Phase-induced vortex pinning in rotating supersolid dipolar systems

Vortices in stationary rotating dipolar supersolids are predicted to be smooth functions of rotation frequency, rather than being fixed at density minima, which is crucial for understanding vortex dynamics in these complex quantum systems.

The gist

vortices are not only pinned at local density minima, but instead their coordinates are smooth functions of the rotation frequency.

System Description and Model Setup

1. The analysis focuses on a stationary rotating dipolar supersolid along the low-density paths between droplets as a function of the rotation frequency.

2. The system is modeled by approximating the wave function through a superposition of localized wave functions of individual droplets, based on the fact that density is concentrated on these droplets surrounded by very low relative density valleys.

3. For a droplet distribution forming a triangular lattice, the analysis requires considering the phases of three neighboring droplets for an accurate description of vortex location.

4. The system is studied using extended Gross-Pitaevskii (eGP) theory, including Lee-Huang-Yang (LHY) correction and dipole-dipole interaction, in a rotating frame where an additional term accounts for rotation.

Vortex Position Estimation

1. The wave function of the droplet system is approximated as:

ψD(r, t) = X Σ k wk(r, omega) e iϕk(t)p Nk(t)

2. For a two-droplet case between neighboring droplets labeled k' and k, the vortex coordinate Yv is obtained by requiring the vanishing of the wave function at the vortex core:

Yv(t) = φ(t)/π + 2l + 1/π¯hmdomega

3. The position of a vortex along a specific path between two vertices (yv1 and yv2) is given by the solution to Equation (11):

r N0 / N1 e d(d − √3Yv)2a2 + 2 cos md¯homegaYv = 0

Effect of Rotation Frequency

1. The mean relative distance 'd' between droplet pairs is shown to increase with the rotation frequency, which is mainly attributed to the effect of the centrifugal force acting on the particles.

2. The position of any vortex present in the system can be extracted using a plaquette method and compared to analytical estimates, such as Eq. (9).

3. In stationary configurations, it is observed that the configurations conserve the triangular symmetry both for the density and phase profiles, and we observe that they display vanishing phase differences among droplet centers, i.e., φk = 0, ∀k.

Approximation Accuracy

1. The three-droplet model permits a numerical estimation of vortex positions along the line joining the saddle point and vertex yv1 with accuracy.

2. The three-droplet model is shown to better describe the vortex position as a function of rotation frequency between the saddle ys and vertex yv1.

3. The analysis demonstrates that the inclusion of the third droplet explains the fact that for a given frequency it is more likely to find the vortex near the vertex than in the proximity of the saddle.

4. The analytical ansatz provides an accurate prediction for vortex positions, and the slow variation of the vortex location arises from the imprinted velocity field on the droplets, rather than from density holes that typically pin vortices in non-rotating systems.

Conclusion

1. The approach can be generalized to more complex droplet configurations as long as they are axially symmetric and well defined.

2. Vortices will likely be placed in areas where two or three neighboring droplets are enough to precisely predict their positions, regardless of the lattice structure of the supersolid.

3. The model is valid for less confined systems where more droplets are formed around other vertices of the triangular lattice, as evidenced by observations around the first vertex.

The gist

"Vortices in stationary rotating dipolar supersolids are predicted to be smooth functions of rotation frequency, rather than being fixed at density minima, which is crucial for understanding vortex dynamics in these complex quantum systems."

How it works

1. The analysis begins by considering the stationary configuration of a rotating supersolid dipolar BEC forming an extended triangular lattice of droplets, characterized by a density modulation described by Equation (1).

2. This setup defines paths between droplets; for the specific vertical path considered, the two vertices are located at yv1 = d/√3 and yv2 = 2d/√3, with a saddle point at ys = √3/2d in between.

3. The position of the vortex along these paths is estimated using an ansatz derived from the linear phase acquired by each rotating droplet's wave function on its coordinates.

Vortex Position Estimation

Here are the potential improvements for AI systems derived from the principles and findings of this scientific paper:

1. Improved Modeling of Complex, Structured Data using Phase-Based Predictive Models:

The paper demonstrates a method where vortex positions in rotating supersolids (a complex, structured system) can be accurately predicted by analyzing the linear phase relationship between neighboring components (droplets).

2. Enhanced Computational Physics Simulations for Non-Equilibrium Dynamics:

The work utilizes extended Gross-Pitaevskii (eGP) theory to model the dynamics of a rotating dipolar supersolid, incorporating kinetic energy, trapping potentials, and long-range dipole interactions. This provides a robust framework for simulating non-equilibrium quantum many-body systems.

3. Predictive Modeling for Pinning and Localization Phenomena:

The core finding is that vortices are not pinned at simple density minima but follow smooth functions of rotation frequency along low-density paths (saddle points). An AI system trained on this model could predict the precise location of localized defects (vortices) in complex, rotating media with high accuracy, rather than relying on static pinning site assumptions.

4. Optimized Lattice/Structure Recognition:

The paper shows that the presence or absence of a third neighboring droplet significantly alters the predicted vortex position (e.g., the difference between two-droplet and three-droplet models). An AI system could be trained to recognize the local environment (number and configuration of neighbors) in an evolving physical system to select the most accurate predictive model for that specific region.

5. Modeling of Effective Potentials in Rotating Frames:

The framework includes terms like the centrifugal force term in the energy functional and a modified trap frequency. An AI could be used to dynamically calculate or infer effective potentials acting on particles within a rotating frame, allowing for more accurate predictions of particle trajectories and collective behavior under rotation.

Improved AI System Capabilities:

An AI system based on this research would function as an advanced simulation and predictive engine capable of:

1. Predicting the exact spatial coordinates of topological defects (vortices) within complex, rotating quantum fluids or dipolar materials by inputting parameters like rotation frequency and inter-droplet distances.

2. Simulating the non-equilibrium evolution of structured matter (like supersolids) under external forces (rotation), accurately capturing how localized excitations move and are pinned along specific paths rather than fixed points.

3. Identifying the critical conditions (specific rotation frequencies or lattice configurations) where topological defects transition between different pinning regimes, allowing for the design of materials with predictable defect behaviors.

4. Developing a hierarchical modeling approach: using a simple two-droplet model for general regions and switching to a more complex three-droplet model when high precision is required near specific geometric features (like vertices or saddle points).