Quantum simulation of antiferromagnetic spin chains in an optical lattice

Abstract

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications from high temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers due to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we employ a degenerate Bose gas confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary an applied field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase the interaction between the spins is overwhelmed by the applied field which aligns the spins. In the antiferromagnetic phase the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in-situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, improving our understanding of real magnetic materials.Ensembles of quantum spins arranged on a lattice and coupled to one another through magnetic interactions constitute a paradigmatic model-system in condensed matter physics. Such systems produce a rich array of magnetically-ordered ground states such as paramagnets, ferromagnets and antiferromagnets. Certain geometries and interactions induce competition between these orderings in the form of frustration, resulting in spin liquids [1] and spin glasses [2], as well as phases with topological order [3]. Varying system parameters can induce quantum phase transitions between the various phases [4]. A deeper understanding of the competition and resulting transitions between magnetic phases would provide valuable insights into the properties of complex materials such as high-temperature superconductors [5], and more generally into the intricate behaviours that can emerge when many simple quantum mechanical objects interact with one another.Studying quantum phase transitions of magnetic condensed matter systems is hindered by the complex structure and interactions present in such systems, as well as the difficulty of controllably varying system parameters. With a few notable exceptions [6,7], these issues make it difficult to capture the physics of such systems with simple models. Accordingly, there is a growing effort underway to realize condensed matter simulators using cold atom systems [8,9] which are understood from first principles. The exquisite control afforded by cold atom experiments permits adiabatic tuning of such systems through quantum phase transitions [9,10], enabling investigations of criticality [11,12] and scaling [13]. Time-resolved local readout [14][15]...

Topological spin models in Rydberg lattices

“…7a the dynamics according to the effective Hamiltonian in Eq. (14). We find that the largest excitation probabilities can be found along the lower edge and to the right of the initially excited site.…”

“…(2) to our model in Eq. (14). First, we note that the level shifts induced between Zeeman substates must be large compared to V 0 and hence of the order of 10 MHz.…”

“…One promising perspective is to use this set-up for investigating the rich physics of quantum magnetism [13][14][15] and strongly correlated spin systems that are extremely challenging to simulate on a classical computer. However, the simulation of magnetic phenomena with cold atoms faces two key challenges.…”

Low depth quantum circuits for Ising models

“…All schemes translate naturally into global operations and measurements supplemented by edge addressability. This is natural for certain architectures such as cold trapped atoms in optical lattices [42], or superconducting qubit arrays [43]. Furthermore, this kind of quantum processing can be made fault tolerant without demanding more addressability as shown in [44].…”

Two-channel Bose-Hubbard model of atoms at a Feshbach resonance

“…In this respect the accurate determination of the location and width of the avoided crossings with molecules with center-of-mass excitation at a Feshbach resonance is very important to interpret experimental measurements. Multi-band systems of ultracold atoms [37], especially those employing resonances with repulsively bound states can be used to quantum simulate solid-state systems [38] and might be eventually used to perform also universal quantum computations [39]. The correct description and understanding of both attractively and repulsively bound states in different Bloch bands appearing at a Feshbach resonance could add more flexibility to further extend the capabilities of ultracold atoms in optical lattices.…”