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Physics

Simulating Superconductivity in Optical Lattices

Ryan Wilkinson

Published Dec 12, 2024• 0 citations
Publisher

Abstract

Researchers have devised a way to use atoms in optical lattices to model high-temperature superconductors, whose behavior is not yet fully understood.By Ryan Wilkinson C ertain materials become superconducting when their electrons pair up.This phenomenon is well understood in conventional superconductors, which operate only at extremely low temperatures.But it remains obscure in some unconventional superconductors, which can function at surprisingly high temperatures.Now Henning Schlömer at the University of Munich and his colleagues have proposed a method to investigate electron behavior in these high-temperature superconductors using a quantum simulator based on atoms arranged in lattices of laser light [1].

DOI
10.1103/physics.17.s144

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Researchers have devised a way to use atoms in optical lattices to model high-temperature superconductors, whose behavior is not yet fully understood.By Ryan Wilkinson C ertain materials become superconducting when their electrons pair up.This phenomenon is well understood in conventional superconductors, which operate only at extremely low temperatures.But it remains obscure in some unconventional superconductors, which can function at surprisingly high temperatures.Now Henning Schlömer at the University of Munich and his colleagues have proposed a method to investigate electron behavior in these high-temperature superconductors using a quantum simulator based on atoms arranged in lattices of laser light [1].
The microscopic origin of high-temperature superconductivity in cuprates remains one of the central open questions in condensed matter physics. Growing experimental and theoretical evidence suggests that the bare single-band Fermi-Hubbard model may not fully capture properties of cuprates such as superconductivity, motivating us to revisit the canonical three-band model of the copper-oxide planes - the Emery model - from which the single-band counterpart was originally derived. Here, we propose and analyze a quantum simulation scheme for realizing the Emery model in regimes relevant to cuprates and infinite-layer nickelates with today's ultracold atom quantum simulation platforms, enabling the exploration of the three-band physics on system sizes that are challenging for current numerical methods. Specifically, we show that a two-dimensional optical lattice with a superimposed pattern of repulsive potentials can be designed to study low-temperature properties for variable parameter regimes of the Emery model relevant to cuprates as well as infinite-layer nickelates. Our results pave the way for real material simulations with ultracold atom quantum simulators and a better understanding of the physics of unconventional superconductors.
This thesis explores certain extraordinary phenomena that occur when a gas of neutral atoms is cooled to the coldest temperatures in the universe --- much colder, in fact, than the electromagnetic radiation that permeates the vacuum of interstellar space. At those extreme temperatures, quantum effects dominate and the collective behaviour of the atoms can have unexpected consequences. For example, Bose-Einstein condensation may occur where the atoms lose their individual identities to coalesce into a macroscopic quantum particle. Although such ultracold atomic gases are interesting in their own right, much of the excitement generated in this field is due to the possibility that studying these gases could shed light on intractable problems in other areas of physics. This is predominantly due to the uniquely high degree of control over various physical parameters that ultracold atomic gases afford to experimentalists. Recent technological advances exploit this advantage to study quantum phenomena in a detail that would not be possible in other systems. For instance, atoms can be made to attract or repel each other, the strength of this interaction can be set to almost any value, and external potentials of various geometries and periodicities can be introduced. In this way, atoms can be used to model phenomena as diverse as the quark-gluon plasmas arising in high-energy particle physics, the colour superfluids conjectured to exist in the core of neutron stars, and the high-temperature superconductivity exhibited by electrons on the ion lattice of certain compounds. Indeed, ultracold atomic gases also have a demonstrated applicability to quantum information and computation. Due to a subtle interplay between electronic and nuclear spins known as the hyperfine interaction, atoms can have either an integer or half-integer total spin quantum number, making them either bosonic or fermionic at low temperatures, respectively. With the exception of chapter 7, the work presented here concerns fermionic atoms in periodic potential formed by interfering laser beams. Indeed, the standing light wave created by the interfering beams gives rise to a lattice potential because of the Stark effect which couples the electronic energy levels of the atoms to the spatially undulating electric field. Furthermore, fermionic atoms can be prepared in two different hyperfine states corresponding to the the \\spin-up" and \\spin-down" quantum states, and as such mimic electrons moving in the lattice structure of solids. This system is well described by the famous Hubbard model which we introduce in chapter 2 and, under certain conditions, undergoes a phase transition into the N eel state which believed to be a precursor to superconductivity in certain high-temperature superconductors. In chapter 3, we calculate precisely how the N eel state may be achieved in an ultracold fermionic atom gas. When the number of spin-up and spin-down atoms is unequal the system becomes spin-canted and exhibits both ferro- and antiferromagnetic characteristics, as we show in chapter 4. We also nd there are topological excitations present in the quantum spin texture known as merons which have never unambiguously been observed before. In order to form a Bose-Einstein condensate, fermionic atoms must rst form pairs, and can do so in two contrasting ways. The relationship between these two qualitatively di erent forms of pairing is described in chapter 5, and we examine how these two types of pairs transform into one another in an optical lattice in chapter 6. Finally, chapter 7 is a detailed eld-theoretic study of pairing as it occurs in an ultracold Bose gas. There, we nd there is an intriguing bosonic analogy of the two forms of fermion pairing and explore the properties of these pairs.
The simulation of high-temperature superconducting materials by implementing strongly correlated fermionic models in optical lattices is one of the major objectives in the field of analog quantum simulation. Here we show that local control and optical bilayer capabilities combined with spatially resolved measurements create a versatile toolbox to study fundamental properties of both nickelate and cuprate high-temperature superconductors. On the one hand, we present a scheme to implement a mixed-dimensional (mixD) bilayer model that has been proposed to capture the essential pairing physics of pressurized bilayer nickelates. This allows for the long-sought realization of a state with long-range superconducting order in current lattice quantum simulation machines. In particular, we show how coherent pairing correlations can be accessed in a partially particle-hole transformed and rotated basis. On the other hand, we demonstrate that control of local gates enables the observation of d -wave pairing order in the two-dimensional (single-layer) repulsive Fermi-Hubbard model through the simulation of a system with attractive interactions. Lastly, we introduce a scheme to measure momentum-resolved dopant densities, providing access to observables complementary to solid-state experiments—which is of particular interest for future studies of the enigmatic pseudogap phase appearing in cuprates. Published by the American Physical Society 2024
We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature range around a tenth of the Fermi temperature, accessible with present experimental techniques: at zero chemical potential, besides a conventional s -wave superconducting phase, unconventional superconductivity with non-local bond pairing arises. In a temperature vs. doping phase diagram, the unconventional superconducting phase exhibits a dome structure, reminiscent of the phase diagram for high-temperature superconductors and heavy fermions.
We investigate the feasibility of simulating different model Hamiltonians used in high-temperature superconductivity. We briefly discuss the most common models and then focus on the simulation of the so-called $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ Hamiltonian using ultra-cold atoms in optical lattices. For this purpose, previous simulation schemes to realize the spin interaction term JJJ are extended. We especially overcome the condition of a filling factor of exactly one, which otherwise would restrict the phase of the simulated system to a Mott-insulator. Using ultra-cold atoms in optical lattices allows simulation of the discussed models for a very wide range of parameters. The time needed to simulate the Hamiltonian is estimated and the accuracy of the simulation process is numerically investigated for small systems.