Polarization-dependent atomic dipole traps behind a circular aperture for neutral-atom quantum computing

The neutral-atom quantum computing community has successfully implemented almost all necessary steps for constructing a neutral-atom quantum computer. We present computational results of a study aimed at solving the remaining problem of creating a quantum memory with individually addressable sites for quantum computing. The basis of this quantum memory is the diffraction pattern formed by laser light incident on a circular aperture. Very close to the aperture, the diffraction pattern has localized bright and dark spots that can serve as red-detuned or blue-detuned atomic dipole traps. These traps are suitable for quantum computing even for moderate laser powers. In particular, for moderate laser intensities ($~100$ W/${\mathrm{cm}}^2$) and comparatively small detunings ($~1000$–10 000 linewidths), trap depths of $~1$ mK and trap frequencies of several to tens of kilohertz are achieved. Our results indicate that these dipole traps can be moved by tilting the incident laser beams without significantly changing the trap properties. We also explored the polarization dependence of these dipole traps. We developed a code that calculates the trapping potential energy for any magnetic substate of any hyperfine ground state of any alkali-metal atom for any laser detuning much smaller than the fine-structure splitting for any given electric field distribution. We describe details of our calculations and include a summary of different notations and conventions for the reduced matrix element and how to convert it to SI units. We applied this code to these traps and found a method for bringing two traps together and apart controllably without expelling the atoms from the trap and without significant tunneling probability between the traps. This approach can be scaled up to a two-dimensional array of many pinholes, forming a quantum memory with single-site addressability, in which pairs of atoms can be brought together and apart for two-qubit gates for quantum computing.

Figure 1

Diabatic trapping potential energy for a single laser beam (${\sigma }^{+}$ polarization was used) incident on a circular aperture at an angle of $\gamma =0.055$ rad. (a) Diagram of setup. (b) Intensity pattern. (c) Trapping potential energy for the light-polarization-independent $F=1$, $m_F=0$ magnetic substate of ${}^{87}\mathrm{Rb}$, for a laser intensity of 364 W/cm${}^2$ and a laser detuning of $-$10 000 $\Gamma$. (d) Trapping potential energy for the $F=1$, $m_F=0$ magnetic substate of ${}^{87}\mathrm{Rb}$, for a laser intensity of 116 W/cm${}^2$ and a laser detuning of 1000 $\Gamma .$

Figure 2

Diabatic trapping potential energy along the laser axis and along the paths of weakest confinement (“escape paths”) for red-detuned and blue-detuned traps, for a single laser beam (${\sigma }^{+}$ polarization was used) incident at $\gamma =0.055$ rad, for the light-polarization-independent $F=1$, $m_F=0$ magnetic substate of ${}^{87}\mathrm{Rb}$. (a) Axial path (solid line) and escape path (dashed line) for a laser intensity of 364 W/cm${}^2$ and a laser detuning of $-$10 000 $\Gamma$. (b) Trapping potential energy along the laser axis for red-detuned trap [solid line in (a)]. (c) Trapping potential energy along the escape path for red-detuned trap [dashed line in (a), weakest trap direction]. (d) Axial path (solid line) and escape path (dashed line) for a laser intensity of 116 W/cm${}^2$ and a laser detuning of 1000 $\Gamma .$ (e) Trapping potential energy along the laser axis for the blue-detuned trap [solid line in (b)]. (f) Trapping potential energy along the escape path for the blue-detuned trap [dashed line in (b), weakest trap direction].

Figure 3

Diabatic trapping potential energy for two laser beams of opposite circular polarization incident on a circular aperture at an angle of $\gamma =0.055$ rad. (a) Diagram of setup. (b) Intensity pattern, normalized to the incident intensity of one incident circularly polarized laser beam. (c)–(j) Trapping potential energy of the intensity pattern in (b) for the eight magnetic substates of the hyperfine ground-state manifold in ${}^{87}\mathrm{Rb}$ for a laser intensity of 364 W/cm${}^2$ and a laser detuning of $-$10 000 $\Gamma$ from the transitions from the respective F states.

Figure 4

Bringing two traps together. (a) Column showing the intensity pattern, normalized to the incident intensity of one incident circularly polarized laser beam, for several incident angles $\gamma$. (b) Column showing the diabatic potential-energy profile along the $y$ direction at $z=67$ $\mu$m for the $F=1$, $m_F=1$ (solid line) and $m_F=-1$ (dashed line) magnetic substates of ${}^{87}\mathrm{Rb}$ trapped in the intensity pattern from (a) for several incident angles $\gamma$, a laser intensity of 364 W/cm${}^2$, and a laser detuning of $-$10 000 $\Gamma$. (c) Column showing the diabatic potential-energy profile along the $y$ direction at $z=100$ $\mu$m for the $F=1$, $m_F=1$ (solid line) and $m_F=-1$ (dashed line) magnetic substates of ${}^{87}\mathrm{Rb}$ trapped in the intensity pattern from (a) for several incident angles $\gamma$, a laser intensity of 116 W/cm${}^2$, and a laser detuning of 1000 $\Gamma .$

Figure 5

A 2D array of diffraction traps behind a 2D array of circular apertures. For appropriate aperture spacings, e.g., a few microns, individual trap sites can be addressed with a focused laser beam. Two atoms are brought together by tilting the incident laser beams, entangled with a focused laser beam, and moved apart by tilting the laser beams back. (a) Laser beams are tilted to normal incidence, bringing two traps from the same aperture together. (b) Laser beam tilt is increased, bringing two traps from neighboring apertures together.