Simultaneous optical trapping and detection of atoms by microdisk resonators

We propose a scheme for simultaneously trapping and detecting single atoms near the surface of a substrate using whispering gallery modes of a microdisk resonator. For efficient atom-mode coupling, the atom should be placed within approximately $150\mathrm{nm}$ from the disk. We show that a combination of red and blue detuned modes can form an optical trap at such distances while the backaction of the atom on the field modes can simultaneously be used for atom detection. We investigate these trapping potentials including van-der-Waals and Casimir-Polder forces and discuss corresponding atom detection efficiencies, depending on a variety of system parameters. Finally, we analyze the feasibility of nondestructive detection.

Figure 1

The structure under consideration. The evanescent wave from the slab waveguide (1) is coupled into the disk (2) and back through a small gap between them. The adiabatic waveguide tapers (3) serve for coupling light from optical fibers (not shown) into and out of the waveguide. Cold atoms (4) can be brought to the disk side via the magnetic field of a Z-shaped current-carrying wire (5) [9]. However, as explained in this work, such a magnetic trap is not suitable to hold the atoms during detection, and so other means of trapping are described for this operation.

Figure 2

Atom-surface asymptotic forms of the force vs atom distance from the microdisk: Casimir-Polder potential (solid line) and van der Waals potential (dashed line).

Figure 3

The radial potential near the surface of a $30\mathrm{\mu }\mathrm{m}$ disk. (a) Potential formed by blue-detuned light (dash-dotted line) and red-detuned light (dotted), surface potential (solid) and sum potential (dashed). (b) The sum of the optical potentials (solid) and the sum of the optical potentials and the surface potential (dashed). In this example, the number of blue-detuned cavity photons is $N_b=2.4\times {10}^5$, and the number of red-detuned photons is $N_r=3.68\times {10}^5$.

Figure 4

(a) Potential depth and (b) position of the trap minimum vs photon number $N_r$ in the red-detuned mode for different values of $N_b$, the photon number in the blue-detuned mode. The disk diameter is $30\mathrm{\mu }\mathrm{m}$.

Figure 5

Contour plot of the potential depth (in mK) vs position of the trap minimum $r_{\min }$ and photon number $N_b$ in the blue-detuned mode for a disk diameter of $15\mathrm{\mu }\mathrm{m}$.

Figure 6

Contour plot of the potential depth (in mK) vs position of the trap minimum $r_{\min }$ and photon number $N_b$ in the blue-detuned mode for a disk diameter of $30\mathrm{\mu }\mathrm{m}$.

Figure 7

(a) Signal-to-noise ratio and (b) total (red and blue) scattered photon number vs distance from the disk and blue-detuned photon number for a disk diameter of $15\mathrm{\mu }\mathrm{m}$. The integration time is $125\mathrm{\mu }\mathrm{s}$.

Figure 8

(a) Signal-to-noise ratio and (b) total scattered photon numbers vs distance from the disk and blue-detuned photon number for a disk diameter of $30\mathrm{\mu }\mathrm{m}$. The integration time is $75\mathrm{\mu }\mathrm{s}$.

Figure 9

Performance characteristics of a disk with diameter $D=15\mathrm{\mu }\mathrm{m}$ and for a $125\mathrm{\mu }\mathrm{s}$ integration time, at different blue-detuned photon numbers and atom distances. The area confined by the lines represents $S>5$, heating probability $<5\%$, and tunneling probability of $<2\%$ contains the parameter region where stable atom trapping and detection can be achieved with high confidence. An analysis of the parameter tolerance shows that for these optimized parameters a change of $\pm 2\%$ in either the blue- or red-detuned light intensity will still lead to another point within the triangle. The arrow represents the change in trap position if the intensity of the red- or blue-detuned light is varied by $\pm 2\%$.

Figure 10

Performance characteristics of a disk with diameter $D=30\mathrm{\mu }\mathrm{m}$ and for a $75\mathrm{\mu }\mathrm{s}$ integration time, at different blue-detuned photon numbers and atom distances. The area confined by the lines of $S=5$, heating probability $7\%$, and curve representing tunneling probability of $2\%$ contains the parameter region where stable atom trapping and detection can be achieved with high confidence. The arrow represents the change in trap center position if the intensity of the red- or blue-detuned light is varied by $\pm 2\%$.

Figure 11

(a) Signal-to-noise ratio and (b) total scattered photon numbers vs distance from the disk and blue-detuned photon number for disk diameter $30\mathrm{\mu }\mathrm{m}$. Integration time is $5\mathrm{\mu }\mathrm{s}$, rms roughness $\sigma =0.2\mathrm{nm}$, and gap size $\sim 0.7\mathrm{\mu }\mathrm{m}$.