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

arXiv:2501.14365 · New Journal of Physics

Open quantum dynamics of Josephson charge pumps

Ankit Kumar, Luis Cort, Marcin Łobejko, Alejandro Jenkins, Michał Horodecki

Published Sep 5, 2025• 0 citations
arXivHTMLPDF

Abstract

Abstract We investigate the macroscopic dynamics of Josephson charge pumps in the light of Alicki et al’s theoretical description of the Josephson junction as an open quantum system described by a Markovian master equation. Once the electrostatic interaction between the terminals is taken into account via nonlinear capacitive terms in the Hamiltonian, we find that the resulting description of pumping is physically reasonable and in good qualitative agreement with experimental observations. We comment on how this approach relates to other theoretical treatments of quantum pumps based on time-dependent potentials or scattering amplitudes. We also highlight the significance of our results in the broader context of the dynamics of charge pumping by active systems.

DOI
10.1088/1367-2630/ae03e4

Related papers

Quantum system dynamics with a weakly nonlinear Josephson junction bath

Jing Yang, Étienne Jussiau, Cyril Elouard +2 more

We investigate the influence of a weakly nonlinear Josephson bath consisting of a chain of Josephson junctions on the dynamics of a small quantum system (LC oscillator). Focusing on the regime where the charging energy is the largest energy scale, we perturbatively calculate the correlation function of the Josephson bath to the leading order in the Josephson energy divided by the charging energy while keeping the cosine potential exactly. When the variation of the charging energy along the chain ensures fast decay of the bath correlation function, the dynamics of the LC oscillator that is weakly and capacitively coupled to the Josephson bath can be solved through the Markovian master equation. We establish a duality relation for the Josephson bath between the regimes of large charging and Josephson energies, respectively. The results can be applied to cases where the charging energy either is nonuniformly engineered or disordered in the chain. Furthermore, we find that the Josephson bath may become non-Markovian when the temperature is increased beyond the zero-temperature limit in that the bath correlation function gets shifted by a constant and does not decay with time.

arXiv:2008.08052•Physical review. B./Physical review. B•Feb 1, 2021•1 citation

Quantum dynamics of semiconductor quantum dot Josephson junctions

Utkan Güngördü, Rusko Ruskov, Silas Hoffman +3 more

Josephson junctions constructed from superconductor-semiconductor-superconductor heterostructures have been used to realize a variety of voltage-tunable superconducting quantum devices, including qubits and parametric amplifiers. To date, theoretical descriptions of these systems have been restricted to small quantum fluctuations of the junction phase, making them inapplicable to many experiments. In this paper, we relax this, employing a path-integral formulation where the phase quantum dynamics is obtained self-consistently from an underlying many-body formalism. Our method recovers previously known results for small phase fluctuations, and predicts effects outside of that limit: (i) system capacitances undergo a gate-voltage-dependent renormalization; and (ii) an additional charge offset appears for asymmetric junctions. Our main results can be summarized in terms of a single-particle Hamiltonian, which can be directly compared to that of an ordinary Josephson junction. This more general theory could be a first step towards designing new quantum devices that go qualitatively beyond voltage-tunable variants of previously known circuits.

arXiv:2402.10330•Physical review. B./Physical review. B•Jun 2, 2025•2 citations

Josephson junction in the quantum mesoscopic electric circuits with charge discreteness

Hassan Pahlavani

A quantum mesoscopic electrical LC-circuit with charge discreteness including a Josephson junction is considered and a nonlinear Hamiltonian that describing the dynamic of such circuit is introduced. The quantum dynamical behavior (persistent current probability) is studied in the charge and phase regimes by numerical solution approaches. The time evolution of charge and current, number-difference and the bosonic phase and also the energy spectrum of a quantum mesoscopic electric LC-circuit with charge discreteness that coupled with a Josephson junction device are investigated. We show the role of the coupling energy and the electrostatic Coulomb energy of the Josephson junction in description of the quantum behavior and the spectral properties of a quantum mesoscopic electrical LC-circuits with charge discreteness.

International Journal of Modern Physics B•Feb 22, 2018•2 citations

Markovian Dynamics of Josephson Parametric Amplification

Waldemar Kaiser, Michael Haider, Johannes A. Russer +2 more

Abstract. In this work, we derive the dynamics of the lossy DC pumped non-degenerate Josephson parametric amplifier (DCPJPA). The main element in a DCPJPA is the superconducting Josephson junction. The DC bias generates the AC Josephson current varying the nonlinear inductance of the junction. By this way the Josephson junction acts as the pump oscillator as well as the time varying reactance of the parametric amplifier. In quantum-limited amplification, losses and noise have an increased impact on the characteristics of an amplifier. We outline the classical model of the lossy DCPJPA and derive the available noise power spectral densities. A classical treatment is not capable of including properties like spontaneous emission which is mandatory in case of amplification at the quantum limit. Thus, we derive a quantum mechanical model of the lossy DCPJPA. Thermal losses are modeled by the quantum Langevin approach, by coupling the quantized system to a photon heat bath in thermodynamic equilibrium. The mode occupation in the bath follows the Bose-Einstein statistics. Based on the second quantization formalism, we derive the Heisenberg equations of motion of both resonator modes. We assume the dynamics of the system to follow the Markovian approximation, i.e. the system only depends on its actual state and is memory-free. We explicitly compute the time evolution of the contributions to the signal mode energy and give numeric examples based on different damping and coupling constants. Our analytic results show, that this model is capable of including thermal noise into the description of the DC pumped non-degenerate Josephson parametric amplifier.

Advances in radio science•Sep 21, 2017•2 citations

0 Nonlinear quantum model for atomic Josephson junctions with one and two bosonic species

G. Mazzarella, Marco Moratti, Luca Salasnich +1 more

We study atomic Josephson junctions (AJJs) with one and two bosonic species confined by a double-well potential. Proceeding from the second quantized Hamiltonian, we show that it is possible to describe the zero-temperature AJJ microscopic dynamics by means of extended Bose–Hubbard (EBH) models, which include usually neglected nonlinear terms. Within the mean-field approximation, the Heisenberg equations derived from such two-mode models provide a description of AJJ macroscopic dynamics in terms of ordinary differential equations (ODEs). We discuss the possibility of distinguishing the Rabi, Josephson and Fock regimes in terms of the macroscopic parameters which appear in the EBH Hamiltonians, and then in the ODEs. We compare the predictions for the relative populations of the Bose gas atoms in the two wells obtained from the numerical solutions of the two-mode ODEs, with those deriving from the direct numerical integration of the Gross–Pitaevskii equations (GPEs). Our investigations show that the nonlinear terms of the ODEs are crucial to achieve a good agreement between the ODE and GPE approaches, and in particular to give quantitative predictions of the self-trapping regime.

•Aug 18, 2016•14 citations

Quantum synchronization in presence of shot noise

Florian Höhe, Lukas Danner, Ciprian Padurariu +3 more

Abstract Synchronization is a widespread phenomenon encountered in many natural and engineered systems with nonlinear classical dynamics. How synchronization concepts and mechanisms transfer to the quantum realm and whether features are universal or platform specific are timely questions of fundamental interest. They can be studied in superconducting electrical circuits which provide a well-established platform for nonlinear quantum dynamics. Here, we consider a Josephson-photonics device, where a dc-biased Josephson junction creates (non-classical) light in a microwave cavity. The combined quantum compound constitutes a self-sustained oscillator: a system susceptible to synchronization. This is due to the inherent effect of an in-series resistance, which realizes an autonomous feedback mechanism of the charge transport on the driving voltage. Accounting for the full counting statistics of transported charge not only yields phase diffusion, but allows us to describe phase locking to an ac-signal and the mutual synchronization of two such devices. Thereby one can observe phase stabilization leading to a sharp emission spectrum as well as unique charge transport statistics revealing shot noise induced phase slips. Two-time perturbation theory is used to obtain a reduced description of the oscillators phase dynamics in form of a Fokker–Planck equation in generalization of classical synchronization theories.

arXiv:2306.15292•New Journal of Physics•Feb 1, 2025•4 citations
Abstract We investigate the macroscopic dynamics of Josephson charge pumps in the light of Alicki et al’s theoretical description of the Josephson junction as an open quantum system described by a Markovian master equation. Once the electrostatic interaction between the terminals is taken into account via nonlinear capacitive terms in the Hamiltonian, we find that the resulting description of pumping is physically reasonable and in good qualitative agreement with experimental observations. We comment on how this approach relates to other theoretical treatments of quantum pumps based on time-dependent potentials or scattering amplitudes. We also highlight the significance of our results in the broader context of the dynamics of charge pumping by active systems.
We investigate the influence of a weakly nonlinear Josephson bath consisting of a chain of Josephson junctions on the dynamics of a small quantum system (LC oscillator). Focusing on the regime where the charging energy is the largest energy scale, we perturbatively calculate the correlation function of the Josephson bath to the leading order in the Josephson energy divided by the charging energy while keeping the cosine potential exactly. When the variation of the charging energy along the chain ensures fast decay of the bath correlation function, the dynamics of the LC oscillator that is weakly and capacitively coupled to the Josephson bath can be solved through the Markovian master equation. We establish a duality relation for the Josephson bath between the regimes of large charging and Josephson energies, respectively. The results can be applied to cases where the charging energy either is nonuniformly engineered or disordered in the chain. Furthermore, we find that the Josephson bath may become non-Markovian when the temperature is increased beyond the zero-temperature limit in that the bath correlation function gets shifted by a constant and does not decay with time.
Josephson junctions constructed from superconductor-semiconductor-superconductor heterostructures have been used to realize a variety of voltage-tunable superconducting quantum devices, including qubits and parametric amplifiers. To date, theoretical descriptions of these systems have been restricted to small quantum fluctuations of the junction phase, making them inapplicable to many experiments. In this paper, we relax this, employing a path-integral formulation where the phase quantum dynamics is obtained self-consistently from an underlying many-body formalism. Our method recovers previously known results for small phase fluctuations, and predicts effects outside of that limit: (i) system capacitances undergo a gate-voltage-dependent renormalization; and (ii) an additional charge offset appears for asymmetric junctions. Our main results can be summarized in terms of a single-particle Hamiltonian, which can be directly compared to that of an ordinary Josephson junction. This more general theory could be a first step towards designing new quantum devices that go qualitatively beyond voltage-tunable variants of previously known circuits.
A quantum mesoscopic electrical LC-circuit with charge discreteness including a Josephson junction is considered and a nonlinear Hamiltonian that describing the dynamic of such circuit is introduced. The quantum dynamical behavior (persistent current probability) is studied in the charge and phase regimes by numerical solution approaches. The time evolution of charge and current, number-difference and the bosonic phase and also the energy spectrum of a quantum mesoscopic electric LC-circuit with charge discreteness that coupled with a Josephson junction device are investigated. We show the role of the coupling energy and the electrostatic Coulomb energy of the Josephson junction in description of the quantum behavior and the spectral properties of a quantum mesoscopic electrical LC-circuits with charge discreteness.
Abstract. In this work, we derive the dynamics of the lossy DC pumped non-degenerate Josephson parametric amplifier (DCPJPA). The main element in a DCPJPA is the superconducting Josephson junction. The DC bias generates the AC Josephson current varying the nonlinear inductance of the junction. By this way the Josephson junction acts as the pump oscillator as well as the time varying reactance of the parametric amplifier. In quantum-limited amplification, losses and noise have an increased impact on the characteristics of an amplifier. We outline the classical model of the lossy DCPJPA and derive the available noise power spectral densities. A classical treatment is not capable of including properties like spontaneous emission which is mandatory in case of amplification at the quantum limit. Thus, we derive a quantum mechanical model of the lossy DCPJPA. Thermal losses are modeled by the quantum Langevin approach, by coupling the quantized system to a photon heat bath in thermodynamic equilibrium. The mode occupation in the bath follows the Bose-Einstein statistics. Based on the second quantization formalism, we derive the Heisenberg equations of motion of both resonator modes. We assume the dynamics of the system to follow the Markovian approximation, i.e. the system only depends on its actual state and is memory-free. We explicitly compute the time evolution of the contributions to the signal mode energy and give numeric examples based on different damping and coupling constants. Our analytic results show, that this model is capable of including thermal noise into the description of the DC pumped non-degenerate Josephson parametric amplifier.
We study atomic Josephson junctions (AJJs) with one and two bosonic species confined by a double-well potential. Proceeding from the second quantized Hamiltonian, we show that it is possible to describe the zero-temperature AJJ microscopic dynamics by means of extended Bose–Hubbard (EBH) models, which include usually neglected nonlinear terms. Within the mean-field approximation, the Heisenberg equations derived from such two-mode models provide a description of AJJ macroscopic dynamics in terms of ordinary differential equations (ODEs). We discuss the possibility of distinguishing the Rabi, Josephson and Fock regimes in terms of the macroscopic parameters which appear in the EBH Hamiltonians, and then in the ODEs. We compare the predictions for the relative populations of the Bose gas atoms in the two wells obtained from the numerical solutions of the two-mode ODEs, with those deriving from the direct numerical integration of the Gross–Pitaevskii equations (GPEs). Our investigations show that the nonlinear terms of the ODEs are crucial to achieve a good agreement between the ODE and GPE approaches, and in particular to give quantitative predictions of the self-trapping regime.
Abstract Synchronization is a widespread phenomenon encountered in many natural and engineered systems with nonlinear classical dynamics. How synchronization concepts and mechanisms transfer to the quantum realm and whether features are universal or platform specific are timely questions of fundamental interest. They can be studied in superconducting electrical circuits which provide a well-established platform for nonlinear quantum dynamics. Here, we consider a Josephson-photonics device, where a dc-biased Josephson junction creates (non-classical) light in a microwave cavity. The combined quantum compound constitutes a self-sustained oscillator: a system susceptible to synchronization. This is due to the inherent effect of an in-series resistance, which realizes an autonomous feedback mechanism of the charge transport on the driving voltage. Accounting for the full counting statistics of transported charge not only yields phase diffusion, but allows us to describe phase locking to an ac-signal and the mutual synchronization of two such devices. Thereby one can observe phase stabilization leading to a sharp emission spectrum as well as unique charge transport statistics revealing shot noise induced phase slips. Two-time perturbation theory is used to obtain a reduced description of the oscillators phase dynamics in form of a Fokker–Planck equation in generalization of classical synchronization theories.