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arXiv:2607.19467

Quantum Simulation of Semiconductor Excitons in Ultracold Dipolar Fermi Gases

F. Hirsch, Oriana K. Diessel, Rafał Ołdziejewski, Richard Schmidt

Published Jul 21, 2026• 0 citations
arXivHTMLPDF

Abstract

Inspired by the progress on the study of exciton physics in atomically thin transition metal dichalcogenide (TMD) semiconductors, we investigate the formation of analogs of excitons in cold atomic systems. To this end, we consider single-component fermions comprised of ultracold ground-state molecules or dipolar atoms in a hexagonal optical lattice. An energy offset between triangular sublattices opens up a band gap with degeneracies at the K/K' points as in TMDs. We predict the existence of cold atomic excitons and show that cold atoms allow us to study excitons from the weak-coupling regime, where effective mass models apply, to the strong-interaction regime, described by flat-band models. We demonstrate how these excitons can be observed using lattice modulation spectroscopy, and how their wave functions can be mapped out using quantum gas microscopy. Firmly establishing the idea of quantum simulation of semiconductor physics, this work lays the foundation for simulating complex electronic states such as trions, polarons and excitonic insulators.

DOI
10.48550/arxiv.2607.19467

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Inspired by the progress on the study of exciton physics in atomically thin transition metal dichalcogenide (TMD) semiconductors, we investigate the formation of analogs of excitons in cold atomic systems. To this end, we consider single-component fermions comprised of ultracold ground-state molecules or dipolar atoms in a hexagonal optical lattice. An energy offset between triangular sublattices opens up a band gap with degeneracies at the K/K' points as in TMDs. We predict the existence of cold atomic excitons and show that cold atoms allow us to study excitons from the weak-coupling regime, where effective mass models apply, to the strong-interaction regime, described by flat-band models. We demonstrate how these excitons can be observed using lattice modulation spectroscopy, and how their wave functions can be mapped out using quantum gas microscopy. Firmly establishing the idea of quantum simulation of semiconductor physics, this work lays the foundation for simulating complex electronic states such as trions, polarons and excitonic insulators.
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This tutorial is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules that interact via dipolar forces, and that are cooled below the quantum degeneracy temperature, typically in the nK range. When such a degenerate quantum gas is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur. These systems realize then extended Hubbard-type models, and can be brought to a strongly correlated regime. The physical properties of such gases, dominated by the long-range, anisotropic dipole-dipole interactions, are discussed using the mean-field approximations, and exact Quantum Monte Carlo techniques (the Worm algorithm).
A generic scenario of a crossover between weak-coupling and strong-coupling limits of a many-body quantum system is studied. Powerful numerical methods of investigating the strongly correlated regime are developed and applied to answering a number of important questions of the strongly correlated fermions physics. The internal structure of an exciton in an insulating medium is studied throughout the crossover between the (analytically solvable) strong- and weak-coupling limits. In the intermediate regime, accurate results for the exciton ground state are obtained and used to establish the limits of applicability of the corresponding limiting cases for the first time. A novel combination of the diagrammatic determinant Monte Carlo and the worm algorithm is developed and used for investigating the unitarity regime of the BEC-BCS crossover via simulating the dilute Fermi-Hubbard model. Superfluid phase transition and thermodynamic properties of the normal state are characterized for both lattice fermions and continuum unitary Fermi gas. The relation to current experiments with trapped ultracold quantum gases is discussed.
Optical lattices provide ideal experimental tools for simulating a wide variety of physical systems. They exhibit excellent coherence properties, their microscopic dynamics are well-understood, and they can be dynamically controlled with great precision. Recent advances in cooling and trapping gases of dipolar molecules and Rydberg atoms have further increased the versatility of optical lattices as quantum simulators, particularly for solid state systems possessing long-range interactions. In this thesis we further examine the microscopic properties of cold atoms trapped in an optical lattice, going beyond the case where the lattice axes are orthogonal. We present a transformation of the single-particle energy eigenstates to a complete, orthonormal basis of so-called 'generalised Wannier functions' that are localised to each lattice site. Generalised Wannier functions, as opposed to ordinary Wannier functions, are formed by mixing states between bands and are required when the bands are degenerate. We modify an algorithm devised by Marzari and Vanderbilt (Phys. Rev. B 56(20) 12847) for calculating maximally localised generalised Wannier functions, specifically to determine these functions for optical lattice systems of arbitrary geometry, including those with degenerate lower bands. Moreover, we overcome an issue with the initialisation of the original algorithm to find the maximally localised set without fail. We then present results for a variety of optical lattice systems in one- and two-dimensions, including hexagonal and Kagomé geometries. In each case we use the generalised Wannier functions to calculate the hopping and interaction parameters, and thus determine a reduced form of the system's Hamiltonian that contains only local interactions. We also study two spin-1/2 systems with long-range interactions as paradigm examples of the models that can be simulated using optical lattices loaded with dipolar molecules. We first examine the critical properties of a 1D spin-1/2 Ising chain possessing exponentially decaying interactions as the range of the interactions is increased. Using the infinite density matrix renormalisation group method, we calculate the location of the critical point and observe a smooth approach to the classical mean-field result in the limit of infinite-ranged interactions. We go on to consider the quantum dynamics of a single spin-1/2 coupled to a bath of interacting spins as a model for decoherence in solid state quantum memories. The large degree of symmetry of the bath, described by the infinite-ranged Lipkin-Meshkov-Glick model, allows us to find parameter regimes where the initial qubit state is revived at well-defined times after the qubit preparation. We observe that these times may become independent of the bath size for large baths and thus enable faithful qubit storage even in the presence of strong coupling to the bath.
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Ultracold atomic gases may be the ultimate quantum simulator.These isolated systems have the lowest temperatures in the observable universe, and their properties and interactions can be precisely and accurately tuned across a full spectrum of behaviors, from few-body physics to highly-correlated many-body effects.The ability to impose potentials on and tune interactions within ultracold gases to mimic complex systems mean they could become a theorist's playground.One of their great strengths, however, is also one of the largest obstacles to this dream: isolation.This thesis touches on both of these themes.First, methods to characterize phases and quantum critical points, and to construct finite temperature phase diagrams using experimentally accessible observables in the Bose Hubbard model are discussed.Then, the transition from a weakly to a strongly interacting Bose-Fermi mixture in the continuum is analyzed using zero temperature numerical techniques.Real materials can be emulated by ultracold atomic gases loaded into optical lattice potentials.We discuss the characteristics of a single boson species trapped in an optical lattice (described by the Bose Hubbard model) and the hallmarks of the quantum critical region that separates the superfluid and the Mott insulator ground states.We propose a method to map the quantum critical region using the single, experimentally accessible, local quantity R, the ratio of compressibility to local number fluctuations.The procedure to map a phase diagram with R is easily generalized to inhomogeneous systems and generic many-body Hamiltonians.We illustrate it here using quantum Monte Carlo simulations of the 2D Bose Hubbard model.Secondly, we investigate the transition from a degenerate Fermi gas weakly coupled List of Tables Table Page 2.1 Techniques to Probe Atoms in Optical Lattices . . . . . .