Models of spin-orbit-coupled oligomers

Area of Science:

• Quantum physics
• Atomic physics
• Condensed matter physics

Background:

• Bose-Einstein condensates (BECs) offer a platform for studying quantum phenomena.
• Binary BECs with attractive interactions and spin-orbit (SO) coupling exhibit complex dynamics.
• Droplet arrays in BECs can model various physical systems.

Purpose of the Study:

• Investigate the stability and dynamics of eigenmodes in linearly shaped strings of droplets within a binary BEC.
• Analyze the influence of spin-orbit coupling on eigenmode formation and persistence.
• Explore the transition of linear eigenmodes to nonlinear states.

Main Methods:

• Theoretical analysis of eigenmodes in dimer, trimer, tetramer, and pentamer strings.
• Employing spin-orbit (SO) coupling via laser fields in a binary BEC.
• Analytical continuation of linear eigenmodes to nonlinear regimes.
• Numerical methods for analyzing nonlinear states and their stability.

Main Results:

• SO coupling facilitates the creation of specific eigenmode types in droplet strings.
• Linear eigenmodes with zero eigenvalues (chemical potential) for dimer, trimer, and pentamer systems maintain an exact analytical form in the nonlinear regime.
• Tetramer systems do not allow this continuation due to the absence of a zero eigenvalue.
• Stability regions for these modes decrease with increasing nonlinearity.
• Other nonlinear states, originating from nonzero eigenvalues, are found numerically, exhibiting varying stability across different string lengths.

Conclusions:

• Spin-orbit coupling is crucial for engineering eigenmodes in binary BEC droplet systems.
• The analytical tractability of certain eigenmodes simplifies their study in nonlinear physics.
• Systematic analysis reveals distinct behaviors for different string lengths (dimers to pentamers and beyond).
• Nonlinearity significantly impacts mode stability, with tetramers showing limited stability regions for nonlinear states.