Photonic crystal optical waveguides for on-chip Bose-Einstein condensates

We propose an on-chip optical waveguide for Bose-Einstein condensates based on the evanescent light fields created by surface states of a photonic crystal. It is shown that the modal properties of these surface states can be tailored to confine the condensate at distances from the chip surface significantly longer that those that can be reached by using conventional index-contrast guidance. We numerically demonstrate that by index-guiding the surface states through two parallel waveguides, the atomic cloud can be confined in a two-dimensional trap at about $1\mu \mathrm{m}$ above the structure using a power of $0.1\mathrm{mW}$.

Figure 1

(Color) Schematic picture of the structure proposed for BEC waveguiding. The system consists of a one-dimensional photonic crystal with a defect layer on its top. In the defect layer two parallel index-guiding waveguides are included. As sketched in the figure, for a suitable design of the system, the BEC cloud can be confined in the region between these waveguides. The reference system used throughout the text, together with the geometrical parameters defining the structure are also shown.

Figure 2

(Color) (a) Projected band structure of the semi-infinite one-dimensional photonic crystal considered in this work [see the profile of dielectric constant in (b)]. Red-shaded areas show the regions where there exist extended states inside the PhC. Gray-shaded area corresponds to eigenmodes that are propagating in air. Orange, blue, and magenta lines represent the dispersion relations of the surface states for several values of the thickness of the top layer. Green-shaded region corresponds to possible confined states of any defect layer if it lies on top of a uniform dielectric substrate with $ϵ={ϵ}_{lo}$. (b) Dielectric constant (black line) and electric field intensity profiles along the direction perpendicular to the interface PhC-air. Three surfaces states with frequencies close to the light line are displayed for $W_d=0.07a$.

Figure 3

(Color) Main panel: Total atomic potential for the case of Cs atoms as a function of the distance to the dielectric surface. The results for several decay lengths of the evanescent light field are shown. The optical dipole potential is assumed to be created by a Ti:sapphire laser at a wavelength of $839\mathrm{nm}$. All the cases plotted in this figure were computed for the same intensity $I_0=2.67\times {10}^6\mathrm{mW}∕{\mathrm{cm}}^2$ evaluated just above the PhC-air interface. Inset: Total, optical, gravitational, and Casimir-Polder potentials (blue, green, red, and black, respectively) for the case of $\Lambda =0.3\mu \mathrm{m}$. The minimum for the total potential is found at $y_0=1.1\mu \mathrm{m}$.

Figure 4

(Color) 2D total atomic potential produced by the structure sketched in Fig. 1 in the $xy$ plane for the case of Cs atoms. Color scale codes the potential in units of microkelvins. The minimum is found at $(x_0,y_0)=(3.3,1.1)\mu \mathrm{m}$. Left and right insets show cross sections of the potential along the lines $y_0=1.1\mu \mathrm{m}$ and $x_0=3.3\mu \mathrm{m}$, respectively.