Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms (1612.08436v1)

Abstract: Many exotic phenomena in strongly correlated electron systems emerge from the interplay between spin and motional degrees of freedom. For example, doping an antiferromagnet gives rise to interesting phases including pseudogap states and high-temperature superconductors. A promising route towards achieving a complete understanding of these materials begins with analytic and computational analysis of simplified models. Quantum simulation has recently emerged as a complementary approach towards understanding these models. Ultracold fermions in optical lattices offer the potential to answer open questions on the low-temperature regime of the doped Hubbard model, which is thought to capture essential aspects of the cuprate superconductor phase diagram but is numerically intractable in that parameter regime. A new perspective is afforded by quantum gas microscopy of fermions, which allows readout of magnetic correlations at the site-resolved level. Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a 2D square lattice of approximately 80 sites. Using site-resolved imaging, we detect (finite-size) antiferromagnetic long-range order (LRO) through the development of a peak in the spin structure factor and the divergence of the correlation length that reaches the size of the system. At our lowest temperature of T/t = 0.25(2) we find strong order across the entire sample. Our experimental platform enables doping away from half filling, where pseudogap states and stripe ordering are expected, but theoretical methods become numerically intractable. In this regime we find that the antiferromagnetic LRO persists to hole dopings of about 15%, providing a guideline for computational methods. Our results demonstrate that quantum gas microscopy of ultracold fermions in optical lattices can now address open questions on the low-temperature Hubbard model.

• The paper demonstrates the experimental realization of long-range antiferromagnetic order in a 2D Hubbard model using ultracold 6Li atoms and quantum gas microscopy.
• It achieves site-resolved observation of magnetic correlations at temperatures as low as T/t=0.25 in an 80-site optical lattice.
• Doping experiments show antiferromagnetism persists up to 15% doping, offering insights for high-temperature superconductivity research.

Experimental Realization of a Long-Range Antiferromagnet in the Hubbard Model with Ultracold Atoms

This paper reports on a significant experimental achievement in the paper of quantum magnetism through the realization of long-range antiferromagnetic order using ultracold atoms in an optical lattice. The researchers successfully employed quantum gas microscopy to observe site-resolved magnetic correlations in a two-dimensional (2D) Fermi gas simulated by the Hubbard model. This work allows for exploration into the low-temperature regime of the doped Hubbard model, which has significant implications for understanding high-temperature superconductivity and other phenomena associated with strongly correlated electron systems.

Theoretical Context

The Hubbard model serves as a fundamental framework for examining the interplay between electron kinetic energy and on-site interactions. At half-filling and strong coupling (i.e., where the interaction energy $U$ predominates over the kinetic energy $t$), it reduces to the Heisenberg model, predicting antiferromagnetic order. Away from half-filling, this model exhibits complex many-body interactions, posing challenges for numerical methods due to the fermion sign problem. The transition from a commensurate to incommensurate long-range order in finite systems as doping increases remains a critical area of paper.

Experimental Setup

The team's experimental platform consists of a 2D square optical lattice populated by a mixture of fermionic atoms (specifically $^6$Li). It is capable of achieving temperatures ($T/t = 0.25(2)$) low enough to induce strong antiferromagnetic long-range order across an array of approximately 80 lattice sites. Achieving such low temperatures and uniformity in density within the atomic cloud were pivotal for the observation. The setup allows for precise manipulation and imaging facilitated by a quantum gas microscope.

Observations and Results

Magnetization and Correlations: The paper documents the observation of site-resolved magnetization, demonstrating an antiferromagnetic checkerboard pattern that signals long-range order. The spin structure factor shows a clear peak at wavevector $(\pi/a,\pi/a)$, indicative of antiferromagnetic order. At the lowest temperatures studied, the staggered magnetization approaches values predicted by the ground state of the Heisenberg model.

Doping Investigations: Upon doping the system away from half-filling, antiferromagnetic long-range order persisted up to a doping level of approximately 15%. Beyond this, the staggered magnetization decreases significantly, aligning with expectations of the limitations of theoretical methods at such dopings. This result provides crucial guidance for numerical simulations and comparisons to predictions for high-temperature cuprate superconductors.

Temperature Dependence: The correlation length measured follows an exponential relationship with inverse temperature, validating expectations from the quantum non-linear sigma model. The fitted spin stiffness was found to be in agreement with theoretical predictions, underlying a strong yet finite antiferromagnetic order in the finite-sized system.

Implications and Future Directions

This experimental realization of a 2D antiferromagnetic state provides a powerful platform for probing quantum phases of the Hubbard model at parameter regimes inaccessible to classical simulations. It opens the potential for studies into complex phenomena such as pseudogap states and stripe order in high-temperature superconductors. Future developments may include examining transitions to d-wave superconductivity as temperatures are further reduced or introducing novel states through modifications of the lattice geometry or interactions—potentially with the inclusion of synthetic gauge fields or long-range interactions. The ability to directly measure entanglement and coherent dynamics in non-equilibrium states holds promise for significant advancements in quantum simulation.

Overall, this demonstration strengthens the capability of ultracold atom systems to simulate condensed matter phenomena and addresses longstanding questions in many-body physics.