Momentum Space Bose-Einstein Condensates Demonstrate Self-Trapping and Dynamical Phase Transition

Self-trapping, a fundamental phenomenon in nonlinear dynamics with implications for areas like band structure engineering and phase transition dynamics, receives fresh investigation through the study of Bose-Einstein condensates. Colby Schimelfenig, Federico Serrano, and Corey Halverson, all from Washington State University, alongside Annesh Mukhopadhyay, Qingze Guan, and Peter Engels, demonstrate self-trapping within a spin-orbit coupled Bose-Einstein condensate held in a stationary optical lattice. The team achieves this by carefully controlling atomic interactions and inducing a coupling between momentum states, revealing a distinct shift from a freely flowing atomic current to a self-trapped state. Crucially, the researchers observe non-analytic behaviour in the atomic current following a rapid change in experimental conditions, indicating a dynamical phase transition and offering new insights into the behaviour of these quantum systems.

Spin-Orbit Coupling Drives Dynamic Phase Transition

Scientists investigated the behavior of Bose-Einstein condensates subjected to spin-orbit coupling, revealing a dynamic phase transition characterized by a change in the system’s properties as the strength of an applied optical lattice is varied. The research team meticulously calibrated their experimental setup, employing laser cooling and trapping techniques to create and manipulate the Bose-Einstein condensate, and utilizing Raman lasers to induce the spin-orbit coupling. Detailed numerical simulations, based on the Gross-Pitaevskii equation, accurately mirrored the experimental results, validating the observed transition and providing insights into the underlying physics. This rigorous methodology, combined with detailed error analysis, provides strong evidence for the observed dynamic phase transition and enhances understanding of these complex quantum systems, opening new avenues for exploring the properties of spin-orbit coupled Bose-Einstein condensates and their potential applications in quantum technologies.

Raman BEC Creates Spin-Orbit Coupling Platform

Scientists pioneered a new experimental platform to investigate macroscopic quantum self-trapping and dynamical phase transitions by creating a Raman-induced spin-orbit coupled Bose-Einstein condensate. They harnessed a Bose-Einstein condensate of Rubidium-87 atoms, utilizing three internal states to engineer the spin-orbit coupling with Raman lasers. An accompanying optical lattice further refined the system, enhancing coupling between momentum states and facilitating the creation of two-state spin mixtures. By precisely controlling the lattice intensity, scientists tuned the system’s dynamics, promoting either delocalized behavior or the self-trapped regime.

Detailed mapping of state transfer dynamics under a controlled ramp of the Raman beams provided crucial evidence for the onset of self-trapping. Quenching the Raman detuning induced oscillatory behavior in the momentum-state populations, allowing the team to probe the dynamical phase transition. Both a two-mode model and Gross-Pitaevskii simulations accurately described the experimental observations, revealing that spatial excitations arising from finite-size effects can modify the critical behavior of the transition. This work provides a versatile platform for exploring nonlinear dynamics and opens avenues for future research into the interplay between spin and spatial degrees of freedom.

Self-Trapping in Spin-Orbit Coupled Bose-Einstein Condensates

Scientists observed self-trapping in a Bose-Einstein condensate subjected to both spin-orbit coupling and a stationary optical lattice. They employed Raman-induced spin-orbit coupling, complemented by a lattice that connects momentum states within the spin-orbit coupled system, to probe atomic current flow and identify distinct delocalized and self-trapped regimes. Measurements revealed a shift in the transition point due to the influence of an additional hyperfine state. Experiments demonstrated that the system exhibits distinct behavior depending on the strength of the optical lattice, with a transition between regimes characterized by either self-trapping or a delocalized mixed state.

At weak lattice strengths, the spin dynamics were strongly influenced by the ramp direction, exhibiting hysteresis due to self-trapping. Further analysis of the long-term dynamics revealed a dynamical phase transition closely related to self-trapping, characterized by a slowing down of observable evolution. The team confirmed the reliability of their measurements by demonstrating convergence of the dynamics for sufficiently long ramp times, ensuring that the observed effects were intrinsic to the system.

Self-Trapping and Phase Transition in BECs

This research demonstrates the observation of self-trapping and a dynamical phase transition within a spin-orbit coupled Bose-Einstein condensate. By employing Raman-induced spin-orbit coupling and an optical lattice, the team identified a distinction between a delocalized state and a self-trapped regime, evidenced by non-analytic behavior in the time-averaged atomic current. This work represents the first observation of macroscopic quantum self-trapping and a dynamical phase transition in momentum space within a Bose-Einstein condensate, opening new avenues for exploring nonlinear dynamics and potential applications in areas such as non-equilibrium criticality and quantum enhanced metrology. The researchers acknowledge that defects emerge after a short period, introducing instability and limiting the two-mode description of the system, and suggest that a more complex model will be necessary to fully capture the system’s behavior. Future work will focus on developing this extended model to provide a more complete understanding of the observed dynamical phase diagram.