Jirayu Mongkolkiattichai of the University of Virginia and colleagues have extended quantum gas microscopy to study three-flavor Fermi lattice gases, achieving site- and flavor-resolved detection to map the phase diagram of the three-flavor Hubbard model. The work reveals signatures of flavor-selective localization and selective pairing at temperatures down to the tunneling energy scale, offering new insight into strongly correlated many-body systems.
These three-component fermionic systems mirror the three flavors found in quantum chromodynamics, potentially paving the way to study phenomena like color superfluidity with increased phase space density and the observation of a novel pair Mott phase.
Quantum Gas Microscopy Maps Three-Flavor Hubbard Systems
The team’s experiments use a quantum gas microscope capable of distinguishing between three internal states, or “flavors,” of fermionic atoms trapped in a lattice of light. This precise control and measurement are important for exploring the complex interplay of interactions in these systems. The research focuses on breaking the SU(2) symmetry inherent in the standard Hubbard model by introducing these additional species, which in turn generates a wider range of potential exotic quantum phases.
Three-component fermionic systems serve as analogous models for quantum chromodynamics, where the three flavors represent the fundamental constituents of matter. By tuning the interactions between these flavors, the researchers investigated the resulting phase diagram, revealing the emergence of distinct behaviors depending on the interaction strengths. Specifically, they observed the onset of a three-flavor Mott insulating state, where electrons are localized due to strong repulsive interactions, alongside selective pairing of specific flavor combinations.
Measurements revealed a competition in the formation of doublons, pairs of atoms occupying the same lattice site, between flavors 1 and 3, and flavors 2 and 3, with a significant fraction of triplons also present. “In the CAP regime there is a competition in the formation of doublons and doublons and we find a significant triplon fraction,” the researchers state in their published work. This observation highlights the complex correlations arising from the interplay of multiple flavors and interactions.
The team also detected both ferromagnetic and antiferromagnetic correlations between different flavors within the same system, further demonstrating the rich magnetic properties of these gases. The ability to directly measure flavor densities, pairing correlations, and triply occupied sites through quantum gas microscopy is central to these findings. Liyu Liu, also of the University of Virginia, and Sohail Dasgupta and Kaden R. A. Hazzard of Rice University contributed to the development of this technique.
Peter Schauss, affiliated with both the University of Virginia and Universität Hamburg, also participated in the research. These observations confirm predictions made by numerical linked-cluster expansion calculations, validating the experimental approach and providing a foundation for future investigations into more complex quantum phenomena.
Site- and Flavor-Resolved Imaging of Fermi Lattice Gases
Flavor-resolved quantum gas microscopy now allows direct observation of triply occupied sites within three-flavor Fermi lattice gases, a capability demonstrated through imaging systems with equal flavor populations and broken SU(3) symmetry. This technique enables investigation of the interplay between pairs of flavors, focusing on balanced mixtures where three-body losses are minimized, and revealing details previously inaccessible in these complex quantum systems. Researchers achieved single-site resolution using a flavor-resolved quantum gas microscope, extending its application to the Hubbard regime and opening new avenues for studying exotic quantum phases.
Tunable Interactions Define Three-Flavor System Parameters
Researchers now directly observe the interplay between flavor pairs within three-flavor Fermi lattice systems, using a flavor-resolved quantum gas microscope to achieve single-site resolution. This imaging technique allows for the investigation of these systems with tunable, unequal interactions across a broad parameter range, focusing on flavor-balanced mixtures where three-body losses are minimized.
The ability to manipulate interactions is key, as the team explores regimes predicted to host diverse quantum phases, including distinct Mott insulating states dependent on interaction strengths. The experimental setup relies on precise control of magnetic fields to achieve target interactions, with atoms loaded into a square lattice using an optimized ramp.
Flavor-Selective Localization and Pairing Signatures Observed
Site- and flavor-resolved detection reveals a subtle interplay between pairing and localization within three-flavor Fermi lattice gases, allowing for detailed mapping of the Hubbard model’s phase diagram at low temperatures. Researchers observed suppression of density variance and compressibility, a hallmark of Mott insulators, confirming the localization of atoms at unit density and providing evidence for this quantum state. This observation relies on the ability to extract these quantities using flavor-resolved data, a key advancement in the technique.
The team attributes deviations between measured correlations and theoretical predictions at higher densities to a small amount of atomic hopping during the imaging process, a refinement of the experimental methodology. Further evidence for selective pairing emerges from measurements of flavor-density compressibility, revealing that the compressibility of flavor |1⟩ remains low at densities exceeding one, a behavior consistent with the theoretical model and indicative of unique pairing dynamics.
This contrasts with the behavior of flavors |2⟩ and |3⟩, which exhibit a rise in compressibility, suggesting differing pairing strengths across the three flavors. Analysis of on-site pairing correlations, specifically those between flavor pairs and, allowed researchers to delineate three distinct regimes: a Mott insulating (MI) state, a flavor-selective pairing (FSP) state, and a competing attractive-pairing (CAP) state.
The MI state is characterized by suppressed on-site pairs when both and are negative, while the FSP state, observed when is negative and is positive, shows a significant fraction of doublons at higher densities. This work demonstrates the consistency between different measurement methods, validating the results obtained through both direct detection and theoretical calculations. By sorting data based on the sign of on-site pairing correlations, the team established clear boundaries between the observed phases, providing a detailed phase diagram for a balanced three-flavor Fermi Hubbard system.
6Li Atomic Stability Enables Three-Component Mixtures
The unusual stability of lithium-6 allows for the creation of three-component fermionic mixtures, a key requirement for recent advances in quantum gas microscopy. Researchers used this stability to image three-flavor Fermi lattice systems with single-site resolution, enabling detailed study of interactions between the flavors.
This capability is not universally available. Many atomic species experience high loss rates in three-component mixtures. But 6Li presents a notable exception, as characterized by its three-body loss rate coefficient at various fields for equal populations and population imbalance. These images directly reveal intra- and inter-flavor correlations, including pairing between any two flavors, a level of detail previously inaccessible.
The experimental setup involves rapidly increasing the lattice depth to 50 ER to freeze atomic motion, followed by a Stern-Gerlach separation to isolate and image flavor pairs. Analysis of the resulting images allows for the reconstruction of doublon densities, the density of sites with an atom of flavor α and an atom of flavor β. This difference arises from the lower interaction strength, U(23), between flavors 2 and 3, demonstrating the sensitivity of the technique to subtle variations in atomic interactions.
The observed agreement with atomic limit calculations further validates the experimental approach. Precise control over the atomic populations is achieved through fine-tuning pulse durations, transferring one-third of the population with each pulse. This standardization allows for consistent data acquisition and analysis. Measurements of the loss rate as a function of magnetic field provide further insight into the dynamics of these complex quantum systems.
SU(N) Systems and Exotic Spin Ordering in Optical Lattices
The ability to probe exotic quantum phases has expanded with the realization of SU(N) systems, moving beyond the more commonly studied SU(2) models. Introducing additional species fundamentally alters the behavior predicted by the Hubbard model. Three-component fermionic systems, specifically, offer a compelling analog for quantum chromodynamics, mirroring the three flavors present in that theory and providing a platform for exploring related physics with ultracold atoms.
These components can be represented by multiple nuclear spin states, allowing for precise control and manipulation. This level of resolution allows for a deeper understanding of how interactions between these components drive the emergence of distinct quantum phases, a feat previously limited by experimental constraints. The current work builds on a decade of progress in studying SU(N) Fermi-Hubbard models using alkaline-earth-like atoms. Comparisons with numerical linked-cluster expansion calculations validate the experimental findings.
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