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Effect of Dissipation on the Dynamics of Superconducting Single Electron Transistors

Shuchao Meng

Published Aug 30, 2012• 0 citations
OpenAlex

Abstract

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.

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This thesis presents the results of an experimental study on single-charge effects in nanoscale Josephson junctions and Cooper pair transistors (CPTs). In nanoscale Josephson junctions the charging energy EC becomes significant at sub-Kelvin temperatures and single-charge effects, such as the Coulomb blockade of Cooper pair tunneling, influence the transport properties. In order to observe charging effects in a single Josephson junction, the impedance of the electromagnetic environment surrounding the junction has to be larger than the quantum resistance (RQ=h/4e2≈6.45kΩ). In this work the high impedance environment is obtained by biasing the sample under test (single Josephson junction or CPT) with four one-dimensional Josephson junction arrays having SQUID geometry. The advantage of this configuration is the possibility of tuning in situ the effective impedance of the electromagnetic environment. By applying a magnetic field perpendicular to the SQUID loops, the Josephson energy EJ of the SQUIDs is suppressed, resulting in an increase of the measured zero bias resistance of the arrays of several orders of magnitude (104< R0 (Ω) <109). This bias method enables the measurement of the same sample in environments with different impedance. As the impedance of the environment is increased, the current-voltage characteristics (IVCs) of the single Josephson junction and of the CPT show a well defined Coulomb blockade feature with a region of negative differential resistance, signature of the coherent tunneling of single Cooper pairs. The measured IVCs of a single Josephson junction with SQUID geometry in the high impedance environment show a qualitative agreement with the Bloch band theory as the EJ/EC ratio of the junction is tuned with the magnetic field. We also studied a single nontunable Josephson junction with strong coupling (EJ/EC > 1), where the exact dual of the overdamped Josephson effect is realized, resulting in a dual shape of the IVC, where the roles of current and voltage are exchanged. Here, we make for the first time a detailed quantitative comparison with a theory which includes the effect of fluctuations due to the finite temperature of the environment. The measurements on CPTs in the high impedance environment showed that the Coulomb blockade voltage is modulated periodically by the gate-induced charge. The gate-voltage dependence of the CPT changes from e-periodic to 2e-periodic as the impedance of the environment is increased. The high impedance environment reduces quasiparticle tunneling rates, thereby restoring the even parity of the CPT island. This behavior suggests that high impedance leads can be used to effectively suppress quasiparticle poisoning.

•Jan 1, 2006•5 citations
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 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 .
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.
We have studied the temperature dependence of escape phenomena in various underdamped Josephson junctions (JJs). The junctions had different Josephson coupling energies E J which were relatively small, but larger than the charging energy E C . Upon increasing the temperature T , we first observe the usual cross-over between macroscopic quantum tunnelling and thermally activated (TA) behaviour at temperatures k B T ∼ ℏω p , where ω p is the plasma frequency of the junction. Increasing T further, the width of the switching current distribution has, counterintuitively, a non-monotonic temperature dependence. This can be explained by the novel cross-over from TA behaviour to underdamped phase diffusion. We show that this cross-over is expected to occur at temperatures such that k B T ∼ E J (1 − 4/π Q ) 3 /2, where Q is the quality factor of the junction at the plasma frequency, in agreement with experiment. Our findings can be compared with detailed model calculations which take into account dissipation and level quantization in a metastable well. Particular attention is paid to the sample with the smallest E J , which shows extensive phase diffusion even at the lowest temperatures. This sample consists of a dc-SQUID and a single JJ close to each other, such that the SQUID acts as a tunable inductive protection for the single junction from fluctuations of a dissipative environment. By varying the flux through the dc-SQUID, we present, for the first time, experimental evidence of the escape of a JJ from the phase diffusion regime to the free running state in a tunable environment. We also show that in the zero voltage state the losses mainly occur at frequencies near the plasma resonance.
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 investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.
This thesis presents the results of an experimental study on single-charge effects in nanoscale Josephson junctions and Cooper pair transistors (CPTs). In nanoscale Josephson junctions the charging energy EC becomes significant at sub-Kelvin temperatures and single-charge effects, such as the Coulomb blockade of Cooper pair tunneling, influence the transport properties. In order to observe charging effects in a single Josephson junction, the impedance of the electromagnetic environment surrounding the junction has to be larger than the quantum resistance (RQ=h/4e2≈6.45kΩ). In this work the high impedance environment is obtained by biasing the sample under test (single Josephson junction or CPT) with four one-dimensional Josephson junction arrays having SQUID geometry. The advantage of this configuration is the possibility of tuning in situ the effective impedance of the electromagnetic environment. By applying a magnetic field perpendicular to the SQUID loops, the Josephson energy EJ of the SQUIDs is suppressed, resulting in an increase of the measured zero bias resistance of the arrays of several orders of magnitude (104< R0 (Ω) <109). This bias method enables the measurement of the same sample in environments with different impedance. As the impedance of the environment is increased, the current-voltage characteristics (IVCs) of the single Josephson junction and of the CPT show a well defined Coulomb blockade feature with a region of negative differential resistance, signature of the coherent tunneling of single Cooper pairs. The measured IVCs of a single Josephson junction with SQUID geometry in the high impedance environment show a qualitative agreement with the Bloch band theory as the EJ/EC ratio of the junction is tuned with the magnetic field. We also studied a single nontunable Josephson junction with strong coupling (EJ/EC > 1), where the exact dual of the overdamped Josephson effect is realized, resulting in a dual shape of the IVC, where the roles of current and voltage are exchanged. Here, we make for the first time a detailed quantitative comparison with a theory which includes the effect of fluctuations due to the finite temperature of the environment. The measurements on CPTs in the high impedance environment showed that the Coulomb blockade voltage is modulated periodically by the gate-induced charge. The gate-voltage dependence of the CPT changes from e-periodic to 2e-periodic as the impedance of the environment is increased. The high impedance environment reduces quasiparticle tunneling rates, thereby restoring the even parity of the CPT island. This behavior suggests that high impedance leads can be used to effectively suppress quasiparticle poisoning.