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Physical Review A

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

Katharina Gillen-Christandl, Bert Copsey

Published Feb 9, 2011• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.83.023408

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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 ( 100~100 100 W/cm2{\mathrm{cm}}^{2}cm2) and comparatively small detunings ( 1000~1000 1000--10 000 linewidths), trap depths of  1~1 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.
Neutral atom quantum computing is a promising avenue toward the realization of a physical quantum computer. The diffraction pattern formed by laser light immediately behind a circular aperture can be used as optical atomic dipole traps, and has the potential to be scaled up to create a two dimensional array of individually addressable qubit sites. In working towards experimental demonstration of the dipole traps, we are constructing a MOT. The function of the MOT is to cool and trap 87Rb in a localized cloud in our vacuum chamber, which will be used to load the dipole traps. One critical aspect to the functioning of the MOT is the precise tuning of the trapping laser to the red of the F=2→F’=3 hyperfine transition and the pump laser to the F=1→F’=2 hyperfine transition. We have successfully constructed a saturated absorption apparatus which works to distinguish the hyperfine structure of Rb within the Doppler broadened transition peaks. The saturated absorption scans serve to correlate the voltage applied to the piezo with the laser light frequencies causing hyperfine transitions in Rb, allowing for the precise tuning of the lasers needed to trap atoms.
We experimentally demonstrate novel structures for the realization of registers of atomic qubits: We trap neutral atoms in one- and two-dimensional arrays of far-detuned dipole traps obtained by focusing a red-detuned laser beam with a microfabricated array of microlenses. We are able to selectively address individual trap sites due to their large lateral separation of 125 microm. We initialize and read out different internal states for the individual sites. We also create two interleaved sets of trap arrays with adjustable separation, as required for many proposed implementations of quantum gate operations.
In this work we present the results of studies of one-dimensional (1D) and twodimensional (2D) optical lattices on a chip.We have developed a method to create 1D and 2D optical lattices above an optical waveguide.The method is based on the destructive interference of the evanescent waves of two modes of the waveguide, resulting in a periodic array of nodes above the waveguide surface.For blue-detuned light, this constitutes an array of optical dipole traps for neutral atoms.One pair of modes coupled into a ridge waveguide creates a 1D array of nodes in this manner, and two orthogonal pairs of modes in a slab waveguide result in a 2D array of nodes.Computational analysis of our method showed that these optical atom chips may be suitable for use as a quantum register, and for studies of atom-surface interactions between the trapped atoms and the waveguide surface.Using realistic waveguide materials and laboratory laser parameters we found that for a laser power of ~100 mW nodes can be created ~100 nm above the waveguide surface.The nodes constitute atom traps that are ~1mK deep, and have trap frequencies ~1MHz and ground state sizes of ~10 nm.The spacing between traps is ~1 µm enabling individual addressing with a focused laser beam.iii With the implementation of two-qubit gates in mind, initial investigations of extensions of the basic 2D optical lattice were conducted.Computational results for a counter-propagating 2D optical lattice with very close trap spacing (~λ/4) in one dimension, and for a 2D optical lattice with adjustable spacing between pairs of traps in one dimension are presented.An experimental setup for the realization of the proposed 2D optical lattices on a chip was designed and built.Several cooling and trapping steps necessary to prepare a cold atom sample for loading of the 2D optical lattice have been implemented successfully.In the course of previous studies of atom-surface interactions, a novel surfaceionization detector for 2D imaging of neutral atom samples was built and characterized.We find a detection efficiency ~50 %, a spatial resolution of 20 µm and a time response < 1/30 s. iv To my family.v ACKNOWLEDGMENTS First and foremost I would like to thank my advisor Greg Lafyatis for everything that he taught me.I also want to thank Frank DeLucia for always being there with his advice when I needed it.I appreciate Eric Herbst and Junko Shigemitsu for being willing to serve on
Quantum computing may still be decades away from realization but the pieces necessary for the construction of the first quantum chip are beginning to come together. One piece still eluding researchers is the ability to address individual atoms within a scalable quantum chip structure. The resolution to this issue may be found in any one of several promising implementations, including the use of neutral atoms trapped in 2D optical lattices. One method of constructing such lattices, which has been shown to be computationally viable, employs the diffraction pattern just behind a circular aperture. Laser wavelength stability plays a crucial role in this approach, which entails constructing a 2D optical lattice with an array of pinholes, populating the lattice with atoms collected by a magneto optical trap (MOT), and manipulating the atoms trapped within the lattice structure for quantum computations. Experimental work was done toward achieving the laser wavelength stability required for these tasks. First, we investigated inadequate temperature control of the laser diodes and a thermal mass issue attributed to the laser mounts was resolved. We proceeded to analyze the electronics of the laser locking feedback system, which were failing to hold the lasers steady at a desired wavelength. Several noise sources contributing to signal instability were identified and eliminated, but drifting of the error signal was persistent. A subsequent fix was then made to the locking electronics and sufficient laser wavelength stability was demonstrated when atoms were trapped for the first time in the Cal Poly MOT on September 2, 2011.
Many types of quantum systems are being explored for use in quantum computers. One type of quantum system that shows promise for quantum computing is trapped neutral atoms. They have long coherence times, since they have multiple stable ground states and have minimal coupling with other atoms and their environment, and they can be trapped in arrays, making them individu- ally addressable. Once trapped, they can be initialized and operated on using laser pulses. This experiment utilizes a pinhole diffraction pattern, which can trap atoms in both bright and dark areas. To maximize trap strength, an injection-locked laser amplification system is used to provide a high-power, precisely tunable light source for the diffraction pattern. This amplification system depends on the coupling between a “seed” laser and a “receiving” laser. In previous analyses of the coupling between these two laser diodes, the effects on injection locking when varying temperature and current of both lasers have been shown to be highly nonlinear, and few general trends have been identified. In this project, in order to optimize and better characterize the system, automation of the data-taking and varying parameters was implemented. High efficiency lock zones of laser currents and temperatures were identified, and these locking zones will allow us to create strong atom traps for our experiment.
Quantum computers are devices that are able to perform calculations not achievable for classical computers. Although there are many methods for creating a quantum computer, using neutral atoms offers the advantage of being stable when compared to other methods. The purpose of this investigation is to explore possible optical dipole trap configurations that would be useful for implementing a quantum computer with neutral atoms. Specifically, we computationally investigate arrays of pinholes, the diffraction pattern generated by them, and the onset of the Talbot effect in these traps. We manipulate the radius of the pinholes, the number of pinholes in the array, and the distance between adjacent pinholes in order to create trap configurations where the presence/absence of the Talbot effect contributes to the usefulness of the trap for quantum computing. We find configurations with pinhole distances of 80 μm and 100/110 μm respectively satisfied an absence and a strong presence of the Talbot effect.