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arXiv:0805.2437 · Quantum Information and Computation

Scalable, efficient ion-photon coupling with phase Fresnel lenses for large-scale quantum computing

Erik W. Streed, B. G. Norton, J.J. Chapman, D. Kielpinski

Published Mar 1, 2009• 13 citations
arXivHTMLPDF

Abstract

Efficient ion-photon coupling is an important component for large-scale ion-trap quantum computing. We propose that arrays of phase Fresnel lenses (PFLs) are a favorable optical coupling technology to match with multi-zone ion traps. Both are scalable technologies based on conventional micro-fabrication techniques. The large numerical apertures (NAs) possible with PFLs can reduce the readout time for ion qubits. PFLs also provide good coherent ion-photon coupling by matching a large fraction of an ion's emission pattern to a single optical propagation mode (TEM$_{00}$). To this end we have optically characterized a large numerical aperture phase Fresnel lens (NA=0.64) designed for use at 369.5 nm, the principal fluorescence detection transition for Yb$^+$ ions. A diffraction-limited spot $w_0=350\pm15$ nm ($1/e^2$ waist) with mode quality $M^2= 1.08\pm0.05$ was measured with this PFL. From this we estimate the minimum expected free space coherent ion-photon coupling to be 0.64\%, which is twice the best previous experimental measurement using a conventional multi-element lens. We also evaluate two techniques for improving the entanglement fidelity between the ion state and photon polarization with large numerical aperture lenses.

DOI
10.26421/qic9.3-4-2

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Efficient ion-photon coupling is an important component for large-scale ion-trap quantum computing. We propose that arrays of phase Fresnel lenses (PFLs) are a favorable optical coupling technology to match with multi-zone ion traps. Both are scalable technologies based on conventional micro-fabrication techniques. The large numerical apertures (NAs) possible with PFLs can reduce the readout time for ion qubits. PFLs also provide good coherent ion-photon coupling by matching a large fraction of an ion's emission pattern to a single optical propagation mode (TEM00_{00}00​). To this end we have optically characterized a large numerical aperture phase Fresnel lens (NA=0.64) designed for use at 369.5 nm, the principal fluorescence detection transition for Yb+^++ ions. A diffraction-limited spot w0=350±15w_0=350\pm15w0​=350±15 nm (1/e21/e^21/e2 waist) with mode quality M2=1.08±0.05M^2= 1.08\pm0.05M2=1.08±0.05 was measured with this PFL. From this we estimate the minimum expected free space coherent ion-photon coupling to be 0.64%, which is twice the best previous experimental measurement using a conventional multi-element lens. We also evaluate two techniques for improving the entanglement fidelity between the ion state and photon polarization with large numerical aperture lenses.
Efficient ion-photon coupling is an important component for large-scale ion-trap quantum computing. We propose that phase Fresnel lenses (PFLs) are a favorable optical coupling technology to match with multi-zone ion traps. Both are scalable technologies based on conventional micro-fabrication techniques. Large numerical aperture (NA) PFLs can reduce the readout time for ion qubits and provide good coherent coupling to a single optical mode. From optical characterization of a suitable PFL we predict a coherent coupling efficiency of >0.64%, twice the best experimental efficiency achieved to date. In addition, high NA entanglement fidelity limits can be removed by optical filtering.
To efficiently collect light from ions in a trapped ion quantum computer, a lens with a high numerical aperture is advantageous. Using phase Fresnel lenses with large working distances and high numerical apertures, we can couple a large fraction of the fluorescence from an ion into a single optical propagation mode (TEM00). We have optically profiled a phase Fresnel lens with a numerical aperture of 0.64 and a focal length of 3 mm. A 350ᱵ nm beam waist and a beam quality M2 of 1.08ᰮ05 was measured near the diffraction limit.
Trapped ions are a leading system for realizing quantum information processing (QIP). Most of the technologies required for implementing large-scale trapped-ion QIP have been demonstrated, with one key exception: a massively parallel ion-photon interconnect. Arrays of microfabricated phase Fresnel lenses (PFL) are a promising interconnect solution that is readily integrated with ion trap arrays for large-scale QIP. Here we show the first imaging of trapped ions with a microfabricated in-vacuum PFL, demonstrating performance suitable for scalable QIP. A single ion fluorescence collection efficiency of 4.2±1.5% was observed. The depth of focus for the imaging system was 19.4±2.4 μm and the field of view was 140±20 μm. Our approach also provides an integrated solution for high-efficiency optical coupling in neutral atom and solid-state QIP architectures.
We developed techniques to design higher efficiency diffractive optical elements (DOEs) with large numerical apertures (NA) for quantum computing and quantum information processing.Large NA optics encompass large solid angles and thus have high collection efficiencies.Qubits in ion trap architectures are commonly addressed and read by lasers 1 .Large-scale ion-trap quantum computing 2 will therefore require highly parallel optical interconnects.Qubit readout in these systems requires detecting fluorescence from the nearly isotropic radiation pattern of single ions, so efficient readout requires optical interconnects with high numerical aperture.Diffractive optical element fabrication is relatively mature and utilizes lithography to produce arrays compatible with large-scale ion-trap quantum computer architectures.The primary challenge of DOEs is the loss associated with diffraction efficiency.This is due to requirements for large deflection angles, which leads to extremely small feature sizes in the outer zone of the DOE.If the period of the diffractive is between  (the free space wavelength) and 10 the element functions in the vector regime.DOEs in this regime, particularly between 1.5 and 4 have significant coupling to unwanted diffractive orders, reducing the performance of the lens.Furthermore, the optimal depth of the zones with periods in the vector regime differs from the overall depth of the DOE.We will present results indicating the unique behaviors around the 1.5 and 4 periods and methods to improve the DOE performance.
Trapped ion quantum networking aims at distributing quantum information between distant parties. Entanglement links between distant ions are mediated with photonic qubits, necessitating the need for efficient ion-photon interfaces. This thesis reports on progress towards improving the main limitations of creating a practical quantum network by using diffractive optics for high numerical aperture imaging of trapped ions. The diffractive optics are near-planar, patterned structures which are fabricated to collimate a large fraction of ion uorescence, with low aberration, for high resolution imaging. Patterning the central grounding electrode on a chip trap allows the ion to be within less than 100 microns of the surface. Large scale quantum networks will require a large number of ions and ion-photon interfaces. To scale the ion trap system, microfabricated surface traps can be used allowing for the opportunity to etch diffractive mirrors directly onto the trap surface. Collecting ion uorescence with the diffractive mirror, we show the highest ion-single mode optical fibre coupling efficiency, which enhances the entanglement rate of a quantum network. We then build a high resolution UV spectrometer to distinguish between frequency entangled photonic qubits. Frequency qubits offer more robust encoding when compared with polarisation qubits, as a result of energy conservation. Using the spectrometer we demonstrate correlations between the ion's internal state and the frequency state of an entangled photonic qubit. Quantum networks will require local quantum information processing using ion-ion gates to distribute entanglement over the entire network. Typically, the speed of these gates is presently limited to ~10 µs by the secular trap frequency. We demonstrate the first steps towards a fast ion-ion gate, not limited by the secular frequency, based on strong optical forces generated by the coherent, resonant absorption and stimulated emission of light from an ultrafast, pulsed laser. A full-scale quantum network will require many ion trap installations each with their own laser systems. For this challenge we demonstrate simple, robust, and cost-effective methods to lock the 399 nm photoionisation laser, based on polarisation spectroscopy through a hollow cathode lamp, and an opto-mechanical switch which allows locking of multiple lasers to a wavelength meter. Another scalable diffractive optic used is a phase Fresnel lens integrated into a 3D quadrupole ion trap system. The limits of imaging with this lens are tested by demonstrating force sensing at a sub-attoNewton level with super-resolution imaging techniques to find the ion location.