplitude dependent. For sufficiently strong couplings we find that a regime emerges where the phase diffusion is no longer minimized when the average resonator energy is maximized. Finally we show that the current noise of the SSET provides a way of measuring both the linewidth and energy relaxation rate.

Quantum Dynamics of a Resonator Coupled to a SET

We study the quantum dynamics of a resonator driven by a superconducting single-electron transistor. We prove the existence of the Minimal Quantum Dynamical Semigroup \({\mathcal {T}^{\,({\rm min})}}\) solving the evolution equation for the density matrix, then we prove that \({\mathcal {T}^{\,({\rm min})}}\) is Markov. Moreover we prove the existence and uniqueness of a faithful normal stationary state and show that the dynamics converges towards this stationary state when time goes to infinity.