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Physical Review A

Transverse-mode beam splitter of a light beam and its application to quantum cryptography

Hiroyuki Sasada, Megumi Okamoto

Published Jul 23, 2003• 101 citations
Publisher

Abstract

We have theoretically and experimentally studied how a Mach-Zehnder interferometer with an additional mirror transforms a light beam composed of the second lowest transverse modes, ${\mathrm{HG}}_{10},$ ${\mathrm{HG}}_{01},$ ${\mathrm{LG}}_{01},$ and ${\mathrm{LG}}_{0\ensuremath{-}1}$ (HG denotes Hermite-Gaussian mode; LG denotes Laguerre-Gaussian mode). In certain conditions, the interferometer divides the incident beam into the ${\mathrm{HG}}_{10}$ and ${\mathrm{HG}}_{01}$ components as a transverse-mode beam splitter. We propose a practical device involving the two interferometers for quantum cryptography, in which a photon carries two bits corresponding to the polarization and the transverse mode.

DOI
10.1103/physreva.68.012323

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We have theoretically and experimentally studied how a Mach-Zehnder interferometer with an additional mirror transforms a light beam composed of the second lowest transverse modes, HG10,{\mathrm{HG}}_{10},HG10​, HG01,{\mathrm{HG}}_{01},HG01​, LG01,{\mathrm{LG}}_{01},LG01​, and LG0\ensuremath−1{\mathrm{LG}}_{0\ensuremath{-}1}LG0\ensuremath−1​ (HG denotes Hermite-Gaussian mode; LG denotes Laguerre-Gaussian mode). In certain conditions, the interferometer divides the incident beam into the HG10{\mathrm{HG}}_{10}HG10​ and HG01{\mathrm{HG}}_{01}HG01​ components as a transverse-mode beam splitter. We propose a practical device involving the two interferometers for quantum cryptography, in which a photon carries two bits corresponding to the polarization and the transverse mode.
We theoretically demonstrate that a photonic crystal microcavity coupled to waveguides works as an optical beam splitter. Numerical simulations illustrate that spatially separated two output modes have a relative phase close to $\ensuremath{\pi}/2$ and tunable transmission coefficients. The general transformation of this beam splitter gives a single-qubit rotation operator about the xxx axis. Using such beam splitters, we show single-photon interference via the Mach-Zehnder interferometer and two-photon entanglement via Hong-Ou-Mandel effect. This system may have great applications in constructing interferometers and integrated circuits for optical quantum information processing with solid-state materials.
Beam splitters are key elements in optical and photonic systems and are therefore employed in both classical and quantum technologies. Depending on the intended application, these devices can split incident light according to its power, polarization state, or wavelength. In this work, we theoretically present a type of beam splitter capable of separating a light beam into its two-mode bright and dark components. We propose a prototype based on an optical cross-cavity system resonantly coupled to a $\mathrm{\ensuremath{\Lambda}}$-type three-level atom. The dark component of the incoming light is transmitted because the antisymmetric collective mode of the cavity setup is decoupled from the atom. Meanwhile, the bright component is reflected due to a quantum interference, which arises from the high cooperativity between the atom and the symmetric collective mode of the cavity setup. Although the device requires only a two-level atom to operate, using a three-level atom allows the device to be turned on or off by controlling the atomic ground states. Our results pave the way for applications of beam splitters that leverage the collective properties of light. Manipulating and exploiting this additional degree of freedom can advance the field of quantum optics and contribute to the development of quantum technologies.
Beam splitter Compared with other fundamental experiments in physics, optical tests of quantum mechanics are often distinguished by their simplicity. Most quantum optical experiments do not require a whole industry - an optical table of equipment and a few people are often sufficient. Good ideas, good research problems are more important. “Research is to see what everybody has seen and to think what nobody has thought” (Jammer, 1989). A simple optical beam splitter, for instance, is already a nice device to demonstrate the quantum nature of light. Quite a number of puzzling quantum effects have been seen by splitting or recombining photons at a small cube of glass. Additionally, the beam splitter serves as a theoretical paradigm for other linear optical devices. Interferometers, semitransparent mirrors, dielectric interfaces, wave guide couplers, and polarizers are all described sufficiently well by a simple beam splitter model. The quantum effects of almost all passive optical devices can be understood assuming appropriate beam splitter models. (It's all done with mirrors.) Heisenberg picture An ideal beam splitter is a reversible, lossless device in which two incident beams may interfere to produce two outgoing beams. For instance, a dielectric interface inside a cube or plate of glass splits a light beam into two, see Fig. 5.1. We may reverse this situation by sending the two beams back to the cube, where they interfere constructively to restore the original beam.
Photoexcitation of trapped ions by Hermite–Gaussian (HG) modes from guided beam structures is proposed and investigated theoretically. In particular, simple analytical expressions for the matrix elements of induced atomic transitions are derived that depend both on the parameters of HG beams and on the geometry of an experiment. By using these general expressions, the (Formula presented.) electric octupole (E3) transition is investigated in an Yb+ ion, localized in the low–intensity center of the HG10 and HG01 beams. It is shown how the corresponding Rabi frequency can be enhanced by properly choosing the polarization of incident light and the orientation of an external magnetic field, which defines the quantization axis of a target ion. The calculations, performed for experimentally feasible beam parameters, indicate that the achieved Rabi frequencies can be comparable or even higher than those observed for the conventional Laguerre–Gaussian (LG) modes. Since HG-like modes can be relatively straightforwardly generated with high purity and stability from integrated photonics, these results suggest that they may form a novel tool for investigating highly-forbidden atomic transitions.