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The two Josephson junction flux qubit with large tunneling amplitude

V. I. Shnyrkov, A. A. Soroka, Sergiy Melnyk

Published Jan 1, 2008• 4 citations
OpenAlex

Abstract

In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling \namplitude between the two macroscopic states. The latter can be controlled via the height and form of \nthe potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest \ncircuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. \nThe tunneling amplitude between two macroscopically different states can be essentially increased, by \nengineering of the qubit circuit, if tunnel junction is replaced by a ScS contact. However, only Josephson \ntunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with preset- \nday technology. To overcome this difficulty we consider here the flux qubit with high-level energy separation \nbetween «ground» and «excited» states, which consists of a superconducting loop with two lowcapacitance \nJosephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition \nbetween the two macroscopic states the tunneling amplitude can reach values greater than 1 K. Analytical \nresults for the tunneling amplitude obtained within semiclassical approximation by instanton technique \nshow good correlation with a numerical solution.

Related papers

The two-Josephson-junction flux qubit with large tunneling amplitude

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In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling amplitude between the two macroscopic states. The latter can be controlled via the height and form of the potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest circuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. The tunneling amplitude between two macroscopically different states can be increased substantially by engineering of the qubit circuit if the tunnel junction is replaced by a ScS contact. However, only Josephson tunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with present-day technology. To overcome this difficulty we consider here a flux qubit with high energy-level separation between the “ground” and “excited” states, consisting of a superconducting loop with two low-capacitance Josephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition between the two macroscopic states the tunneling amplitude can reach values greater than 1K. Analytical results for the tunneling amplitude obtained within the semiclassical approximation by the instanton technique show good correlation with a numerical solution.

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Low Temperature Physics•Jan 1, 2007•10 citations
In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling \namplitude between the two macroscopic states. The latter can be controlled via the height and form of \nthe potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest \ncircuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. \nThe tunneling amplitude between two macroscopically different states can be essentially increased, by \nengineering of the qubit circuit, if tunnel junction is replaced by a ScS contact. However, only Josephson \ntunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with preset- \nday technology. To overcome this difficulty we consider here the flux qubit with high-level energy separation \nbetween «ground» and «excited» states, which consists of a superconducting loop with two lowcapacitance \nJosephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition \nbetween the two macroscopic states the tunneling amplitude can reach values greater than 1 K. Analytical \nresults for the tunneling amplitude obtained within semiclassical approximation by instanton technique \nshow good correlation with a numerical solution.
In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling amplitude between the two macroscopic states. The latter can be controlled via the height and form of the potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest circuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. The tunneling amplitude between two macroscopically different states can be increased substantially by engineering of the qubit circuit if the tunnel junction is replaced by a ScS contact. However, only Josephson tunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with present-day technology. To overcome this difficulty we consider here a flux qubit with high energy-level separation between the “ground” and “excited” states, consisting of a superconducting loop with two low-capacitance Josephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition between the two macroscopic states the tunneling amplitude can reach values greater than 1K. Analytical results for the tunneling amplitude obtained within the semiclassical approximation by the instanton technique show good correlation with a numerical solution.
The consequences of the transition to a quantum description of magnetic flux motion in the superconducting ring closed by an ScS type Josephson junction are considered. Here we review the principal results regarding macroscopic quantum tunneling (MQT) of Bose condensate consisting of a macroscopically large number of Cooper electron pairs. These phenomena are illustrated by the original data obtained from the study of MQT and coherent states in a modified flux qubit with energy level depletion ΔE01 ≈ 2·10–23 J (ΔE01/h ≈ 30 GHz). State superposition properties in a two-well potential and the issues associated with quantum measurements of local curvature of qubits’ superposition energy levels are analyzed.
We theoretically study macroscopic quantum entanglement in two superconducting flux qubits. To manipulate the state of two flux qubits, a Josephson junction is introduced in the connecting loop coupling the qubits. Increasing the coupling energy of the Josephson junction makes it possible to achieve relatively strong coupling between the qubits, causing two-qubit tunneling processes to be even dominant over the single-qubit tunneling processes in the states of two qubits. It is shown that due to the two-qubit tunneling processes, both the ground state and excited states of the coupled flux qubits can be a Bell type of maximally entangled state, in experimentally accessible regimes. The parameter regimes for the Bell states are discussed in terms of magnetic flux and Josephson coupling energies.
Abstract. Superconducting circuits with Josephson tunnel junctions are interesting systems for research on quantummechanical behavior of macroscopic degrees of freedom. A particular realization is a small superconducting loop containing three Josephson junctions. Close to magnetic frustration 1=2, the physics of this system corresponds to a double well, whose minima correspond to persistent currents of opposite sign. We present DC measurements of the flux indicating a smooth transition close to the degeneracy point even at very low temperatures. Furthermore, microwavespectroscopy experiments allow for the excitation to the next excited state. The dependence of the energy of the resonance on the applied flux clearly indicates the nature of these states as tunneling-splitted superpositions of flux states. We theoretically analyze the system using a generalized master-equation formulation of the spin-boson model. We address the nature of the measuring process by a switching DC SQUID and the possible interpretation of the spectroscopy data in terms of quantum coherence. We discuss these aspects in the context of further applications as a quantum bit.
Flux qubits, small superconducting loops interrupted by Josephson junctions, are successful realizations of quantum coherence for macroscopic variables. Superconductivity in these loops is carried by ∼106\sim 10^6∼106 -- 101010^{10}1010 electrons, which has been interpreted as suggesting that coherent superpositions of such current states are macroscopic superpositions analogous to Schrödinger's cat. We provide a full microscopic analysis of such qubits, from which the macroscopic quantum description can be derived. This reveals that the number of microscopic constituents participating in superposition states for experimentally accessible flux qubits is surprisingly but not trivially small. The combination of this relatively small size with large differences between macroscopic observables in the two branches is seen to result from the Fermi statistics of the electrons and the large disparity between the values of superfluid and Fermi velocity in these systems.
A quantum detector whose working principle is based on magnetic-field modulation of a circulating supercurrent in the quantum ground state of a macroscopic superconducting loop with a Josephson junction. Under the influence of an external magnetic flux equal to Φ0∕2 (or Φ0), two (or three) classical states are coupled to each other by quantum tunneling through a potential barrier, and therefore the detector is a two-level (or three-level) system. In the low-temperature region and under the condition of very weak damping, the mean value of the circulating supercurrent reflects the character of the variation of the quantum superposition of macroscopic states, which is sensitive to the symmetry of the potential. The variations of the current are amplified and detected in a measurement scheme similar to the signal registration in a nonhysteretic rf SQUID. It is shown by a numerical analysis that in comparison with a qubit detector based on an SIS junction, a detector with an ScS junction is faster and has much larger amplitudes of energy splitting at the same parameters. The results presented for double- and triple-well potentials clearly indicate that a qubit with an ScS junction can act as a detector with a sensitivity determined by the quantum noise of the amplifier.