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arXiv:2505.09207 · Entropy

Disentanglement—Induced Superconductivity

Eyal Buks

Published Jun 13, 2025• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.3390/e27060630

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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.
1. Introduce quantum phase transition in the Bose-Hubbard model. 2. Emphasize vanishing energy scales and universality at the quantum critical point. 3. Introduce microscopic theories to describe the quantum phase transition, and explicitly show the vanishing of energy scales and the critical exponents. 4. Illustrate the emergent Lorentz symmetry and the Higgs mode at the quantum critical point of the Bose-Hubbard model with the particle-hole symmetry. 5. Discuss an experimental probe of the superfluid to the Mott insulator phase transition. 6. Show that the repulsive and the attractive Fermi-Hubbard models are related by the particle-hole symmetry. 7. Discuss the origin of antiferromagnetic order in the repulsive Fermi-Hubbard model at half-filling. 8. Introduce the enlarged SO(4)SO(4)SO(4) symmetry of the Fermi-Hubbard model at half-filling and zero spin imbalance and its physical concequence. 9. Introduce important unsolved challenge issues in the Fermi-Hubbard model. 10. Introduce the concept of eigenstate thermalization hypothesis and many-body localization as opposite to thermalization. 11. Introduce a few metrics to characterize the many-body localization. 12. Emphasize the role of entanglement entropy in characterizing quantum thermalization, and discuss how to measure entanglement entropy in ultracold atom systems.
We investigate the Josephson current through a suspended carbon nanotube double quantum dot which, at sufficiently low temperatures, is characterized by the ground state of the electronic subsystem. Depending on parameters such as a magnetic field or the interdot coupling, the ground state can either be a current-carrying singlet or doublet, or a blockaded triplet state. Since the electron-vibration interaction has been demonstrated to be electrostatically tunable, we study in particular its effect on the current-phase relation. We show that the coupling to the vibration mode can lift the current-suppressing triplet blockade by inducing a quantum phase transition to a ground state of a different total spin. Our key finding is the development of a triple point in the Josephson current parametrized by the resonator coupling and the Josephson phase. The quantum phase transitions around the triple point are directly accessible through the critical current and resilient to moderately finite temperatures. The proposed setup makes the mechanical degree of freedom part of a superconducting hybrid device which is interesting for ultrasensitive displacement detectors.
Abstract Superconductivity is reformulated as a phenomenon in which a stable velocity field is created by a U (1) phase neglected by Dirac in the Schrödinger representation of quantum mechanics. The neglected phase gives rise to a U (1) gauge field expressed as the Berry connection from many-body wave functions. The inclusion of this gauge field transforms the standard particle-number non-conserving formalism of superconductivity to a particle-number conserving one with many results of the former unaltered. In other words, the new formalism indicates that the current standard one is an approximation that effectively takes into account this neglected U (1) gauge field by employing the particle-number non-conserving formalism. Since the standard and new formalisms are physically different, conflicting results are predicted in some cases. We reexamine the Josephson relation and show that a capacitance contribution of the Josephson junction to the U (1) phase is missing in the standard formalism, and inclusion of it indicates that the standard theory actually does not agree with the experiment while the new one does. It is also shown that the dissipative quantum phase transition in Josephson junctions predicted in the standard theory does not exist in the new one in accordance with a recent experiment (Murani et al 2020 Phys. Rev. X 10 021003).
This thesis comprises a wide range of topics. The first work revolves around an active matter system, where a bound state between two run-and-tumble probe particles is induced by a thermal medium, whose interactions with the probe are purely repulsive. The bound state is then induced by the self-trapping behavior of the active particles and the density profile of the thermal particles. There is a surprising analogy between the formation of these bound states and the formation of Cooper pairs in superconductors. The electron, as described by the Dirac equation, may be seen as obeying a master equation of precisely the same form as the master equation of the run-and-tumble particle. Taking this view literally, Cooper pairs are bound states of two run-and-tumble particles whose binding is enabled by the thermal medium in which they reside. The second chapter revolves around these zig-zag electrons which are described by this master-equation formulation of the Dirac equation. This zig-zag behavior may be visualized by the calculation of trajectories that form an extension of Bohmian trajectories. These tools of visualization are then applied to the famous Stern-Gerlach experiment. The third part of the thesis concerns superconductivity, and more specifically the Josephson effect. Josephson junctions form the cornerstone of superconducting quantum technology, providing anharmonicity to qubits and phase sensitivity to SQUIDs. The physics of Josephson junctions is very rich, with features such as Andreev bound states playing a crucial part in the understanding of the Josephson current and the current-phase relation. Yet the microscopic modeling of Josephson junctions remains challenging, and many things remain unexplained. One of the issues addressed in this thesis is the issue of current conservation in the modeling of Josephson junctions, but also in mean-field superconductivity generally. We show that ensuring current conservation has a dramatic effect on the Andreev states and on the current-phase relation, challenging assumptions which have long become standard in the literature. The final part of the thesis is concerned with superconducting qubits, and the effect of the precise shape of the CPR on qubit properties. We uncover resonances of the Andreev bound states, and show that these resonances correspond to lessened anharmonicity for transmon qubits.