Quasiparticle spectra of mixtures of dipolar and non-dipolar condensates at zero and finite temperatures

TL;DR

This work analyzes the low-lying quasiparticle spectra of a quasi-one-dimensional binary Bose-Einstein condensate comprising a dipolar and a non-dipolar species using Hartree-Fock-Bogoliubov theory. By modeling a Cr–Rb system in an infinite pancake geometry, the authors show that dipolar interactions drive a miscibility transition, evidenced by the hardening of an extra zero-energy mode and discontinuities in higher-lying modes, as well as phase swapping at large intercomponent repulsion. Finite-temperature effects promote mixing and cause dipole-mode hardening, accompanied by a loss of long-range coherence captured by the first-order correlation function. Dispersion relations reveal mode mixing and its suppression in the miscible phase, highlighting the role of anisotropic DDIs in shaping the collective excitations and phase behavior of dipolar/non-dipolar TBECs.

Abstract

We examine the low-lying collective quasiparticle modes of a quasi-one-dimensional mixture of Bose-Einstein condensates having dipolar and non-dipolar atomic species. The dipolar atomic species have permanent magnetic dipolar moments. We employ Hartree-Fock-Bogoliubov theory to investigate the distinct collective spectra at zero and finite temperatures corresponding to phase separation phenomena stemming from the dipole-dipole interaction of dipolar atomic species. When the dipolar interaction is tuned to be repulsive, the number of zero-energy modes decreases, reflecting the system's tendency towards mixing. For a large number of atoms, we show that the attractive (repulsive) dipolar interaction strengths lead to ground states with non-dipolar (dipolar) atomic species at the periphery, and this leads to a discontinuity in quasiparticle mode evolution. We finally reveal that miscibility driven by thermal fluctuations at finite temperatures exhibits dipole mode hardening, confirmed by the loss of long-range phase coherence through the correlation function. The mode mixing in the dispersion relations ascertains a dipolar strength-dependent miscibility transition and the low-lying quasiparticle mode evolution.

Figures (6)

• Figure 1: The evolution of low-lying quasiparticle modes energies as a function of the dipole-dipole interaction strength parameter $\varepsilon_{dd}$ for the intercomponent scattering length $a_{12} = 7$ nm. The evolution is shown for zero temperature by incorporating the quantum fluctuations. The inset plots are the density profiles for three different values of $\varepsilon_{dd}$, shows the immiscible to miscible transitions. The values of the $\varepsilon_{dd}$ are indicated by arrows in the main figure. The quasiparticle energies are scaled with the harmonic oscillator energy.
• Figure 2: The evolution of the quasiparticle amplitudes associated with the zero-energy mode for a binary BECs including quantum fluctuations, with a fixed $a_{12} = 7$ nm. As the dipole-dipole interaction shifts from attractive to repulsive, the zero-energy mode of $^{87}\text{Rb}$ transforms to a a dipole mode in the miscible phase.
• Figure 3: Low-lying quasiparticle mode energies obtained using the HFB-Popov approximation, as a function of the dipole-dipole interaction strength parameter $\varepsilon_{dd}$ for $a_{12} = 12$ nm. The inset plots are the density profiles at three representative values of $\varepsilon_{dd}$ showing the phase swapping of species, but remain in the immiscible regime.
• Figure 4: Evolution of the low-lying quasiparticle mode energies as a function of temperature for a fixed attractive dipolar interaction strength, $\varepsilon_{dd} = -0.35$, with $N_1 = N_2 = 100$. As the temperature increases, the non-condensate fraction grows, leading to a transition of the density profile from a sandwich-type to a miscible configuration, as illustrated in the inset. In the main plot, the temperature is scaled by the critical temperature of the non-dipolar species
• Figure 5: First-order correlation functions $g^{(1)}_{\mathrm{Cr}}(0, z)$ (solid lines) and $g^{(1)}_{\mathrm{Rb}}(0, z)$ (dashed lines) for a Cr-Rb mixture at equilibrium, shown for $a_{12} = 7\,\mathrm{nm}$. The correlations are plotted for three different temperatures: $T = 0$ (black), $0.5\,T_c$ (blue), and $0.9\,T_c$ (red). The correlation functions are shown for three $\varepsilon_{dd}$ values mentioned at the top of the plots. Here, spatial coordinate $z$ is in units of oscillator length.