[Paper Review] Long lifetime supersolid in a two-component dipolar Bose-Einstein condensate

Shaoxiong Li, Uyen Ngoc Le+1 more|arXiv (Cornell University)|Mar 18, 2022

Cold Atom Physics and Bose-Einstein Condensates73 references43 citations

TL;DR

This paper proposes a two-component dipolar Bose-Einstein condensate (166Er-87Rb) to stabilize a long-lived supersolid without relying on the Lee-Huang-Yang (LHY) correction, which typically limits lifetime due to high atomic density and three-body losses. By tuning the trap center offset (δ) between components, the system enables Josephson coupling between droplets, enabling long-period out-of-phase Goldstone modes and suppressing atomic loss through reduced effective density and dipolar interaction strength.

ABSTRACT

Recent studies on supersolidity in a single-component Bose-Einstein condensate (BEC) have relied on the Lee-Huang-Yang (LHY) correction for stabilization of self-bound droplets, which however involves a high density inside the droplets, limiting the lifetime of the supersolid. Here we propose a two-component mixture of dipolar and nondipolar BECs, such as an $^{166}$Er-$^{87}$Rb mixture, to create and stabilize a supersolid without the LHY correction, which can suppress the atomic loss and may allow observation of the long-time dynamics of the supersolid. In such a system, supersolidity can be controlled by the difference in the trap centers between the two components.

Motivation & Objective

• To overcome the short lifetime of supersolids stabilized by the Lee-Huang-Yang (LHY) correction, which arises from high atomic density and three-body recombination.
• To demonstrate that a two-component dipolar BEC can stabilize a supersolid without the LHY correction by leveraging effective interaction reduction via quasi-spin dynamics.
• To show that the degree of supersolidity and its dynamics can be controlled via the trap center offset δ between components.
• To enable observation of long-time dynamics, such as slow Goldstone mode oscillations, by suppressing atomic loss through reduced effective density and dipolar strength.

Proposed method

• Uses the coupled nonlocal Gross-Pitaevskii (GP) equations with dipole-dipole interactions (DDI) and contact interactions to model two-component BECs.
• Employs a mean-field approximation at zero temperature with spatially separated harmonic traps for 166Er and 87Rb, where δ represents the relative trap center shift (including gravitational sag).
• Numerically solves the 3D GP equations using a pseudospectral method with spatial resolution dx = dy = dz ≈ 0.3 µm and time step dt ≈ 10 µs.
• Implements imaginary-time evolution to obtain the ground state, and real-time evolution to study dynamics and atomic loss via three-body recombination.
• Treats the 166Er-87Rb mixture with µ1 ≫ µ2 to enhance effective dipolar interaction in the quasi-spin channel, enabling pattern formation without LHY stabilization.
• Analyzes the system’s behavior by varying the inter-species scattering length a12 and the trap offset δ to tune supersolidity and contrast.

Experimental results

Research questions

• RQ1 Can a supersolid state be stabilized in a two-component dipolar BEC without relying on the Lee-Huang-Yang (LHY) correction?
• RQ2 How does the trap center offset δ between components influence the degree of supersolidity and Josephson coupling between droplets?
• RQ3 What is the effect of using a 166Er-87Rb mixture with a large magnetic moment difference on suppressing atomic loss and extending supersolid lifetime?
• RQ4 Can long-period out-of-phase Goldstone modes emerge in the absence of LHY stabilization?
• RQ5 How does the effective interaction strength in the quasi-spin channel compare to the single-component case, and what role does it play in pattern formation?

Key findings

• A stable, long-lived supersolid is achieved in a 166Er-87Rb two-component dipolar BEC without the Lee-Huang-Yang (LHY) correction, significantly reducing atomic loss.
• The system exhibits a long-lived supersolid phase with a contrast C ≈ 0.98 at δ = 1.7 µm, indicating strong periodic density modulation.
• The contrast C increases with δ, reaching C ≈ 0.98 at δ = 1.7 µm, demonstrating enhanced supersolidity through Josephson coupling.
• At a12 = 100aB, the system supports a stable 1D and 2D supersolid lattice with a contrast of approximately 0.98, even without LHY stabilization.
• The time evolution shows that atomic loss is suppressed, with Nj decreasing slowly over 120 s, indicating a significantly extended lifetime compared to LHY-stabilized droplets.
• A long-period out-of-phase Goldstone mode emerges when δ is increased, confirming the presence of coherent superflow between droplets in the supersolid state.