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Journal of Physics Conference Series

Measuring the switching current of a superconducting single electron transistor in a tunable dissipative environment

S Meng, L. R. Yaraskavitch, Andy S. Sachrajda, Jan B. Kycia

Published Dec 17, 2012• 0 citations
Publisher

Abstract

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 .

DOI
10.1088/1742-6596/400/4/042046

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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 investigate the switching current of a Cooper pair transistor with tunable Josephson energy. The junctions are fabricated in a superconducting quantum interference device (SQUID) geometry which allows for an in situ tunable effective Josephson energy by application of a magnetic field. We find a 2e2e2e-periodic switching current versus gate charge. As the magnetic field is increased the switching current stays 2e2e2e-periodic but the magnitude is suppressed. At a magnetic field of half a flux quantum through the SQUID's the switching current is minimum. We can theoretically model the experimental data by assuming a switching current which is proportional to the ideal critical current squarred. We show that such a dependence is expected in the limit where the effect of thermal fluctuations on the system is strong.
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 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. Within linear response, the S-SET conductance varies nonmonotonically with increasing 2DEG impedance. We find good agreement between our experimental results and a model incorporating electromagnetic fluctuations in both the S-SET leads and the 2DEG, as well as low-frequency switching of the S-SET offset charge.
We analyze the current and zero-frequency current noise properties of a superconducting single-electron transistor (SSET) coupled to a resonator, focusing on the regime where the SSET is operated in the vicinity of the Josephson quasiparticle resonance. We consider a range of coupling strengths and resonator frequencies to reflect the fact that in practice the system can be tuned to quite a high degree with the resonator formed either by a nanomechanical oscillator or a superconducting stripline fabricated in close proximity to the SSET. For very weak couplings the SSET acts on the resonator like an effective thermal bath. In this regime the current characteristics of the SSET are only weakly modified by the resonator. Using a mean-field approach, we show that the current noise is nevertheless very sensitive to the correlations between the resonator and the SSET charge. For stronger couplings, the SSET can drive the resonator into limit-cycle states where self-sustained oscillation occurs and we find that regions of well-defined bistability exist. Dynamical transitions into and out of the limit-cycle state are marked by strong fluctuations in the resonator energy, but these fluctuations are suppressed within the limit-cycle state. We find that the current noise of the SSET is strongly influenced by the fluctuations in the resonator energy and hence should provide a useful indicator of the resonator's dynamics.
We measure the effect of dissipation on the minimum zero-bias conductance, G(min)0, of a superconducting single electron transistor (sSET) capacitively coupled to a two-dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure. Depleting the 2DEG with a back gate voltage decreases the dissipation experienced by the sSET in situ. We find that G(min)0 increases as the dissipation is increased or the temperature is reduced; the functional forms of these dependences are compared with the model of Wilhelm et al. in which the leads coupled to the sSET are represented by lossy transmission lines.