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Journal of Physics Conference Series

Spectroscopy of charge states of a superconducting single-electron transistor in an engineered electromagnetic environment

Eisuke Abe, Yuki Kimura, Y. Hashimoto, Y. Iye, Shingo Katsumoto

Published Mar 1, 2009• 0 citations
Publisher

Abstract

We study charge states of a superconducting single-electron transistor (SSET) fabricated on a heterostructure substrate that can be switched from insulating to conductive. We probe the charge states by microwave irradiation and subsequent observation of photon-assisted Josephson quasiparticle current, which allow us to obtain the energy dispersion relation in the quasicharge space. When the substrate is insulating, the charge states show an energy-dispersion curve with a gap, manifesting that coherent superposition of the two charge states is realized. When the substrate becomes conductive, its two-dimensional electrons capacitively couple to the SSET and modify the degree of dissipation to its electromagnetic environment. The dispersion relation then becomes linear, and its slope agrees with the value estimated from the charging energy including the capacitance of the two-dimensional electrons. This indicates that quantum coherence between the two charge states is lost due to the coupling with the environment.

DOI
10.1088/1742-6596/150/5/052001

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We study charge states of a superconducting single-electron transistor (SSET) fabricated on a heterostructure substrate that can be switched from insulating to conductive. We probe the charge states by microwave irradiation and subsequent observation of photon-assisted Josephson quasiparticle current, which allow us to obtain the energy dispersion relation in the quasicharge space. When the substrate is insulating, the charge states show an energy-dispersion curve with a gap, manifesting that coherent superposition of the two charge states is realized. When the substrate becomes conductive, its two-dimensional electrons capacitively couple to the SSET and modify the degree of dissipation to its electromagnetic environment. The dispersion relation then becomes linear, and its slope agrees with the value estimated from the charging energy including the capacitance of the two-dimensional electrons. This indicates that quantum coherence between the two charge states is lost due to the coupling with the environment.
We experimentally investigated the switching current I sw of a superconducting single electron transistor (sSET), with competitive Josephson coupling energy E J and charging energy E c , in an in situ tunable dissipative environment. At low temperature, averaged I sw shows a clear 1e periodic function of gate induced charge on the island. The relative contrast of this oscillation increases when E J /Ec is lowered. Increasing dissipation reduce the quantum fluctuations of the phase across the sSET, leading to an increased I sw .
In this thesis, I will present the experimental results of the dynamics of \nsuperconducting single electron transistors (sSETs), under the influence of \ntunable dissipation. The sSET, consisting of two dc SQUIDs in series and \nthe third gate electrode, is deposited onto a GaAs/AlGaAs heterostructure \nwhich contains a two dimensional electron gas plane 100nm beneath the \nsubstrate surface. The Josephson coupling energy, charging energy and \ndissipation related Hamiltonian can all be tuned in situ, while keeping \nothers unchanged. We measured the switching current statistics and the \ntransport properties, as a function of the dissipation and gate charge at \ndifferent temperatures. \n \nIf the sSET is in the classical regime where phase is a good quantum \nvariable, we found that the switching current and corresponding Josephson \nenergy decrease as dissipation increases. Our observation agrees qualitatively \nwith the theoretical calculation of a single Josephson junction \nwith dominant Josephson energy, in a frequency dependent dissipative \nenvironment where energy barrier decreases as dissipation increases in \nthermally activated escape regime. This dissipation dependence result can \nbe understood as the consequence of a reduced quantum fluctuations in \nthe charge numbers. \n \nWhereas in the charging regime, the switching current shows a 1e \nperiodicity with respect to gate charge, indicating a pronounced charging \neffect. At a specific gate charge number, quantum fluctuations of the phase \nvariable are compressed as dissipation increases, resulting in an enhanced \nswitching current and Josephson energy. This result matches the theory of a sSET capacitively coupled to a dissipative environment qualitatively. \nThe temperature dependence of the switching current histogram indicates \nthe existence of both quantum and classical thermal phase diffusion. \nMoreover, quantum charge fluctuations are minimized at the degeneracy \npoint, causing a sharp dip on the width of the switching current histogram. \n \nFor a sSET with comparable Josephson energy and charging energy, \nquantum fluctuations of both phase and charge variables are significant. \nThe influence of dissipation on the dynamics of the device is distinct in the \nclassical and charging regimes. Dissipation compresses quantum phase \nfluctuations in the charging regime, whereas reduces the quantum charge \nfluctuations in the classical regime. The transition between these two \nregimes is found to be determined by the tunnel resistance of the SQUID. \nThe competition between Josephson and charging energies, however, is \nnot the intrinsic parameter of this transition. Our results imply that a \ndetailed theoretical calculation of a sSET with comparable Josephson \ncoupling energy and charging energy under the influence of dissipation is \nneeded.
We have investigated charge transport processes in a superconducting single-electron transistor (S-SET) fabricated in close proximity to a two-dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure. The macroscopic bonding pads of the S-SET along with the 2DEG form a microstrip transmission line. We observe a variety of current-carrying cycles in the S-SET which we attribute to simultaneous tunneling of Cooper pairs and emission of photons into the microstrip. We find good agreement between these experimental results and simulations including both photon emission and photon-assisted tunneling due to the electromagnetic environment.
We have developed a novel system consisting of a superconducting single-electron transistor (S-SET) coupled to a two-dimensional electron gas (2DEG), for which the dissipation can be tuned in the immediate vicinity of the S-SET. To analyze our results, we have developed a model of the environment for S-SET/2DEG systems that includes electromagnetic fluctuations coupled both through the S-SET leads and capacitively to the S-SET central island. We analyze this model, treating the leads as finite transmission lines, to find the probability function P(E) for exchanging energy E with the environment. We also allow for the possibility of low-frequency fluctuations of the S-SET offset charge. We compare our calculations with measurements of SET conductance versus 2DEG conductance and find good agreement for temperatures 100 mK, while unexplained discrepancies emerge for lower temperatures. By including the effects of charge averaging we are also able to predict the shape and evolution of IV curves as the 2DEG in the vicinity of the S-SET is changed.
The Josephson quasiparticle (JQP) cycle in a voltage-biased superconducting single-electron transistor (SSET) combines coherent Cooper pair tunneling with incoherent quasiparticle decay. We have measured the influence of current flow through an independently-biased SSET on the JQP cycle when the two SSET's have a strong mutual capacitive coupling. We find, among other effects, that the JQP current in one SSET is enhanced by the presence of a quasiparticle current in the other SSET. A simplified model of the coupled-SSET system is presented which reproduces the enhancement effect.