Resonant Transmission of Cold Atoms through Subwavelength Apertures

Recently, it has been observed that transmission of light through subwavelength apertures, which is usually negligible, can be significantly enhanced when surface plasmons are resonantly excited. Here we introduce the idea that similar effects can be expected for cold atoms in structures supporting surface matter waves. We show that surface matter waves are possible in properly designed structures, and then we theoretically demonstrate 100% transmission of rubidium atoms through an array of slits much narrower than the de Broglie wavelength of the atoms. Our results open up the possibility of using surface matter waves to control the flow of neutral atoms.

Figure 1

Potential function supporting surface matter waves. Here, the crosscut along the direction $z$ orthogonal to the flat surface is shown (black thick line), the potential being independent on $x$ and $y$. The infinite potential barrier models the interface impenetrability. The potential well has one bound state of energy $E_0$ (blue line). The corresponding wave function (red dashed line) is confined to a region close to the interface and propagates parallel to it. The indicated transition (dashed arrow) from a collision state of energy $E_{\mathrm{in}}$ to the SMW is only possible once the surface is modulated (see Fig. 2).

Figure 2

Calculated transmittance of cold ${}^{87}\mathrm{Rb}$ atoms through a film perforated by a periodic array of very narrow slits, as a function of the incident energy. Atoms incide along the direction $z$ normal to the film. Red line: transmittance reaches 100% when the structure supports surface states. The corresponding 2D potential is displayed in the inset (colors code the potential as follows: red (dark gray) $\to V=+\infty$, orange (medium gray) $\to V=0$, blue (light gray) $\to V=V_0=\mathrm{const}<0$; see crosscut along direction $z$ in Fig. 1). Black dashed line: transmittance is negligible when no potential well is available, i.e., when $V_0=0$. In the computer simulations, the corners of the rectangular areas have been rounded with radius $r=64\mathrm{nm}$.

Figure 3

(a) 2D total potential for ${}^{87}\mathrm{Rb}$ cold atoms impinging on an array of cylindrical dielectric fibers carrying a blue-detuned optical guided mode. The white circles represent the fibers’ cross section. Color scale codes potential energies in units of ${10}^{-11}\mathrm{eV}$. Blue and green regions correspond to an attractive potential well. The effective slit width is of the order of $0.05\mu \mathrm{m}$. (b) Black line: crosscut along the vertical $z$ line of potential shown in left panel. Green and magenta lines: van der Waals and dipolar contribution to the total potential, respectively. The energy of the fourth level of this 1D potential is represented by the blue line, and the red dashed line shows the corresponding wave function.

Figure 4

(a) Transmittance of cold ${}^{87}\mathrm{Rb}$ atoms orthogonally incident on the structure shown in Fig. 3a, as a function of the incident energy. The various lines correspond to different optical powers $P$ carried by the fibers. Thus, $P$ controls the switch functionality of the structure. (b) Modulus of the matter wave function $|\psi (\mathbf{r})|$ for the left peak of the curve corresponding to $P=P_0$ in panel (a). The scale is normalized to the incident amplitude. The plot corresponds to 100% transmission.