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Single charge transistor based on superconducting nanowire in high impedance environment

T. T. Hongisto, Alexander B Zorin

Published Sep 16, 2011• 1 citation
OpenAlex

Abstract

We propose a transistor-like circuit including two serially connected segments of narrow superconducting nanowire joint by a wider segment with capacitively coupled gate in between. This circuit is made of amorphous NbSi film and embedded in a network of on-chip Cr microresistors ensuring sufficiently high external electromagnetic impedance. Assuming virtual regime of quantum phase slips (QPS) in two narrow segments of the wire, leading to correlated single Cooper pair tunneling, this circuit is dual to the dc SQUID. Our samples demonstrated appreciable Coulomb blockade voltage (analog of critical current of the SQUIDs) and periodic modulation of this blockade by electrostatic gate (analog of flux modulation in the SQUIDs). The model of this QPS transistor is discussed.

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We propose a transistorlike circuit including two serially connected segments of a narrow superconducting nanowire joint by a wider segment with a capacitively coupled gate in between. This circuit is made of amorphous NbSi film and embedded in a network of on-chip Cr microresistors ensuring a sufficiently high external electromagnetic impedance. Assuming a virtual regime of quantum phase slips (QPS) in two narrow segments of the wire, leading to quantum interference of voltages on these segments, this circuit is dual to the dc SQUID. Our samples demonstrated appreciable Coulomb blockade voltage (analog of critical current of the SQUIDs) and periodic modulation of this blockade by an electrostatic gate (analog of flux modulation in the SQUIDs). The model of this QPS transistor is discussed.

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The single Cooper pair josephson transistor is a device that exhibits at the same time charge quantization and phase coherence. Coherent quantum phase slip phenomenon is “dual” the Josephson phase coherence, while the charge quantization is dual to the flux quantization. We present the experimental demonstration and the theoretical description of a new superconducting device–single flux transistor, which is dual to the single Cooper pair transistor. Our transport measurements show the periodic modulation of the critical voltage by the external magnetic field. The obtained current-voltage characteristics show the hysteretic behavior, which we attribute to the intrinsic self-heating of charge carriers.

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Coulomb blockade due to quantum phase slips illustrated with devices

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Quantum effects in nanoscale Josephson junction circuits

S. Corlevi

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

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C H Webster, J. C. Fenton, T. T. Hongisto +3 more

We present a detailed report of microwave irradiation of ultranarrow superconducting nanowires. In our nanofabricated circuits containing a superconducting NbSi nanowire, a dc blockade of current flow was observed at low temperatures below a critical voltage ${V}_{\mathrm{c}}$, a strong indicator of the existence of quantum phase-slip (QPS) in the nanowire. We describe the results of applying microwaves to these samples, using a range of frequencies and both continuous-wave and pulsed drive, in order to search for dual Shapiro steps which would constitute an unambiguous demonstration of quantum phase-slip. We observed no steps, and our subsequent thermal analysis suggests that the electron temperature in the series CrO resistors was significantly elevated above the substrate temperature, resulting in sufficient Johnson noise to wash out the steps. To understand the system and inform future work, we have constructed a numerical model of the dynamics of the circuit for dc and ac bias (both continuous-wave and pulsed drive signals) in the presence of Johnson noise. Using this model, we outline important design considerations for device and measurement parameters which should be used in any future experiment to enable the observation of dual Shapiro steps at experimentally accessible temperatures and, thus, lead to the development of a QPS-based quantum current standard.

arXiv:1302.2808•Physical Review B•Apr 18, 2013•54 citations

Asymmetric Cooper pair transistor in parallel to a dc SQUID: Two coupled quantum systems

Aurélien Fay, Wiebke Guichard, O. Buisson +1 more

We present a theoretical analysis of a superconducting quantum circuit based on a highly asymmetric Cooper pair transistor (ACPT) in parallel to a dc superconduction quantum intereference device (SQUID). Starting from the full Hamiltonian we show that the circuit can be modeled as a charge qubit (ACPT) coupled to an anharmonic oscillator (dc SQUID). Depending on the anharmonicity of the SQUID, the Hamiltonian can be reduced either to one that describes two coupled qubits or to the Jaynes-Cummings Hamiltonian. Here the dc SQUID can be viewed as a tunable micrometer-sized resonator. The coupling term, which is a combination of a capacitive and a Josephson coupling between the two qubits, can be tuned from the very strong- to the zero-coupling regime. It describes very precisely the tunable coupling strength measured in this circuit [A. Fay et al., Phys. Rev. Lett. 100, 187003 (2008)] and explains the ``quantronium'' as well as the adiabatic quantum transfer readout.

Physical Review B•May 17, 2011•11 citations
We propose a transistor-like circuit including two serially connected segments of narrow superconducting nanowire joint by a wider segment with capacitively coupled gate in between. This circuit is made of amorphous NbSi film and embedded in a network of on-chip Cr microresistors ensuring sufficiently high external electromagnetic impedance. Assuming virtual regime of quantum phase slips (QPS) in two narrow segments of the wire, leading to correlated single Cooper pair tunneling, this circuit is dual to the dc SQUID. Our samples demonstrated appreciable Coulomb blockade voltage (analog of critical current of the SQUIDs) and periodic modulation of this blockade by electrostatic gate (analog of flux modulation in the SQUIDs). The model of this QPS transistor is discussed.
We propose a transistorlike circuit including two serially connected segments of a narrow superconducting nanowire joint by a wider segment with a capacitively coupled gate in between. This circuit is made of amorphous NbSi film and embedded in a network of on-chip Cr microresistors ensuring a sufficiently high external electromagnetic impedance. Assuming a virtual regime of quantum phase slips (QPS) in two narrow segments of the wire, leading to quantum interference of voltages on these segments, this circuit is dual to the dc SQUID. Our samples demonstrated appreciable Coulomb blockade voltage (analog of critical current of the SQUIDs) and periodic modulation of this blockade by an electrostatic gate (analog of flux modulation in the SQUIDs). The model of this QPS transistor is discussed.
The single Cooper pair josephson transistor is a device that exhibits at the same time charge quantization and phase coherence. Coherent quantum phase slip phenomenon is “dual” the Josephson phase coherence, while the charge quantization is dual to the flux quantization. We present the experimental demonstration and the theoretical description of a new superconducting device–single flux transistor, which is dual to the single Cooper pair transistor. Our transport measurements show the periodic modulation of the critical voltage by the external magnetic field. The obtained current-voltage characteristics show the hysteretic behavior, which we attribute to the intrinsic self-heating of charge carriers.
To illustrate the emergence of Coulomb blockade from coherent quantum phase-slip processes in thin superconducting wires, we propose and theoretically investigate two elementary setups, or devices. The setups are derived from the Cooper-pair box and Cooper-pair transistor, so we refer to them as the QPS box and QPS transistor, respectively. We demonstrate that the devices exhibit sensitivity to a charge induced by a gate electrode, this being the main signature of Coulomb blockade. Experimental realization of these devices will unambiguously prove the Coulomb blockade as an effect of coherence of phase-slip processes. We analyze the emergence of discrete charging in the limit of strong phase slips. We have found and investigated six distinct regimes that are realized depending on the relation between three characteristic energy scales: inductive energy, charging energy, and phase-slip amplitude. For completeness, we include a brief discussion of dual Josephson-junction devices.
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.
We present a detailed report of microwave irradiation of ultranarrow superconducting nanowires. In our nanofabricated circuits containing a superconducting NbSi nanowire, a dc blockade of current flow was observed at low temperatures below a critical voltage Vc{V}_{\mathrm{c}}Vc​, a strong indicator of the existence of quantum phase-slip (QPS) in the nanowire. We describe the results of applying microwaves to these samples, using a range of frequencies and both continuous-wave and pulsed drive, in order to search for dual Shapiro steps which would constitute an unambiguous demonstration of quantum phase-slip. We observed no steps, and our subsequent thermal analysis suggests that the electron temperature in the series CrO resistors was significantly elevated above the substrate temperature, resulting in sufficient Johnson noise to wash out the steps. To understand the system and inform future work, we have constructed a numerical model of the dynamics of the circuit for dc and ac bias (both continuous-wave and pulsed drive signals) in the presence of Johnson noise. Using this model, we outline important design considerations for device and measurement parameters which should be used in any future experiment to enable the observation of dual Shapiro steps at experimentally accessible temperatures and, thus, lead to the development of a QPS-based quantum current standard.
We present a theoretical analysis of a superconducting quantum circuit based on a highly asymmetric Cooper pair transistor (ACPT) in parallel to a dc superconduction quantum intereference device (SQUID). Starting from the full Hamiltonian we show that the circuit can be modeled as a charge qubit (ACPT) coupled to an anharmonic oscillator (dc SQUID). Depending on the anharmonicity of the SQUID, the Hamiltonian can be reduced either to one that describes two coupled qubits or to the Jaynes-Cummings Hamiltonian. Here the dc SQUID can be viewed as a tunable micrometer-sized resonator. The coupling term, which is a combination of a capacitive and a Josephson coupling between the two qubits, can be tuned from the very strong- to the zero-coupling regime. It describes very precisely the tunable coupling strength measured in this circuit [A. Fay et al., Phys. Rev. Lett. 100, 187003 (2008)] and explains the ``quantronium'' as well as the adiabatic quantum transfer readout.