Correlations of a quasi-two-dimensional dipolar ultracold gas at finite temperatures

We study a quasi-two-dimensional dipolar gas at finite, but ultralow, temperatures using the classical field approximation. The method, already used for a contact interacting gas, is extended here to samples with a weakly interacting long-range interatomic potential. We present statistical properties of the system for the current experiment with chromium [Müller, Billy, Henn, Kadau, Griesmaier, Jona-Lasinio, Santos, and Pfau, Phys. Rev. A 84, 053601 (2011)] and compare them with statistics for atoms with larger magnetic dipole moments. Significant enhancement of the third-order correlation function, relevant for the particle losses, is found.

Figure 1

Cuts through single exemplary copies of atomic density (three nonsolid lines) obtained during generation of the canonical ensemble with the Metropolis algorithm, together with the average density over the ensemble (solid black line).

Figure 2

Average fraction of condensed atoms. Parameters: $a=10a_B$, “the dipolar interaction length” corresponds to different atomic species: ${}^{52}$Cr, ${}^{168}$Er, and ${}^{164}$Dy. The average density in the middle of the trap is ${10}^{14}/{\text{cm}}^3$. Note that oscillatory units are different for different species, as described in the text. The exact calculation for ideal gas follows the procedure from [22]. Inset: Fraction of condensed Cr atoms at $T_1=0.015\hslash {\omega }_z/k_B$ but for different values of cutoff.

Figure 3

Cuts of the spatial first-order (a) and the third-order (b) correlation functions at a few chosen temperatures relevant to the experiment [3].

Figure 4

The first-order (a) and the third-order (b) correlation functions at temperature $T=0.020\hslash {\omega }_z/k_B$ ($\approx$30 nK for Cr) for $a=10a_B$ but for different values of $a_{dd}$ corresponding to different atomic species.

Figure 5

The third-order correlation function $g^3(0,0)$. The role of the dipolar interaction increases when approaching the instability border. The temperature $T=0.02\hslash {\omega }_z/k_B$.

Figure 6

(a) Function ${\tilde{V}}^{2\mathrm{D}}$ defined as in Eq. (A10) for $\theta =0$ (polarization in the $Z$ direction) in momentum space. (b) Function $V^{2\mathrm{D}}$ defined as in Eq. (A10) for $\theta =0$ (polarization in the $Z$ direction) in position and (c) its scaling for small and large $\rho$.