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:0911.3016

A lattice gas model of a single Cooper pair box

Robert Alicki

Published Nov 16, 2009• 1 citation
arXivHTMLPDF

Abstract

There exists a large number of experimental and theoretical results supporting the picture of "macroscopic qubits" implemented by nanoscopic Josephson junctions. On the other hand the standard model of such systems given in terms of a single degree of freedom suggests their semiclassical behavior due to a localization mechanism caused by a strong coupling to an environment. Indeed, such a mechanism is observed in an atomic Bose-Einstein condensate (BEC) placed in a double-well potential - a system mathematically equivalent to a Josephson junction. In this note it is shown, on the example of a Cooper pair box, that replacing the BEC-type model for Cooper pairs by a lattice gas model one can reduce the environmental effects of "dequantization" and can explain the experimental data in particular the existing huge differences between the measured values of relaxation times.

DOI
10.48550/arxiv.0911.3016

Related papers

Quantumness of Josephson junctions reexamined

Robert Alicki

There exists an increasing evidence supporting the picture of the Josephson junction (JJ) as a "macroscopic quantum system". On the other hand the interpretation of experimental data strongly depends on the assumed theoretical model. We analyse the possible states of a Cooper pair box ("charge qubit") for the two types of models : two-mode Bose-Hubbard model with its large $N$ aproximations and the many-body description within the mean-field approximation (Gross-Pitaevski equation). While the first class of models supports the picture of JJ being a quantum subsystem of a single degree of freedom, the second approach yields an essentially classical structure of accessible quantum states which, in particular, implies the absence of entanglement for two coupled JJ's. The arguments in favor of the mean-field theory are presented and different experimental tests including a new proposal are briefly discussed.

arXiv:quant-ph/0610008•Oct 1, 2006•5 citations

The macroscopic qubit delusion

Robert Alicki

There exists a large number of experimental and theoretical results supporting the picture of "macroscopic qubits" implemented, for instance, by Rydberg atoms, Josephson junctions or Bose-Einstein condensates - the systems which should rather emerge in localized semiclassical states. In this note it is shown how, under realistic conditions, the false qubit interpretation can be consistent with the restricted set of experimental data collected for semiclassical systems. The recent experiments displaying semiclassical character of Bose-Einstein condensates and possible quantumness tests for a single system are briefly invoked also.

arXiv:0812.0999•Dec 4, 2008•1 citation

BCS models of Josephson qubits I. Energy spectra

Robert Alicki, W. Miklaszewski

There exists a large number of experimental and theoretical results supporting the picture of macroscopic qubits implemented by nanoscopic Josephson junctions of three different types -- charge qubit, flux qubit and phase qubit. The standard unified description of such systems is based on the formal quantization of the phenomenological Kirchhoff equations for the corresponding circuits. In this paper a simplified version of the BCS theory for superconductors is used to derive microscopic models for all types of small Josephson junctions. For these models the state-dependent individual tunneling of Cooper pairs couples ground pair states with excited pair states what leads to a more complicated structure of the lowest lying energy levels. In particular, the highly degenerate levels emerge, which act as probability sinks for the qubit. These models allow also for the coupling to phonons as an efficient mechanism of relaxation for all types of junctions. The alternative formulas concerning basic spectral parameters of superconducting qubits are presented and compared with the experimental data. Finally, the question whether small Josephson junctions can be treated as macroscopic quantum systems is briefly discussed.

arXiv:1012.0140•Dec 1, 2010•0 citations

BCS model of Cooper Pair Box

Robert Alicki

The standard phenomenological Hamiltonian of a small superconducting Josephson junction in the charge regime (Cooper Pair Box) produces a model of the effective charge qubit with possible applications to quantum information processing. In this note a new model based on the BCS Hamiltonian with individual tunneling yields an effective multi-level picture with a highly degenerated level placed between the ground state and the excited state. Unlike in the standard approach, the excited Cooper pairs play here an important role. For such a system coupled to a zero temperature bath the additional levels act as a probability sink. In contrast to the standard large-spin model the coupling to phonons can be an effective source of dissipation. This model provides also alternative explanations of various effects observed in experiments and sheds new light on the issue of Josephson junctions as macroscopic quantum systems.

arXiv:1002.3924•Feb 20, 2010•1 citation

Single-atom box: Bosonic staircase and effects of parity

D. V. Averin, T. H. Bergeman, Pavan Hosur +1 more

We have developed a theory of a Josephson junction formed by two tunnel-coupled Bose-Einstein condensates in a double-well potential in the regime of strong atom-atom interaction for an arbitrary total number $N$ of bosons in the condensates. The tunnel resonances in the junction are shown to be periodically spaced by the interaction energy, forming a single-atom staircase sensitive to the parity of $N$ even for large $N$. One of the manifestations of the staircase structure is the periodic modulation with the bias energy of the visibility of the interference pattern in lattices of junctions.

arXiv:0802.3687•Physical Review A•Sep 3, 2008•16 citations

Observation of nonlinear tunneling of a Bose-Einstein condensate in a single Josephson junction

M. Albiez

In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.

•Jan 1, 2005•9 citations
There exists a large number of experimental and theoretical results supporting the picture of "macroscopic qubits" implemented by nanoscopic Josephson junctions. On the other hand the standard model of such systems given in terms of a single degree of freedom suggests their semiclassical behavior due to a localization mechanism caused by a strong coupling to an environment. Indeed, such a mechanism is observed in an atomic Bose-Einstein condensate (BEC) placed in a double-well potential - a system mathematically equivalent to a Josephson junction. In this note it is shown, on the example of a Cooper pair box, that replacing the BEC-type model for Cooper pairs by a lattice gas model one can reduce the environmental effects of "dequantization" and can explain the experimental data in particular the existing huge differences between the measured values of relaxation times.
There exists an increasing evidence supporting the picture of the Josephson junction (JJ) as a "macroscopic quantum system". On the other hand the interpretation of experimental data strongly depends on the assumed theoretical model. We analyse the possible states of a Cooper pair box ("charge qubit") for the two types of models : two-mode Bose-Hubbard model with its large NNN aproximations and the many-body description within the mean-field approximation (Gross-Pitaevski equation). While the first class of models supports the picture of JJ being a quantum subsystem of a single degree of freedom, the second approach yields an essentially classical structure of accessible quantum states which, in particular, implies the absence of entanglement for two coupled JJ's. The arguments in favor of the mean-field theory are presented and different experimental tests including a new proposal are briefly discussed.
There exists a large number of experimental and theoretical results supporting the picture of "macroscopic qubits" implemented, for instance, by Rydberg atoms, Josephson junctions or Bose-Einstein condensates - the systems which should rather emerge in localized semiclassical states. In this note it is shown how, under realistic conditions, the false qubit interpretation can be consistent with the restricted set of experimental data collected for semiclassical systems. The recent experiments displaying semiclassical character of Bose-Einstein condensates and possible quantumness tests for a single system are briefly invoked also.
There exists a large number of experimental and theoretical results supporting the picture of macroscopic qubits implemented by nanoscopic Josephson junctions of three different types -- charge qubit, flux qubit and phase qubit. The standard unified description of such systems is based on the formal quantization of the phenomenological Kirchhoff equations for the corresponding circuits. In this paper a simplified version of the BCS theory for superconductors is used to derive microscopic models for all types of small Josephson junctions. For these models the state-dependent individual tunneling of Cooper pairs couples ground pair states with excited pair states what leads to a more complicated structure of the lowest lying energy levels. In particular, the highly degenerate levels emerge, which act as probability sinks for the qubit. These models allow also for the coupling to phonons as an efficient mechanism of relaxation for all types of junctions. The alternative formulas concerning basic spectral parameters of superconducting qubits are presented and compared with the experimental data. Finally, the question whether small Josephson junctions can be treated as macroscopic quantum systems is briefly discussed.
The standard phenomenological Hamiltonian of a small superconducting Josephson junction in the charge regime (Cooper Pair Box) produces a model of the effective charge qubit with possible applications to quantum information processing. In this note a new model based on the BCS Hamiltonian with individual tunneling yields an effective multi-level picture with a highly degenerated level placed between the ground state and the excited state. Unlike in the standard approach, the excited Cooper pairs play here an important role. For such a system coupled to a zero temperature bath the additional levels act as a probability sink. In contrast to the standard large-spin model the coupling to phonons can be an effective source of dissipation. This model provides also alternative explanations of various effects observed in experiments and sheds new light on the issue of Josephson junctions as macroscopic quantum systems.
We have developed a theory of a Josephson junction formed by two tunnel-coupled Bose-Einstein condensates in a double-well potential in the regime of strong atom-atom interaction for an arbitrary total number NNN of bosons in the condensates. The tunnel resonances in the junction are shown to be periodically spaced by the interaction energy, forming a single-atom staircase sensitive to the parity of NNN even for large NNN. One of the manifestations of the staircase structure is the periodic modulation with the bias energy of the visibility of the interference pattern in lattices of junctions.
In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.