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

International Conference on Quantum Information

Electron spin entanglement length in a non-equilibrium Superconductor

Llea N. Samuel, Roger Andrews

Published Jan 1, 2011• 0 citations
Publisher

Abstract

The Keldysh formalism is used to obtain the form of an even-mode nonequilibrium superconducting system which has an enhanced order parameter. The disequilibrium is created using phonons emitted by a microwave field. We find the entanglement length of the Cooper pairs contained in such a system to be around 1×10−24m.
DOI
10.1364/icqi.2011.qmi38

Related papers

Entanglement of electron spins in superconductors

Sangchul Oh, Jaewan Kim

We investigate entanglement of two electron spins forming Cooper pairs in an $s$-wave superconductor. The two-electron space-spin density matrix is obtained from the BCS ground state using a two-particle Green's function. It is demonstrated that a two spin state is not given by a spin singlet state but by a Werner state. It is found that the entanglement length, within which two spins are entangled, is not of the order of the coherence length but of the order of the Fermi wave length.

arXiv:quant-ph/0406013•Physical Review B•Apr 29, 2005•35 citations

Entanglement of electrons field-emitted from a superconductor

Kazuya Yuasa, Paolo Facchi A, Rosario Fazio +4 more

Under appropriate circumstances the electrons emitted from a superconducting tip can be entangled. We analyze these nonlocal correlations by studying the coincidences of the field-emitted electrons and show that electrons emitted in opposite directions violate Bell's inequality. We scrutinize the interplay between the bosonic nature of Cooper pairs and the fermionic nature of electrons. We further discuss the feasibility of our analysis in the light of present experimental capabilities.

arXiv:0810.5245•Physical Review B•May 11, 2009•6 citations

Microwave dressed states and vacuum fluctuations in a superconducting condensate

Anoop Dhillon, A. Hamed Majedi

Abstract Microwave dressed states are found to emerge within the superconducting condensate when coupled to a quantized electromagnetic field due to photon-Cooper pair entanglement. This renormalized energy separation exceeds the prediction of BCS theory, yielding an enhancement that depends on the number of photons and persists even in the presence of electromagnetic vacuum fluctuations. Our work introduces an equilibrium quantum model of microwave-enhanced superconductivity, representing a significant departure from the standard non-equilibrium Eliashberg theory. We further demonstrate that the superconducting condensate exerts a back-action on the electromagnetic field, suppressing electric field fluctuations, including those from the vacuum state. This result is consistent with Glauber and Lewenstein’s field quantization in dielectric media.

arXiv:2511.10364•Physica Scripta•Feb 11, 2026•1 citation

Coherence length in superconductors from weak to strong coupling

L. Benfatto, A. Toschi, S. Caprara +1 more

We investigate the evolution of the superconducting coherence length ${\ensuremath{\xi}}_{0}$ from weak to strong coupling, within both an s-wave and a d-wave lattice model. We show that the identification of ${\ensuremath{\xi}}_{0}$ with the Cooper-pair size ${\ensuremath{\xi}}_{\mathrm{pair}}$ in the weak-coupling regime is meaningful only for a fully gapped (e.g., s-wave) superconductor. Instead in a d-wave superconductor, where ${\ensuremath{\xi}}_{\mathrm{pair}}$ diverges, we show that ${\ensuremath{\xi}}_{0}$ is finite (and of the expected order of magnitude) when properly defined as the characteristic length scale for the correlation function of the amplitude of the superconducting order parameter. The strong-coupling regime is quite intriguing, since the interplay between the particle-particle and the particle-hole channel is no more negligible. In the case of s-wave pairing, which allows for an analytical treatment, we show that ${\ensuremath{\xi}}_{0}$ is of the order of the lattice spacing at finite densities. In the diluted regime ${\ensuremath{\xi}}_{0}$ diverges, recovering the behavior of the coherence length of an effective bosonic system. Similar results are expected to hold for d-wave superconductors. We also comment on the consequences of our results with respect to the physics of high-${T}_{c}$ superconducting cuprates.

arXiv:cond-mat/0109486•Physical review. B, Condensed matter•Aug 12, 2002•32 citations

Enhanced quasiparticle lifetime in a superconductor by selective blocking of recombination phonons with a phononic crystal

Karwan Rostem, Pieter de Visser, Edward J. Wollack

When quasiparticles in a BCS superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at $2\mathrm{\ensuremath{\Delta}}$. We show that a phonon band gap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon band gap can be realized and matched to the recombination energy with a phononic crystal, a periodically patterned dielectric membrane. We discuss in detail the nonequilibrium quasiparticle and phonon distributions that arise in a superconductor due to a phonon band gap and a pair-breaking photon signal. Although intrinsically a nonequilibrium effect, the lifetime enhancement in the small-signal regime is remarkably similar to an estimate from an equilibrium formulation. The equilibrium estimate closely follows $exp({\mathrm{\ensuremath{\Omega}}}_{bg}/{k}_{B}{T}_{b})$, where ${\mathrm{\ensuremath{\Omega}}}_{bg}$ is the phonon band gap energy bandwidth above $2\mathrm{\ensuremath{\Delta}}$ and ${T}_{b}$ is the phonon bath temperature of the coupled electron-phonon system. We discuss the impact of a phononic band gap on the performance of a superconducting circuit element and propose a microwave resonator to measure the enhancement in the quasiparticle lifetime.

arXiv:1805.06991•Physical review. B./Physical review. B•Jul 27, 2018•12 citations

Disentanglement—Induced Superconductivity

Eyal Buks

The current study is motivated by a difficulty in reconciling between particle number conservation and superconductivity. An alternative modeling, which is based on the hypothesis that disentanglement spontaneously ocuurs in quantum systems, is explored. The Fermi-Hubbard mode is employed to demonstrate a disentanglement-induced quantum phase transition into a state with a finite superconducting order parameter. Moreover, the effect of disentanglement on Josephson junction's current phase relation is explored.

arXiv:2505.09207•Entropy•Jun 13, 2025•3 citations
We investigate entanglement of two electron spins forming Cooper pairs in an sss-wave superconductor. The two-electron space-spin density matrix is obtained from the BCS ground state using a two-particle Green's function. It is demonstrated that a two spin state is not given by a spin singlet state but by a Werner state. It is found that the entanglement length, within which two spins are entangled, is not of the order of the coherence length but of the order of the Fermi wave length.
Abstract Microwave dressed states are found to emerge within the superconducting condensate when coupled to a quantized electromagnetic field due to photon-Cooper pair entanglement. This renormalized energy separation exceeds the prediction of BCS theory, yielding an enhancement that depends on the number of photons and persists even in the presence of electromagnetic vacuum fluctuations. Our work introduces an equilibrium quantum model of microwave-enhanced superconductivity, representing a significant departure from the standard non-equilibrium Eliashberg theory. We further demonstrate that the superconducting condensate exerts a back-action on the electromagnetic field, suppressing electric field fluctuations, including those from the vacuum state. This result is consistent with Glauber and Lewenstein’s field quantization in dielectric media.
We investigate the evolution of the superconducting coherence length ${\ensuremath{\xi}}_{0}$ from weak to strong coupling, within both an s-wave and a d-wave lattice model. We show that the identification of ${\ensuremath{\xi}}_{0}$ with the Cooper-pair size ${\ensuremath{\xi}}_{\mathrm{pair}}$ in the weak-coupling regime is meaningful only for a fully gapped (e.g., s-wave) superconductor. Instead in a d-wave superconductor, where ${\ensuremath{\xi}}_{\mathrm{pair}}$ diverges, we show that ${\ensuremath{\xi}}_{0}$ is finite (and of the expected order of magnitude) when properly defined as the characteristic length scale for the correlation function of the amplitude of the superconducting order parameter. The strong-coupling regime is quite intriguing, since the interplay between the particle-particle and the particle-hole channel is no more negligible. In the case of s-wave pairing, which allows for an analytical treatment, we show that ${\ensuremath{\xi}}_{0}$ is of the order of the lattice spacing at finite densities. In the diluted regime ${\ensuremath{\xi}}_{0}$ diverges, recovering the behavior of the coherence length of an effective bosonic system. Similar results are expected to hold for d-wave superconductors. We also comment on the consequences of our results with respect to the physics of high-Tc{T}_{c}Tc​ superconducting cuprates.
When quasiparticles in a BCS superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at $2\mathrm{\ensuremath{\Delta}}$. We show that a phonon band gap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon band gap can be realized and matched to the recombination energy with a phononic crystal, a periodically patterned dielectric membrane. We discuss in detail the nonequilibrium quasiparticle and phonon distributions that arise in a superconductor due to a phonon band gap and a pair-breaking photon signal. Although intrinsically a nonequilibrium effect, the lifetime enhancement in the small-signal regime is remarkably similar to an estimate from an equilibrium formulation. The equilibrium estimate closely follows $exp({\mathrm{\ensuremath{\Omega}}}_{bg}/{k}_{B}{T}_{b})$, where ${\mathrm{\ensuremath{\Omega}}}_{bg}$ is the phonon band gap energy bandwidth above $2\mathrm{\ensuremath{\Delta}}$ and Tb{T}_{b}Tb​ is the phonon bath temperature of the coupled electron-phonon system. We discuss the impact of a phononic band gap on the performance of a superconducting circuit element and propose a microwave resonator to measure the enhancement in the quasiparticle lifetime.
The current study is motivated by a difficulty in reconciling between particle number conservation and superconductivity. An alternative modeling, which is based on the hypothesis that disentanglement spontaneously ocuurs in quantum systems, is explored. The Fermi-Hubbard mode is employed to demonstrate a disentanglement-induced quantum phase transition into a state with a finite superconducting order parameter. Moreover, the effect of disentanglement on Josephson junction's current phase relation is explored.