The vortex comb: eliminating vortices from Bose-Einstein condensates using optical lattices

Technical Summary: The Vortex Comb: Eliminating Vortices from Bose-Einstein Condensates Using Optical Lattices

Problem Statement
Quantized vortices are fundamental indicators of superfluidity in Bose-Einstein condensates (BECs) and play a critical role in complex quantum fluid phenomena such as superfluid turbulence. However, vortices often form spontaneously during BEC creation or as a result of motion relative to external potentials, acting as unwanted defects that hinder the precise control and characterization of the condensate's dynamical state. While techniques exist to remove vortices from superconductors, controlled removal from BECs to prepare the system in its motional ground state has received limited attention. Existing removal mechanisms, such as thermal damping and vortex-antivortex annihilation, are often insufficient for rapid, controlled elimination across a wide range of parameters.

Methodology
The authors employ a dual approach combining experimental demonstration and extensive numerical simulation:

1. Experimental Demonstration:

   • System: A highly oblate $^{87}$Rb BEC (up to $1.3 \times 10^6$ atoms) trapped in a hybrid optical-magnetic trap.
   • Vortex Generation: Vortices are introduced via adiabatic stirring using a focused 660-nm laser beam moved in circular trajectories.
   • The "Vortex Comb": A one-dimensional blue-detuned optical lattice (OL) is applied by interfering two 532-nm laser beams. This creates a periodic array of interference fringes (channels) that segment the BEC density without destroying phase coherence between segments.
   • Protocol: The OL is ramped on linearly, held for a specific duration, and ramped off. The efficacy is tested by varying the total ramp time ($T_{tot}$) and the potential depth ($V_0$) relative to the BEC chemical potential ($\mu_0$).
   • Imaging: Vortex counts are performed after time-of-flight expansion along the $\hat{z}$ axis.

2. Numerical Simulations:

   • Model: The dynamics are modeled using the 2D Gross-Pitaevskii equation (GPE) derived from the 3D mean-field theory, justified by the highly oblate nature of the trap ($\omega_z \gg \omega_x, \omega_y$).
   • Dynamics: The simulations include a phenomenological dissipation term ($\gamma$) to account for finite-temperature effects.
   • Parameter Space: The study systematically varies the OL fringe spacing ($x_w$) relative to the healing length ($\xi$) and the comb amplitude ($V_0$) to map vortex removal efficiency. Initial conditions involve a BEC with a pre-existing distribution of vortices generated by a simulated stirring process.

Key Contributions and Results

1. Experimental Proof of Concept:

   • The experiment successfully demonstrates that applying a 1D optical lattice can efficiently remove vortices from a BEC.
   • With optimal parameters ($V_0 \approx 5.9\mu_0$ and $T_{tot} = 4$ s), the mean fraction of remaining vortices dropped to approximately 0.023, with 89% of experimental runs resulting in a completely vortex-free condensate.
   • The process was observed to be robust against moderate changes in ramp times and did not induce significant heating or excitation of the condensate.

2. Identification of Removal Mechanisms:
   Through numerical analysis, the authors identified four distinct mechanisms by which vortices are removed or eliminated during the combing process:

   • Peripherally Channeled Vortices (PCV): Vortices are guided along the density channels created by the OL to the outer edge of the BEC, where they dissipate. This includes scenarios where single vortices or vortex pairs are absorbed at the periphery.
   • Vortex-Antivortex (V-AV) Annihilation: Oppositely charged vortices are brought into proximity by the lattice channels, leading to mutual annihilation. This mechanism is dominant in wider fringe spacings.
   • Damped Vortices (DV): Standard thermal damping causes vortices near the edge to spiral out and dissipate. This is found to be a minor contributor under typical experimental damping coefficients compared to other mechanisms.
   • Density-Phase-Separated Vortices (DPSV): A novel mechanism observed primarily in narrow channels (fringe widths on the order of the vortex core size, $\sim 3\text{--}4\xi$) with sufficient potential depth. In this process, the phase singularity of the vortex detaches from its associated density profile (the core). The phase singularity migrates into the low-density troughs of the lattice and is "lost" at the periphery, while the density excitation morphs into a soliton-like structure (reminiscent of a Jones-Roberts soliton) confined within the channel.

3. Optimization of Parameters:

   • The study identifies an optimal parameter regime for vortex removal located in the "lower-left" corner of the parameter space: narrow fringe spacings ($x_w \approx 3\text{--}4\xi$) combined with moderate comb amplitudes ($V_0 \approx 1.4\text{--}1.8\mu_0$).
   • In this regime, the DPSV mechanism is the dominant driver of removal.
   • The authors note that excessively high amplitudes or very thin fringes can lead to the unintended nucleation of new vortices during the ramp-down phase due to steep density gradients.
   • The optimal removal is robust across variations in atom number, chemical potential, and trap geometry (elliptical vs. circular), though anisotropic traps facilitate removal more effectively due to shorter travel distances to the edge.

Significance
The paper claims to provide a robust and viable experimental toolkit for the controlled removal of vortices from BECs, enabling the preparation of condensates in their motional ground state for subsequent protocols. A primary theoretical contribution is the discovery and characterization of the Density-Phase-Separated Vortex (DPSV) mechanism. The authors state that this mechanism, where the phase singularity spatially separates from the density core in narrow optical-lattice-induced channels, has not been previously reported. This finding adds a new layer of understanding to vortex dynamics in confined geometries and suggests a connection between vortex dynamics and the stability of Jones-Roberts solitons in narrow channels. The work establishes a theoretical and computational backdrop for the "vortex comb" procedure, paving the way for future studies on vortex dynamics in narrow channels and the control of dynamical states in quantum fluids.