[Paper Review] Density-Wave Instability and Collective Modes in a Bilayer System of Dipolar Bosons

E. Akaturk, B. Tanatar+1 more|arXiv (Cornell University)|Jul 22, 2015

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This study investigates density-wave instabilities and collective modes in a bilayer system of dipolar bosons with dipoles polarized perpendicular to the planes. Using hypernetted-chain calculations for intralayer structure factors and random-phase approximation for interlayer interactions, it identifies a critical layer spacing below which the homogeneous state becomes unstable, with counterflow lowering the zero-point energy and inducing dissipationless superfluid drag.

ABSTRACT

We consider a bilayer of dipolar bosons in which the polarization of dipoles are perpendicular to the planes. Using accurate static structure factor $S(q)$ data from hypernetted-chain calculation for single layer dipolar bosons we construct effective screened interactions for intralayer particles. We adopt the random-phase approximation for interlayer interactions. We study the instability of the homogeneous bilayer system against the formation of density waves by investigating the poles of the density-density response function. The dispersion of collective modes of this system also signals the density-wave instability. We also investigate the effect of counterflow on the collective mode dispersion and on the density-wave instability and discuss the dissipationless superfluid drag effect in the presence of a background velocity.

Motivation & Objective

• To investigate the instability of a homogeneous bilayer of perpendicular dipolar bosons toward density wave formation.
• To determine the conditions under which the system becomes unstable, particularly as a function of interlayer spacing and coupling strength.
• To analyze the dispersion of in-phase and out-of-phase collective modes (zero-sound modes) in the bilayer system.
• To examine the effects of counterflow on the density-wave instability and collective mode dispersion.
• To explore the emergence of dissipationless superfluid drag in the presence of a background flow between layers.

Proposed method

• Uses hypernetted-chain (HNC) calculations to obtain accurate static structure factors S(q) for isolated 2D dipolar boson layers.
• Applies the fluctuation-dissipation theorem to extract effective static intralayer interactions from S(q) data.
• Employs the random-phase approximation (RPA) to model effective interlayer interactions.
• Calculates the poles of the static and dynamical density-density response functions to identify instability and mode dispersions.
• Introduces a finite counterflow velocity between layers and computes its effect on zero-point energy and mode dispersion.
• Derives the free energy and current densities to analyze the superfluid drag effect, showing velocity-dependent coupling between layers.

Experimental results

Research questions

• RQ1 At what critical interlayer spacing does the homogeneous bilayer state become unstable to density wave formation?
• RQ2 How do the in-phase and out-of-phase collective mode dispersions evolve with wavevector and layer separation?
• RQ3 How does a finite counterflow between layers affect the zero-point energy and the stability toward density waves?
• RQ4 What is the nature of the superfluid drag effect in this bilayer dipolar boson system?
• RQ5 How does the system's response change when interlayer interactions are treated beyond RPA, especially in the strongly correlated regime?

Key findings

• The homogeneous bilayer state becomes unstable to density wave formation when the interlayer spacing drops below a critical value, regardless of intralayer coupling strength.
• The in-phase and out-of-phase collective modes become degenerate in the long-wavelength limit (q → 0), indicating a soft mode at long wavelengths.
• Counterflow between layers lowers the system's zero-point energy by an amount scaling as ∆E_ZP ≈ –ħC²_dd n²v² / (640π m² v_s⁵ d⁵), with a d⁻⁵ dependence on layer separation.
• The zero-point energy shift is quadratic in counterflow velocity and negative, indicating stabilization of the inhomogeneous density wave state.
• The current densities in each layer depend on the superfluid velocities of both layers, demonstrating a dissipationless superfluid drag effect.
• The superfluid drag coupling strength scales as 1/d⁵ and is proportional to the square of the dipolar coupling constant, indicating strong interlayer correlation in the strongly coupled regime.