Preprint arXiv: 2211.12495 Submitted on 22 Nov 2022

We study induced pairing between two identical fermions mediated by anattractively interacting quantum impurity in two-dimensional systems. Based ona Stochastic Variational Method (SVM), we investigate the influence ofconfinement and finite interaction range effects on the mass ratio beyond whichthe ground state of the quantum three-body problem undergoes a transition froma composite bosonic trimer to an unbound dimer-fermion state. We find thatconfinement as well as a finite interaction range can greatly enhance trimerstability, bringing it within reach of experimental implementations such asfound in ultracold atom systems. In the context of solid-state physics oursolution of the confined three-body problem shows that exciton-mediatedinteractions can become so dominant that they can even overcome detrimentalCoulomb repulsion between electrons in atomically-thin semiconductors. Our workthus paves the way towards a universal understanding of boson-induced pairingacross various fermionic systems at finite density, and opens perspectivestowards realizing novel forms of electron pairing beyond the conventionalparadigm of Cooper pair formation

Dark solitons revealed in Lieb-Liniger eigenstates

We study how dark solitons, i.e. solutions of one-dimensional single-particle nonlinear time-dependent Schr\"odinger equation, emerge from eigenstates of a linear many-body model of contact interacting bosons moving on a ring, the Lieb-Liniger model. This long-standing problem was addressed by various groups, which presented different, seemingly unrelated, procedures to reveal the solitonic waves directly from the many-body model. Here, we propose a unification of these results using a simple Ansatz for the many-body eigenstate of the Lieb-Liniger model, which gives us access to systems of hundreds of atoms. In this approach, mean-field solitons emerge in a single-particle density through repeated measurements of particle positions in the Ansatz state. The post-measurement state turns out to be a wave packet of yrast states of the reduced system.Comment: 8 pages of the main text + 7 pages of appendice

Beyond Gross-Pitaevskii equation for 1D gas: Quasiparticles and solitons

Describing properties of a strongly interacting quantum many-body system poses a serious challenge both for theory and experiment. In this work, we study excitations of one-dimensional repulsive Bose gas for arbitrary interaction strength using a hydrodynamic approach. We use linearization to study particle (type-I) excitations and numerical minimization to study hole (type-II) excitations. We observe a good agreement between our approach and exact solutions of the Lieb-Liniger model for the particle modes and discrepancies for the hole modes. Therefore, the hydrodynamical equations find to be useful for long-wave structures like phonons and of a limited range of applicability for short-wave ones like narrow solitons. We discuss potential further applications of the method.Comment: 27 pages, 11 figures. Submission to SciPos