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arXiv:2203.00104

Entanglement between quasiparticles in superconducting islands mediated by a single spin

Juan Carlos Estrada Saldaña, Alexandros Vekris, Luka Pavešič, Rok Žitko, Kasper Grove‐Rasmussen, Jesper Nygård

Published Feb 28, 2022• 1 citation
arXivHTMLPDF

Abstract

Condensed matter is composed of a small set of identical units, yet it shows an immense range of behaviour. Recently, an array of cold atoms was used to generate long-range quantum entanglement, a property of topological matter. Another approach to strong non-local correlations employs the macroscopic coherence of superconductors. Impurity spins in superconductors are thought to be unamenable to the formation of long-range spin entanglement because each spin tends to be screened by binding to a quasiparticle from the superconductor to form a local singlet. Here we demonstrate that it is possible to attach a second quasiparticle to the spin, overscreening it into a doublet state carrying ferromagnetic correlations between two quasiparticles over a micrometer distance. To demonstrate this effect, which is strongest for equal binding, we symmetrically couple the spin of a quantum dot to two ultrasmall superconducting islands. The overscreened state requires sufficiently large Coulomb repulsion and exchange binding to become well defined. We predict that this state will carry long-range correlations for an alternating chain of quantum dots and superconducting islands, opening a new route to controllable large-scale entanglement in the solid state.

DOI
10.48550/arxiv.2203.00104

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Condensed matter is composed of a small set of identical units, yet it shows an immense range of behaviour. Recently, an array of cold atoms was used to generate long-range quantum entanglement, a property of topological matter. Another approach to strong non-local correlations employs the macroscopic coherence of superconductors. Impurity spins in superconductors are thought to be unamenable to the formation of long-range spin entanglement because each spin tends to be screened by binding to a quasiparticle from the superconductor to form a local singlet. Here we demonstrate that it is possible to attach a second quasiparticle to the spin, overscreening it into a doublet state carrying ferromagnetic correlations between two quasiparticles over a micrometer distance. To demonstrate this effect, which is strongest for equal binding, we symmetrically couple the spin of a quantum dot to two ultrasmall superconducting islands. The overscreened state requires sufficiently large Coulomb repulsion and exchange binding to become well defined. We predict that this state will carry long-range correlations for an alternating chain of quantum dots and superconducting islands, opening a new route to controllable large-scale entanglement in the solid state.
Controlled coupling between distant particles is a key requirement for the implementation of quantum information technologies. A promising platform are hybrid systems of semiconducting quantum dots coupled to superconducting islands, where the tunability of the dots is combined with the macroscopic coherence of the islands to produce states with non-local correlations, e.g. in Cooper pair splitters. Electrons in hybrid quantum dots are typically not amenable to long-distance spin alignment as they tend to be screened into a localized singlet state by bound superconducting quasiparticles. However, two quasiparticles coming from different superconductors can overscreen the quantum dot into a doublet state, leading to ferromagnetic correlations between the superconducting islands. We present experimental evidence of a stabilized overscreened state, implying correlated quasiparticles over a micrometer distance. We propose alternating chains of quantum dots and superconducting islands as a novel platform for controllable large-scale spin coupling.
We present a theoretical study of a system consisting of a superconducting island and two quantum dots, a possible platform for building qubits and Cooper pair splitters, in the regime where each dot hosts a single electron and, hence, carries a magnetic moment. We focus on the case where the dots are coupled to overlapping superconductor states and we study whether the spins are ferromagnetically or antiferromagnetically aligned. We show that if the total number of particles is even the spins align antiferromagnetically in the flatband limit, i.e., when the bandwidth of the superconductor is negligibly small, but they align ferromagnetically if the bandwidth is finite and above some value. If the total number of particles is odd, the alignment is ferromagnetic independently from the bandwidth. This implies that the results of the flatband limit are applicable only within a restricted parameter regime for realistic superconducting qubit systems and that some care is required in applying simplified models to devices such as Cooper pair splitters.
In the field of nanoelectronics, one seeks to combine quantum mechanical effects with macroscopic entities such as currents in order to find new ways of storing and manipulating information. One possibility to accomplish this is to use the quantum correlations found in superconductors. Teaming superconductors with normal metals and magnetic systems, one can obtain novel correlation and fluctuation effects. \n\nIn the first work of this thesis, we examine how charge correlations in a metallic dot are modified due to the presence of a capacitively coupled superconducting island. It is possible to overcome the Coulomb repulsion between electrons in a hybrid double-dot system consisting of a metallic island coupled capacitively to a Cooper-pair box. The superconducting island S acts as a dynamic gate on the metallic island N and in the strong coupling regime the electric charge of the Cooper pairs in S and their fluctuations are able to overscreen the repulsion between electrons in N. This produces an attractive interaction between two additional electrons in the metallic island and results in a non-monotonous charging curve of the metallic island. \n\nThe second part of the thesis considers how the dynamics of a precessing molecular magnetic moment affects the Josephson current. The precession gives rise to a time-dependent tunnel potential which not only creates different tunneling probabilities for spin-up and spin-down quasiparticles, but also introduces a time-dependent spin-flip term. In particular, we study the effects of the spin-flip term alone on the Josephson current between two spin-singlet superconductors as a function of precession frequency and junction transparency. The system displays a nonequilibrium steady-state solution which depends on the precession frequency of the classical spin.\n\n\n
Solid-state spin qubits are promising candidates for the realization of a quantum computer due to their long coherence times and easy electrical manipulation. However, spin-spin interactions, which are needed for entangling gates, have only limited range as they generally rely on tunneling between neighboring quantum dots. This severely constrains scalability. Proposals to extend the interaction range generally focus on coherent electron transport between dots or on extending the coupling range. Here, we study a setup in which such an extension is obtained by using a superconductor as a quantum mediator. Because of its gap, the superconductor effectively acts as a long tunnel barrier. We analyze the impact of spin-orbit (SO) coupling, external magnetic fields, and the geometry of the superconductor. We show that while spin-nonconserving tunneling between the dots and the superconductor due to SO coupling does not affect the exchange interaction, strong SO scattering in the superconducting bulk is detrimental. Moreover, we find that the addition of an external magnetic field decreases the strength of the exchange interaction. Fortunately, the geometry of the superconducting link offers a lot of room to optimize the interaction range, with gains of over an order of magnitude from a two-dimensional (2D) film to a quasi-1D strip. We estimate that for superconductors with weak SO coupling (e.g., aluminum), exchange rates of up to 100 MHz over a micron-scale range can be achieved with this setup in the presence of magnetic fields of the order of 100 mT.
We consider the subgap physics of a hybrid double-quantum dot Cooper-pair splitter with large single-level spacings, in the presence of tunneling between the dots and finite Coulomb intra- and interdot Coulomb repulsion. In the limit of a large superconducting gap, we treat the coupling of the dots to the superconductor exactly. We employ a generalized master-equation method, which easily yields currents, noise, and cross-correlators. In particular, for finite inter- and intradot Coulomb interaction, we investigate how the transport properties are determined by the interplay between local and nonlocal tunneling processes between the superconductor and the dots. We examine the effect of interdot tunneling on the particle-hole symmetry of the currents with and without spin-orbit interaction. We show that spin-orbit interaction in combination with finite Coulomb energy opens the possibility to control the nonlocal entanglement and its symmetry (singlet/triplet). We demonstrate that the generation of nonlocal entanglement can be achieved even without any direct nonlocal coupling to the superconducting lead.
Several recent experiments have shown that long-range exchange interactions can determine collective magnetic ground states of nanostructures in bulk and on surfaces. The ability to generate and control entanglement in a system with long-range interaction will be of great importance for future quantum technology. An important step forward to reach this goal is the creation of entangled states for spins of distant magnetic atoms. Herein, the generation of long-distance entanglement between remote spins at large separations in bulk and on surface is studied theoretically, based on a quantum spin Hamiltonian and time-dependent Schrödinger equation for experimentally realized conditions. We demonstrate that long-distance entanglement can be generated between remote spins by using an appropriate quantum spin chain (a quantum mediator), composed by sets of antiferromagnetically coupled spin dimers. Ground state properties and quantum spin dynamics of entangled atoms are studied. We demonstrate that one can increase or suppress entanglement by adding a single spin in the mediator. The obtained result is explained by monogamy property of entanglement distribution inside a quantum spin system. We present a novel approach for non-local sensing of remote magnetic adatoms via spin entanglement.