Superfluid-mott Transition in Frustrated Triangular Lattices Suppressed by Factor of 2.7(3)

Geometric frustration, a phenomenon that hinders the establishment of simple ordered states in many-body systems, profoundly impacts their physical properties, and researchers continually seek ways to explore its effects. Mehedi Hasan, Luca Donini, and Sompob Shanokprasith, alongside colleagues at various institutions, now investigate this frustration in a novel setting, utilising ultracold atoms trapped in a triangular optical lattice. Their work demonstrates that geometric frustration substantially weakens the conditions required for a transition between a superfluid and a Mott insulator state, reducing the necessary interaction strength by a factor of nearly three. Furthermore, the team reveals that this frustration alters the dynamics of this phase transition, slowing the emergence of long-range order and potentially leading to a saturation of coherence, thereby opening new avenues for studying complex, frustrated systems that are often beyond the reach of classical approaches.

Atoms in Optical Lattices, Strong Correlations

This extensive collection of references details research into ultracold atoms trapped within optical lattices, with a particular focus on strongly correlated systems, quantum phase transitions, and the emergence of exotic states of matter. Researchers create these lattices using lasers, effectively building microscopic structures to control atomic movement and interactions, and explore systems where atomic interactions are significant. A central theme involves quantum phase transitions, shifts between different quantum states of matter driven by changes in conditions like interaction strength, exhibiting critical phenomena and predictable scaling laws. Investigations extend to frustrated magnetism, where competing interactions prevent a system from settling into a simple, ordered state, and explore exotic states of matter like chiral Mott insulators and Potts nematic superfluids.

Researchers are also exploring negative absolute temperatures, a state where the system’s energy distribution is inverted, leading to unusual thermodynamic properties. Ultracold atoms in optical lattices serve as a promising platform for quantum simulation, allowing scientists to use a controllable quantum system to study other complex quantum systems. Key techniques employed include the creation and manipulation of optical lattices, the use of Feshbach resonances to control atomic interactions, and computational methods like Quantum Monte Carlo and Density Matrix Renormalization Group. Notable studies include work by Schmidt and Dias on correlated cluster mean-field theory, and foundational work by Fisher on boson localization and the superfluid-insulator transition. Experimental evidence from Trotzky demonstrates the suppression of the critical temperature, while Spielman has developed techniques for measuring condensate fractions. Pollet provides a comprehensive review of Quantum Monte Carlo methods, and Yamamoto has explored frustrated quantum magnetism with Bose gases at negative absolute temperatures.

Negative Temperatures Stabilize Frustrated Atomic Layers

Researchers have achieved a breakthrough in understanding geometrically frustrated systems by stabilising ultracold potassium atoms in a triangular optical lattice at negative absolute temperatures. This innovative approach allows stable occupation of the highest-energy state, providing access to a frustrated system without the limitations of traditional methods. The team created a Bose-Einstein condensate of approximately 90,000 to 110,000 atoms, minimising thermal effects, within a crossed-beam dipole trap, and then loaded them into a three-dimensional optical lattice. To access the frustrated state, the team realised a negative absolute temperature regime, effectively inverting the sign of the Hamiltonian and absolute temperature while preserving the thermal density matrix.

Measurements of the momentum distribution were performed at various lattice depths to characterise the Mott insulator and superfluid phases, and a ‘booster’ pulse was employed to measure the superfluid regime. The critical interaction strength for the chiral superfluid to Mott insulator transition was found to be suppressed by a factor of 2. 7(3) in the frustrated system compared to the unfrustrated case, demonstrating the significant impact of geometric frustration on the phase transition dynamics.

Negative Temperatures Stabilize Frustrated Quantum System

Scientists have achieved a breakthrough in understanding geometrically frustrated systems by stabilising ultracold potassium atoms in a triangular optical lattice at negative absolute temperatures. This innovative approach allows for the stable occupation of the highest-energy state, providing access to a frustrated system without the limitations of traditional methods. Experiments reveal that geometric frustration suppresses the critical interaction strength for the chiral superfluid to Mott insulator phase transition by a factor of 2. 7(3). Researchers meticulously measured the transition by preparing a deep Mott insulator and then ramping the magnetic field and lattice depth, carefully controlling the interaction strength. Data shows that while the emergence of coherence is continuous in both frustrated and unfrustrated systems, significant differences emerge for longer ramps, with coherence length saturating at only a few lattice constants in the frustrated case, indicating a different critical behaviour.

Frustration Suppresses Quantum Phase Transition Strength

This research demonstrates a significant advance in understanding quantum phase transitions through the experimental study of frustrated systems. Scientists successfully created and examined a superfluid-Mott insulator transition in a triangular optical lattice, both with and without geometric frustration, by utilising negative absolute temperatures to access the frustrated band maxima. The results show that geometric frustration suppresses the critical interaction strength required for the transition by a factor of 2. 7, and also alters the dynamics of the transition itself. Furthermore, the team observed distinct behaviours in the emergence of coherence during the transition. While coherence grows continuously with fast changes to the system, in the frustrated case, coherence length saturates at only a few lattice constants for longer changes, indicating a different critical behaviour compared to the unfrustrated system.