Quantum phases from competing short- and long-range interactions in an optical lattice (1511.00007v2)

Abstract: Insights into complex phenomena in quantum matter can be gained from simulation experiments with ultracold atoms, especially in cases where theoretical characterization is challenging. However these experiments are mostly limited to short-range collisional interactions. Recently observed perturbative effects of long-range interactions were too weak to reach novel quantum phases. Here we experimentally realize a bosonic lattice model with competing short- and infinite-range interactions, and observe the appearance of four distinct phases - a superfluid, a supersolid, a Mott insulator and a charge density wave. Our system is based on an atomic quantum gas trapped in an optical lattice inside a high finesse optical cavity. The strength of the short-ranged on-site interactions is controlled by means of the optical lattice depth. The infinite-range interaction potential is mediated by a vacuum mode of the cavity and is independently controlled by tuning the cavity resonance. When probing the phase transition between the Mott insulator and the charge density wave in real-time, we discovered a behaviour characteristic of a first order phase transition. Our measurements have accessed a regime for quantum simulation of many-body systems, where the physics is determined by the intricate competition between two different types of interactions and the zero point motion of the particles.

• The paper demonstrates the experimental realization of a bosonic lattice model that combines short- and infinite-range interactions using a BEC of Rubidium-87 atoms.
• It employs precise control over optical lattice depth and cavity detuning to map the emergence of four quantum phases: SF, MI, SS, and CDW.
• The findings reveal a first-order phase transition with hysteresis, offering new insights for quantum simulations and potential quantum computing applications.

Quantum Phases in Optical Lattices with Competing Interactions

The investigation conducted by Landig et al. at ETH Zurich presents an experimental realization of a bosonic lattice model characterized by competing short- and infinite-range interactions. This paper leverages a quantum gas in an optical lattice within a high-finesse optical cavity, achieving precise control over interaction strengths. The authors observe and characterize four distinct quantum phases: superfluid (SF), supersolid (SS), Mott insulator (MI), and charge density wave (CDW). This work contributes to the broader field of quantum simulations using ultracold atoms, offering insights into complex quantum phenomena that challenge theoretical descriptions.

Experimental Setup and Methodology

The research employs a Bose-Einstein Condensate (BEC) of Rubidium-87 atoms structured within a two-dimensional (2D) optical lattice system. The experiment integrates short-range on-site interactions, modifiable via lattice depth, with infinite-range interactions mediated by cavity vacuum modes. This environment supports detailed exploration of the interplay between tunneling, on-site, and long-range interactions, yielding a comprehensive phase diagram. The distinct phases emerge under varying strength ratios of these interactions, controlled by tuning the optical lattice depth and cavity resonance detuning.

Observations: Distinct Quantum Phases

The experimental results highlight specific conditions under which different phases manifest. The transition from SF to MI is marked by loss of spatial coherence, observable by a transition in the momentum distribution upon lattice ramping. The SF phase is characterized by prevalent atomic delocalization, transitioning to MI as on-site interactions dominate, indicative of atom localization at individual lattice sites.

In the presence of significant long-range interactions, supersolid and charge density wave phases emerge. The SS phase still supports superfluidity while introducing lattice symmetry breaking, leading to density modulations visible as additional interference peaks. Conversely, the CDW phase foregoes superfluidity, supporting a pronounced imbalanced distribution of particles across alternating lattice sites.

Phase Transition Dynamics

The paper reports a distinctive first-order phase transition between the CDW and MI phases, evidenced by hysteretic behavior in the transition dynamics. In controlled deviations from initial detuning conditions, the system demonstrates bistability—a haLLMark of first-order transitions. This finding underscores the role of potential energy barriers in inhibiting direct phase change until a critical interaction imbalance is exceeded, prompting abrupt system reconfiguration.

Implications and Speculations for Future Research

This paper advances understanding of quantum phase transitions in lattices where interaction types coexist with competing influences. Observations align with theoretical predictions regarding interaction-induced symmetry breaking and emergent phases. From a theoretical standpoint, these findings further elucidate many-body dynamics in lattice models, potentially informing studies on complex quantum systems exhibiting unconventional phases like supersolids in nature.

Practically, the results hint at applications in quantum computing where control over specific quantum states is essential. The experimental strategy and methodology provide a robust framework for further exploration of lattice systems under varied interaction conditions, including potential realizations in other ultracold atom setups or photonic lattices.

In conclusion, the research offers a meticulous investigation into the quantum phases arising from a novel interaction scheme within an optical lattice, pushing forward the boundaries of quantum simulation and expanding the horizons for future experimental and theoretical work in ultracold quantum gases.