Quantum diatomic chain: a supersolid structure in three-component Bose mixture

TL;DR

The paper demonstrates a new route to a supersolid state in a three-component Bose mixture ($^{23}$Na, $^{39}$K, $^{41}$K) where two self-bound droplets $(1,2)$ and $(2,3)$ are bound by the shared component 2, forming a ground-state dimer, and further arranged into an extended diatomic linear chain with a robust superfluid fraction. The authors formulate a MF+LHY density-functional theory and solve the coupled Gross-Pitaevskii equations to characterize static dimer states and their vibrational spectra, revealing mass–spring-like dimer dynamics and hydrodynamic modes. They then realize a periodic chain by a controlled modulation, showing a lattice constant $a_L\simeq 3.23\,\mu\text{m}$ and bond length $d=a_L/2\simeq 1.61\,\mu\text{m}$, with $f_s\simeq 0.71$ and a dominant contribution from species 2. The chain supports diatomic-chain phonons with zone-edge and zone-center modes and exhibits low-frequency Goldstone-like excitations, illustrating coexistence of crystal order and global superfluidity. This mediated-binding mechanism provides a tunable, experimentally accessible route to supersolidity beyond dipolar or band-structure realizations, with prospects to explore vortices, dimensionality, and driven dynamics.

Abstract

The formation and properties of a supersolid structure in a three-component ultracold Bose gas mixture at T=0 are investigated theoretically. The system consists of 23Na, 39K, and 41K atomic species, in which the binary mixtures of (23Na,39K) and (39K,41K) can form self-bound quantum droplets stabilized by quantum fluctuations. Two such droplets can bind together by the shared 39K component, forming a stable "dimer" structure, which displays vibrational modes analogous to a classical diatomic molecule. A simple protocol is proposed to create a stable linear chain formed by periodic repetition of this basic building block, i.e. an alternating sequence of (23Na,39K) and (39K,41K) droplets. This structure exhibits both periodic density modulations from the droplet ordering and global phase coherence due to the shared 39K component, satisfying the criteria for supersolidity. This expands the class of known supersolids by adding a system where mediated binding, rather than intrinsic long-range interactions or engineered band-structures as in previously known supersolids, is the key organizing principle, thereby offering new directions for both theory and experiment. The low-energy excitation spectrum, probed by density perturbations, identifies modes corresponding to droplet vibrations close to the ones expected from a classical diatomic chain, coexisting with low-energy superfluid (Goldstone-type) modes.

Figures (11)

• Figure 1: Density profiles of the individual self-bound droplets made of liquid (2,3) (upper panel) and (1,2) (lower panel). Dotted line: species $1$; solid line: species $2$; dashed line: species $3$.
• Figure 2: Dimer density profile along the line passing through its axis, for the case $a_{23}=-200\,a_0$. Dotted line: species $1$; solid line: species $2$; dashed line: species $3$.
• Figure 3: Total density map corresponding to the dimer structure shown in Fig.\ref{['fig2']}. The droplet (2,3) is on the left, the droplet (1,2) on the right. The density units are the same as in Fig.\ref{['fig2']})
• Figure 4: Total density map corresponding to the dimer structure with $a_{23}=-70\,a_0$. The droplet (2,3) is on the left, the droplet (1,2) on the right. The density units are the same as in Fig.\ref{['fig2']}.
• Figure 5: Spectrum for the dimer oscillations. Solid line: $a_{23}=-200\,a_0$, dotted line: $a_{23}=-70\,a_0$.