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arXiv:1406.0679 · Journal of Applied Physics

Single flux transistor: The controllable interplay of coherent quantum phase slip and flux quantization

Sergey G. Kafanov, N. M. Chtchelkatchev

Published Aug 21, 2013• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.4818706

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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.
Recent experimental demonstration of the quantum coherent phase slip and current quantization in the superconductors, the fundamental phenomena dual to the coherent Cooper pair tunneling and voltage quantization (Shapiro steps), enables the development of a new quantum device, the Bloch transistor (BT). BT has a unique functionality: it can deliver quantized non-dissipative current to the quantum circuit. BT consists of two coupled Josephson Junctions (JJ) in the regime of coherent quantum phase slip. At the heart of the BT operation is a new mechanism for phase-locking the Bloch oscillations in JJs to microwaves via induced charge. The charge phase locking allows not only quantization of current but also gate voltage control of this quantization through the Aharonov-Casher effect. We study the operation of the BT and analyze its parameters. BT technology is scalable and compatible with other superconducting quantum devices, making it part of an emerging cryogenic quantum technology platform.
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.
The phenomenon of coherent quantum phase-slips (CQPS) in superconducting nanowires was some time ago proposed to be the exact dual of the Josephson effect, a proposal accompanied by predictions of a new quantum current standard dual to the Josephson voltage standard. Unambiguous experimental observation of CQPS in nanowire structures has only recently been achieved through microwave spectroscopy which showed an avoided crossing between flux states for a superconducting ring interrupted by a superconducting nanowire. This observation raises expectations that the CQPS quantum current standard and a slew of CQPS devices dual to devices containing Josephson junction might be realised, including a tunable capacitance, a sensitive charge detector and small-signal detector. To date, experimental evidence for CQPS in a dc transport geometry has not been considered conclusive, and the impact of decoherence in CQPS devices still remains to be evaluated. We present experimental work which has enabled us to crystallise pertinent issues which have prevented the realisation of CQPS in dc transport experiments to date.
In a system where two small-area (100 nm x 100 nm) superconducting tunnel junctions are connected in series, the Josephson effect which tends to impose the phase competes with the charging effects in the central electrode (the of the device) which tend to set the charge of the island. By applying a voltage on an electrode capacitively coupled to the island (the electrode) one can arbitrate this competition in favour of either effect. This is can be seen in particular on the supercurrent which can flow through the junctions : it is modulated periodically by the gate voltage (hence the name of given to the system). This modulation shows sharp peaks when two charge states of the island are degenerate with respect to the electrostatic energy. The system is then in a state which has no classical description : it is in a coherent superposition of states. In this thesis we demonstrate experimentally the behaviour of this transistor and we analyse the theoretical and practical problems which can prevent the observation of the coherent superposition of states through the modulation of the supercurrent. In particular we show that the parity of the electron number in the island must be rigorously controlled and that the impedance connected to the circuit plays a crucial role in setting the magnitude of the measured supercurrent.
We have studied dynamic properties of a special Josephson charge qubit. The device consists of a single-Cooper-pair transistor (with capacitive gate) closed by a superconducting inductive loop. The phase bias is implemented by an external flux that threads the loop. Restricting ourselves to a two-band model, we have derived analytical expressions for the oppositely circulating ring currents in terms of gate charge and phase bias. They permit the determination of important device characteristics such as critical current, loop parameters, and Josephson inductance. For the purpose of measurements in connection with macroscopic quantum coherence, we investigate the qubit's microwave response within the frame of Bloch equations with phenomenological relaxation rates. We find the (nonlinear) qubit impedance in terms of quality, detuning, and the quantum resistance unit, which reflects the competition between irradiation and dephasing.
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.