Anisotropic coherence properties in a trapped quasi-two-dimensional dipolar gas

We consider a trapped quasi-two-dimensional dipolar Bose-Einstein condensate with a polarization tilted into the plane of motion. We show that by tilting the polarization axis, the coherence properties are anisotropic. Such a system will have density fluctuations, the amplitude of which depends on their trap location. Additionally, interference contrast will also be anisotropic despite an isotropic density profile. The anisotropy is related to a rotonlike mode that becomes unstable and supports local collapse along the polarization axis.

Figure 1

(a) The total density, (b) $g_1(x,0;0,0)$ (solid line) and $g_1(0,y;0,0)$ (dashed line), and (c) $g_2(x,0;0,0)$ (solid line) and $g_2(0,y;0,0)$ (dashed line) at $T/T_C=0.50$ and for $N=2000$ (blue), 3000 (red), and 4000 (black) from top to bottom. The total density is isotropic in the center, yet the correlation function is significantly anisotropic at short range.

Figure 2

(a) The Bogoliubov–de Gennes spectrum is shown as a function of particle number for $g_d=0.025$ for $\alpha /\pi =0.25$. (b) and (c) A contour plot of the roton quasiparticle modes ($u_{\gamma }$) which go soft for a dipolar system with tilted polarization axis are also shown. The dashed black line is $\sqrt{n_0}$ and for $u_{\gamma }$ the shaded regions are less than zero. The contours at 0.25, 0.5, and 0.75 the maximum values of the individual wave functions.

Figure 3

(a) The total density and (b) the compressibility $kT\kappa \left(\vec{\rho }\right)$ for the dipolar gas along the $x$ (solid) and $y$ (dashed) axes for particles numbered 2000 (blue, lower), 3000 (red, middle), and 4000 (black, top).