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arXiv:1708.06826 · Physical Review A

Bipolarons bound by repulsive phonon-mediated interactions

John Sous, Mona Berciu, Roman V. Krems

Published Dec 22, 2017• 15 citations
arXivHTMLPDF

Abstract

When dressed particles (polarons) exchange quantum phonons, the resulting interactions are generally attractive. If the particles have hard-core statistics and the coupling to phonons is through the kinetic energy terms, phonon-mediated interactions are repulsive. Here, we show that such repulsive phonon-mediated interactions bind dressed particles into bipolarons with unique properties. These bipolaron states appear in the gap between phonon excitations, above the two-polaron continuum. While thermodynamically unstable, the bipolaron is protected by energy and momentum conservation and represents a quasiparticle with a large dispersion and a negative effective mass near zero momentum. We discuss possible experimental implementation of the conditions for the formation of such repulsively bound bipolarons.

DOI
10.1103/physreva.96.063619

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When dressed particles (polarons) exchange quantum phonons, the resulting interactions are generally attractive. If the particles have hard-core statistics and the coupling to phonons is through the kinetic energy terms, phonon-mediated interactions are repulsive. Here, we show that such repulsive phonon-mediated interactions bind dressed particles into bipolarons with unique properties. These bipolaron states appear in the gap between phonon excitations, above the two-polaron continuum. While thermodynamically unstable, the bipolaron is protected by energy and momentum conservation and represents a quasiparticle with a large dispersion and a negative effective mass near zero momentum. We discuss possible experimental implementation of the conditions for the formation of such repulsively bound bipolarons.
Quasiparticles and their interactions are a key part of our understanding of quantum many-body systems. Quantum simulation experiments with cold atoms have in recent years advanced our understanding of isolated quasiparticles, but so far they have provided limited information regarding their interactions and possible bound states. Here, we show how exploring mobile impurities immersed in a Bose-Einstein condensate (BEC) in a two-dimensional lattice can address this problem. First, the spectral properties of individual impurities are examined, and in addition to the attractive and repulsive polarons known from continuum gases, we identify a new kind of quasiparticle stable for repulsive boson-impurity interactions. The spatial properties of polarons are calculated showing that there is an increased density of bosons at the site of the impurity both for repulsive and attractive interactions. We then derive an effective Schrödinger equation describing two polarons interacting via the exchange of density oscillations in the BEC, which takes into account strong impurity-boson two-body correlations. Using this, we show that the attractive nature of the effective interaction between two polarons combined with the two-dimensionality of the lattice leads to the formation of bound states - i.e. bipolarons. The wave functions of the bipolarons are examined showing that the ground state is symmetric under particle exchange and therefore relevant for bosonic impurities, whereas the first excited state is doubly degenerate and odd under particle exchange making it relevant for fermionic impurities. Our results show that quantum gas microscopy in optical lattices is a promising platform to explore the spatial properties of polarons as well as to finally observe the elusive bipolarons.
In this thesis, I investigate the behavior of particles dressed by quantum field excitations and random interactions. First I consider two-carrier states in the Peierls model describing the modulation of the particle hopping due to lattice distortions. I compute the spectral response using the Momentum Average approximation. Combining accurate numerical techniques and analytical arguments, I provide a complete picture of the Peierls bipolarons. It is found that polarons bind into strongly bound yet light bipolarons in the singlet sector, even at large values of the electron-phonon coupling strength. At finite electron fillings, these bipolarons may condense into a high-Tc superconductor. On the other hand, phonons mediate a repulsive interaction in the triplet sector, or equivalently (in one dimension), between two hard-core particles, in which case the ground-state dimers bound by sufficiently attractive bare interactions exhibit two sharp transitions, one of which is the first known example of a self-trapping transition at the two-carrier level. In both situations, phonons mediate pair-hopping effective interactions between the carriers. I further study some aspects of the excited spectrum for the two hard-core particles, a situation relevant to ultracold quantum simulators. It is found that the repulsive phonon-mediated interaction binds a repulsive bipolaron embedded in the excited spectrum. I then turn to the study of quenched randomness in an ultracold molecular plasma. I argue that the quenched ultracold plasma presents an experimental platform for studying quantum many-body physics of disordered systems in the long-time and finite energy-density limits. I analyze an experiment that quenches a plasma of nitric oxide to an ultracold system of Rydberg molecules, ions and electrons that exhibits a long-lived state of arrested relaxation. The qualitative features of this state fail to conform with classical models. I develop a microscopic quantum description for the arrested phase based on an effective many-body spin Hamiltonian that includes both dipole-dipole and van der Waals interactions. This effective model appears to offer a way to envision the essential quantum disordered non-equilibrium physics of this system. This thesis thus examines the quantum many-body response in interacting systems coupled to bosonic fields or in disordered environments.
Impurities immersed in a Bose-Einstein condensate (BEC) can interact indirectly through the exchange of Bogoliubov excitations. These impurities, which form dressed quasiparticles known as Bose polarons due to their interaction with the BEC, can pair up to form a bound state called a bipolaron, via an induced interaction. Previous studies on induced interactions have focused primarily on cases with an isotropic excitation spectrum. In this work, we investigate the properties of induced interactions and bipolarons mediated by anisotropic Bogoliubov excitations using field theory. Taking a BEC with spin-orbit coupling as an example, we show that the induced interaction becomes anisotropic. Notably, a double-minima feature appears in the induced interaction in momentum space due to the exchange of roton excitations. Additionally, we calculate the binding energy and wave functions of these bipolarons induced by anisotropic interactions. Unlike previously studied bipolarons formed through the exchange of isotropic phonon excitations, we identify an alternative type of bipolaron whose wave functions feature a double-peak structure under strong impurity-boson interactions. Our work extends the theory of induced interactions from isotropic to anisotropic systems, and it reveals the novel features in both the induced interactions and bipolarons arising from BEC with an unconventional excitation spectrum.
We investigate the ground-state properties of the bipolaron coupled to quantum dispersive optical phonons in the one-dimensional Holstein-Hubbard model. We concentrate on the interplay between the phonon dispersion and the Coulomb repulsion and their mutual effect on the bipolaron effective mass, the binding energy, and the phase diagram. Most surprisingly, the sign of the curvature of the optical phonon dispersion plays a decisive role in the bipolaron binding energy in the presence of the Coulomb repulsion UUU. In particular, when the sign of the phonon dispersion curvature matches the sign of the electron dispersion curvature, the bipolaron remains bound in the strong-coupling limit even when $U\ensuremath{\rightarrow}\ensuremath{\infty}$ and the binding emanates from the exchange of phonons between two electrons residing on adjacent sites. At moderate electron-phonon coupling a light bipolaron exists up to large values of UUU. Finally, an intuitive explanation of the role of the phonon dispersion on the bipolaron binding energy is derived using the strong-coupling limit where the binding emanates from the exchange of phonons between two electrons residing on adjacent sites which leads to enhanced stability of bipolarons at elevated Coulomb repulsion.
In this paper we have studied the properties of a two-fermion system interacting with the phonon field in the framework of the Holstein Hubbard model in one, two and three dimensions. We have chosen the modified Lang-Firsov variational wave function with on-site and nearest-neighbour lattice distortion for the phonon subsystem to obtain an effective electronic Hamiltonian. This effective electronic Hamiltonian is then solved exactly to obtain the binding energy and effective mass of the bipolaron. We investigated the stability of the bipolaronic phase by comparing the ground-state energy of a bipolaron and two free polarons. We observed a critical repulsive on-site Hubbard interaction U c below which the bipolaronic phases are stable for a fixed electron-phonon coupling g . In the absence of on-site repulsion, bipolaronic phases are stable over the entire range of electron-phonon coupling for one dimension, whereas there is a critical electron-phonon coupling g c for formation of a stable bipolaron in two and three dimensions.
A large polaron is a quasiparticle that consists of a nearly free electron interacting with the phonons of a material, whose lattice parameters are much smaller than the polaron scale. The electron-phonon interaction also leads to an attractive interaction between electrons, which can allow two polarons to pair up and form a bipolaron. It has been shown that large bipolarons can form in theory due to strong one-electron--one-phonon coupling, but they have not been seen in real materials because the critical value of the required electron-phonon interaction is too large. Here, we investigate the effect of one-electron--two-phonon coupling on the large bipolaron problem. Starting from a generalization of the Fr\"ohlich Hamiltonian that includes both the standard one-electron--one-phonon interaction as well as an anharmonic one-electron--two-phonon interaction, we use the path-integral method to find a semianalytical upper bound for the bipolaron energy that is valid at all values of the Fr\"ohlich coupling strength $\ensuremath{\alpha}$. We find the bipolaron phase diagram and conditions for the bipolaron stability by comparing the bipolaron energy to the energy of two free polarons. The critical value of the Fr\"ohlich coupling strength ${\ensuremath{\alpha}}_{\text{crit}}$ is calculated as a function of the strength of the one-electron--two-phonon interaction. The results suggest that large bipolaron formation is more likely in materials with significant one-electron--two-phonon interaction as well as strong one-electron--one-phonon interaction, such as strontium titanate.