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arXiv:1710.08925 · Physical review. B./Physical review. B

Angle-resolved photoemission spectroscopy with quantum gas microscopes

Annabelle Bohrdt, Daniel Greif, Eugene Demler, Michael Knap, Fabian Grusdt

Published Mar 13, 2018• 66 citations
arXivHTMLPDF

Abstract

Quantum gas microscopes are a promising tool to study interacting quantum many-body systems and bridge the gap between theoretical models and real materials. One of the most powerful experimental methods in solids is angle-resolved photoemission spectroscopy (ARPES), which measures the single-particle spectral function. The authors propose a measurement scheme to experimentally access the momentum- and energy-resolved spectral function in a quantum gas microscope. As an example for possible applications, the spectrum of a single hole excitation in one-dimensional $t$-$J$ models is calculated and analyzed. A sharp asymmetry in the distribution of spectral weight, reminiscent of the Fermi arcs observed in the pseudogap phase of cuprates, appears in the case of an isotropic Heisenberg spin chain.

DOI
10.1103/physrevb.97.125117

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Quantum gas microscopes are a promising tool to study interacting quantum many-body systems and bridge the gap between theoretical models and real materials. One of the most powerful experimental methods in solids is angle-resolved photoemission spectroscopy (ARPES), which measures the single-particle spectral function. The authors propose a measurement scheme to experimentally access the momentum- and energy-resolved spectral function in a quantum gas microscope. As an example for possible applications, the spectrum of a single hole excitation in one-dimensional ttt-JJJ models is calculated and analyzed. A sharp asymmetry in the distribution of spectral weight, reminiscent of the Fermi arcs observed in the pseudogap phase of cuprates, appears in the case of an isotropic Heisenberg spin chain.
Angle-resolved photoemission spectroscopy (ARPES) has revealed peculiar properties of mobile dopants in correlated antiferromagnets (AFMs). But, describing them theoretically, even in simplified toy models, remains a challenge. Here, we study ARPES spectra of a single mobile hole in the $t\ensuremath{-}J$ model. Recent progress in the microscopic description of mobile dopants allows us to use a geometric decoupling of spin and charge fluctuations at strong couplings, from which we conjecture a one-to-one relation of the one-dopant spectral function and the spectrum of a constituting spinon in the undoped parent AFM. We thoroughly test this hypothesis for a single hole doped into a two-dimensional Heisenberg AFM by comparing our semianalytical predictions to previous quantum Monte Carlo results and our large-scale time-dependent matrix product state calculations of the spectral function. Our conclusion is supported by a microscopic trial wave function describing spinon-chargon bound states, which captures the momentum and t/Jt/Jt/J dependence of the quasiparticle residue. From our conjecture we speculate that ARPES measurements in the pseudogap phase of cuprates may directly reveal the Dirac-fermion nature of the constituting spinons. Specifically, we demonstrate that our trial wave function provides a microscopic explanation for the sudden drop of spectral weight around the nodal point associated with the formation of Fermi arcs, assuming that additional frustration suppresses long-range AFM ordering. We benchmark our results by studying the crossover from two to one dimension, where spinons and chargons are confined and deconfined, respectively.
Quantum simulation experiments have started to explore regimes that are not accessible with exact numerical methods. To probe these systems and enable new physical insights, the need for measurement protocols arises that can bridge the gap to solid-state experiments, and at the same time make optimal use of the capabilities of quantum simulation experiments. Here we propose applying time-dependent photoemission spectroscopy, an established tool in solid-state systems, in cold atom quantum simulators. Concretely, we suggest combining the method with large magnetic field gradients, unattainable in experiments on real materials, to drive Bloch oscillations of spinons, the emergent quasiparticles of spin liquids. We show in exact diagonalization simulations of the one-dimensional $t\text{\ensuremath{-}}J$ model with a single hole that the spinons start to populate previously unoccupied states in an effective band structure, thus allowing us to visualize states invisible in the equilibrium spectrum. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons. In numerical simulations of small two-dimensional systems, spectral weight appears at the ground-state energy at momentum $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$, where the equilibrium spectral response is strongly suppressed up to higher energies, indicating a possible route toward solving the mystery of the Fermi arcs in the cuprate materials.
The ability to study ultracold atomic Fermi gases holds the promise of significant advances in testing fundamental theories of many-body quantum physics. Of particular interest are strongly interacting Fermi gases in the BCS to BEC crossover that exhibit a transition to a superfluid state at temperatures near 0.2TF , where TF is the Fermi temperature. This transition, as a fraction of TF, is extremely high compared to any known superfluid or superconductor. These gases are also in a universal regime where the physics is independent of the details of the atomic interactions and is therefore relevant to fields as diverse as condensed matter, nuclear physics and astrophysics. In this thesis, I present an experimental probe of atomic gases that uses momentum-resolved RF spectroscopy to realize an analog of angle-resolved photoemission spectroscopy (ARPES) in materials. This measurement reveals the energy and momentum of single-particle states in the strongly interacting Fermi gas. In condensed matter, ARPES has proved to be one of the most powerful experimental techniques for studying the electronic structure of strongly correlated electron materials. The ability to perform analogous measurements in ultracold Fermi gases constitutes a significant advance in our ability to directly connect ultracold atomic gases to strongly correlated electron systems. Taking advantage of this new measurement technique, I investigate a long-standing problem in the field of strongly interacting fermions, namely whether a pseudogap state consisting of incoherent fermion pairs exists at temperatures above the critical temperature for superfluidity. The photoemission data I present provide strong evidence for this state and have implications for fundamental theories of strongly interacting Fermi gases and strongly correlated electron materials. I also discuss the experimental confirmation of recently predicted universal relations for strongly interacting Fermi gases, as well as some of the first experiments involving atomic Fermi gases with p-wave pairing.
In many cases the standard perturbation approach appears to be too simple to describe precisely the angle-resolved photoemission spectrum of a strongly correlated electron system. In particular, to describe the momentum asymmetry observed in the photoemission spectra of high-Tc{T}_{c}Tc​ cuprates, a phenomenological approach based on an extremely correlated Fermi-liquid model has been recently introduced. Here we analyze the general structure of the Green's function of quasiparticles in strongly correlated electron systems and stress that it is defined not only by the self-energy of Hubbard quasiparticles but also by a strength operator. The latter leads to an additional odd momentum contribution to the spectral function and alone can explain the observed asymmetry. So, the asymmetry of the angle-resolved photoemission spectra can be a measure of the strength of electron correlations in materials.
We investigate a momentum-resolved Raman spectroscopy technique which is able to probe the one-body spectral function and the quasiparticle states of a gas of strongly interacting ultracold atoms. This technique is inspired by angle-resolved photoemission spectroscopy, a powerful experimental probe of electronic states in solid-state systems. Quantitative examples of experimentally accessible spectra are given for the most significant regimes along the BEC-BCS crossover. When the theory is specialized to rf spectroscopy, agreement is found with recent experimental data. The main advantages of this Raman spectroscopy over existing techniques are pointed out.