Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Use of a Coherent-State Formalism in Superconductivity and Josephson-Junction Calculations

lVL Mzla I

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

An investigation is made of the extent to which harmonicoscillator coherent states can bc used to describe superconductivity and Joscphson tunneling phenomena. Recent work has utilized angularmomentum commutation relations for operators that create and annihilate pairs in a Josephson device. This formalism utilizes certain approximations in obtaining angular-momentum commutation rules for the superconducting tunnel junction. We apply the coupled harmonicoscillator approach due to Schwinger to regain angular-momentum commutation relations.

Related papers

Josephson junction coupled to an open transmission line: An application to the theory of macroscopic quantum tunneling

Sudip Chakravarty, Albert Schmid

In view of recent interest in the subject of macroscopic quantum tunneling in Josephson junctions and superconducting quantum interference devices, an extension of the method of calculation of the tunneling rate is made to a distributed circuit model. The current understanding is based on a lumped circuit model. It is hoped that the results derived would be useful in the context of the present experimental efforts.

Physical review. B, Condensed matter•Feb 1, 1986•40 citations

Application of the Schwinger Oscillator Construct of Angular Momentum to an Interpretation of the Superconducting Transmon Qubit

Erickson, R. P.

The Schwinger oscillator construct of angular momentum, applied to the superconducting transmon and its transmission-line readout, modeled as capacitvely coupled quantum oscillators, provides a natural and robust description of a qubit. The construct defines quantum-entangled, two-photon states that form an angular-momentum-like basis, with symmetry corresponding to physical conservation of total photon number, with respect to the combined transmon and readout. This basis provides a convenient starting point from which to study error-inducing effects of transmon anharmonicity, surrounding-environment decoherence, and random stray fields on qubit state and gate operations. Employing a Lindblad master equation to model dissipation to the surrounding environment, and incorporating the effect of weak transmon anharmonicity, we present examples of the utility of the construct. First, we calculate the frequency response associated with exciting the ground state to a Rabi resonance with the lowest-lying spin-1/2 moment, via a driving external voltage. Second, we calculate the frequency response between the three lowest two-photon states, within a ladder-type excitation scheme. The generality of the Schwinger angular-momentum construct allows it to be applied to other superconducting charge qubits.

arXiv:2401.09573•Jan 17, 2024•0 citations

Information-theoretical approach to Josephson tunneling

J. Aliaga, Hilda A. Cerdeira, Araceli N. Proto +1 more

A simplified Hamiltonian model of pair tunneling between two weakly coupled superconductors is used to obtain the ac Josephson current. A closed operator algebra is defined through commutation with the Hamiltonian. With the use of information theory, we find a subalgebra (quasi-angular-momentum operators) that allows us to obtain naturally the dependence of the Josephson current on the phase, as well as a geometric interpretation of the phase. The quasi-spin algebra permits us to find a consistent solution for the imbalance of charge without resorting to further constraints.

Physical review. B, Condensed matter•Sep 1, 1989•4 citations

Reduced quantum fluctuations in the Josephson junction

K. Wódkiewicz

We predict that a Josephson junction can exhibit, under certain conditions, squeezed or reduced quantum fluctuations of the tunneling current. Using the formal analogy of the Josephson junction to a system of two-level atoms, we show that these reduced fluctuations are closely related to the Bloch-state description of the Bardeen-Cooper-Schrieffer wave function and to the angular-momentum algebra of the proper dynamical variables describing the tunneling process.

Physical review. B, Condensed matter•Oct 1, 1985•49 citations

Electrodynamic Study of Josephson Tunneling in Superconducting Junctions

Arnold H. Silver, Robert C. Jaklevic, John Lambe

We have performed a quantitative electrodynamic experiment on a Josephson oxide tunneling junction. Using a current source at 30 Mc/sec, we have verified the time dependence of the Josephson equation, $j={j}_{0}$ $sin [{\ensuremath{\gamma}}_{l}\ensuremath{-}{\ensuremath{\gamma}}_{r}\ensuremath{-}(\frac{2e}{\ensuremath{\hbar}})\ensuremath{\int}\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{dl}]$, where $(\frac{\ensuremath{\partial}}{\ensuremath{\partial}t})[{\ensuremath{\gamma}}_{l}\ensuremath{-}{\ensuremath{\gamma}}_{r}\ensuremath{-}(\frac{2e}{\ensuremath{\hbar}})\ensuremath{\int}{l}^{r}\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{dl}]=\ensuremath{-}(\frac{2eV}{\ensuremath{\hbar}})$. Thus the limiting voltage is shown to obey the quantum relationship relationship, $2eV=\ensuremath{\hbar}\ensuremath{\omega}$. Measurements were made completely in the coherent state showing the diffraction nature of the junction as a function of applied magnetic field. The Josephson (parametric) inductance of the junction was directly observed and is in good agreement with the theory.

Physical Review•Jan 7, 1966•19 citations

On the Interaction Between Two Coupled Coherent Oscillators.

GERALD J. IAFRATE, Mark Croft

The quantum dynamics for two coupled harmonic oscillators is presented. Using the coupled Boson representation, the assumed problem is shown to be isomorphic with a perturbed angular momentum oscillator. The current operator is obtained and its associated expectation values with respect to the number states, coherent states (Glauber states) and atomic coherent states are given. In the limit of weak coupling the results obtained using the coherent states are shown to manifest a Josephson phase relationship. (Author)

•Jun 1, 1974•0 citations
An investigation is made of the extent to which harmonicoscillator coherent states can bc used to describe superconductivity and Joscphson tunneling phenomena. Recent work has utilized angularmomentum commutation relations for operators that create and annihilate pairs in a Josephson device. This formalism utilizes certain approximations in obtaining angular-momentum commutation rules for the superconducting tunnel junction. We apply the coupled harmonicoscillator approach due to Schwinger to regain angular-momentum commutation relations.
The Schwinger oscillator construct of angular momentum, applied to the superconducting transmon and its transmission-line readout, modeled as capacitvely coupled quantum oscillators, provides a natural and robust description of a qubit. The construct defines quantum-entangled, two-photon states that form an angular-momentum-like basis, with symmetry corresponding to physical conservation of total photon number, with respect to the combined transmon and readout. This basis provides a convenient starting point from which to study error-inducing effects of transmon anharmonicity, surrounding-environment decoherence, and random stray fields on qubit state and gate operations. Employing a Lindblad master equation to model dissipation to the surrounding environment, and incorporating the effect of weak transmon anharmonicity, we present examples of the utility of the construct. First, we calculate the frequency response associated with exciting the ground state to a Rabi resonance with the lowest-lying spin-1/2 moment, via a driving external voltage. Second, we calculate the frequency response between the three lowest two-photon states, within a ladder-type excitation scheme. The generality of the Schwinger angular-momentum construct allows it to be applied to other superconducting charge qubits.
A simplified Hamiltonian model of pair tunneling between two weakly coupled superconductors is used to obtain the ac Josephson current. A closed operator algebra is defined through commutation with the Hamiltonian. With the use of information theory, we find a subalgebra (quasi-angular-momentum operators) that allows us to obtain naturally the dependence of the Josephson current on the phase, as well as a geometric interpretation of the phase. The quasi-spin algebra permits us to find a consistent solution for the imbalance of charge without resorting to further constraints.
We have performed a quantitative electrodynamic experiment on a Josephson oxide tunneling junction. Using a current source at 30 Mc/sec, we have verified the time dependence of the Josephson equation, j=j0j={j}_{0}j=j0​ $sin [{\ensuremath{\gamma}}_{l}\ensuremath{-}{\ensuremath{\gamma}}_{r}\ensuremath{-}(\frac{2e}{\ensuremath{\hbar}})\ensuremath{\int}\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{dl}]$, where $(\frac{\ensuremath{\partial}}{\ensuremath{\partial}t})[{\ensuremath{\gamma}}_{l}\ensuremath{-}{\ensuremath{\gamma}}_{r}\ensuremath{-}(\frac{2e}{\ensuremath{\hbar}})\ensuremath{\int}{l}^{r}\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{dl}]=\ensuremath{-}(\frac{2eV}{\ensuremath{\hbar}})$. Thus the limiting voltage is shown to obey the quantum relationship relationship, $2eV=\ensuremath{\hbar}\ensuremath{\omega}$. Measurements were made completely in the coherent state showing the diffraction nature of the junction as a function of applied magnetic field. The Josephson (parametric) inductance of the junction was directly observed and is in good agreement with the theory.
The quantum dynamics for two coupled harmonic oscillators is presented. Using the coupled Boson representation, the assumed problem is shown to be isomorphic with a perturbed angular momentum oscillator. The current operator is obtained and its associated expectation values with respect to the number states, coherent states (Glauber states) and atomic coherent states are given. In the limit of weak coupling the results obtained using the coherent states are shown to manifest a Josephson phase relationship. (Author)