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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical encoding for quantum computation using photonic crystals

Hiroyuki Nihei, Atsushi Okamoto

Published Nov 18, 2003• 0 citations
Publisher

Abstract

We demonstrate optical encoding in an atomic device, considered as a key component in quantum computers. The atomic device consists of a three-level atom embedded in photonic crystals witout external driving lasers. We find that a large amount of population trapping in the upper levels of the atom can be achieved, which is relevant for a strong optical memory effect. Furthermore, the trapped populations keep a memory of the initial atomic state including two-state quantum information, so that the atomic device can be used for a quantum bit encoding the quantum information.

DOI
10.1117/12.529987

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We demonstrate optical encoding in an atomic device, considered as a key component in quantum computers. The atomic device consists of a three-level atom embedded in photonic crystals witout external driving lasers. We find that a large amount of population trapping in the upper levels of the atom can be achieved, which is relevant for a strong optical memory effect. Furthermore, the trapped populations keep a memory of the initial atomic state including two-state quantum information, so that the atomic device can be used for a quantum bit encoding the quantum information.
Abstract There is now great interest in optical memory using a three‐level atom embedded in photonic crystals, which can be used for quantum computing; however, quantum‐information detection from the optical memory has not been demonstrated. In this paper, first, considering the relative position of the photonic band gap (PBG) and two atomic levels split from the upper level of the atom used for the optical memory, we demonstrate that one of the split levels must be outside the PBG for quantum‐information detection. In this case, the quantum state of the atom can be changed by moving the other split level, where the quantum information is maintained or emitted for the cases in which the split level is inside or outside the PBG, respectively. The emitted quantum information can be measured as spontaneous emissions by a photon detector. Next, we propose two methods of moving the split level: one is realized by applying a direct current (DC) field to the atom and the other is realized by changing the intensity of the control laser field. Furthermore, by evaluating the intensities of the DC and the control laser fields, we find that the quantum information can be measured using the fields on the millielectronvolt order. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 87(8): 10–19, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ecjb.10205
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band-gap structure with one resonant frequency near the edge of the photonic band gap. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This nonzero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field-atom interaction exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive, optical memory device on the atomic scale. The protected electric dipole within the photonic band gap provides a basis for a qubit to encode information for quantum computations.
We propose all-optical switching schemes using a single three-level atomic system placed within a 3D photonic crystal that exhibits a complete 3D photonic band gap. The optical schemes we propose can be classified into two types with respect to a physical process that causes the switching effect. One switching type is mediated by changing an atom-field coupling strength. The other switching type is mediated by controlling quantum interference. Furthermore, we consider conditions of realizing a wide range of signals, which contributes to an improvement of the Signal to Noise ratio. The phases and strengths of the external laser fields required for the all-optical switching are revealed. Next, we estimate their switching times. Using these results, we propose the fastest scheme for every configuration of the atomic system, which is important for realizing a high-speed optical memory or switching device on an atomic scale that can be used in novel optical integrated systems, such as quantum computers.
We have demonstrated the coherent control of photonic bandgap (PBG) devices composed of a three-level atom embedded in three-dimensional PBG structures, which enables us to strongly suppress the loss of quantum information not only during its storage but also during its processing. We find that this ultralow-loss optical quantum information processing can be realized by generating the upper atomic level splitting inside the PBG and by tuning one of the split levels to a dark line in the emission spectrum (zeros in the spectrum at certain values of the emitted photon frequency). Furthermore, we show that the coherent control may provide a basis for the universal quantum logic gate operation in quantum computing.
We have so far spoken almost exclusively of photons and linear-optical elements, and seen just how powerful those two components can be for information processing. They provide unbreakable cryptographic tools, and allow for efficient quantum computing. However, many more possibilities become available when we allow photons to interact with atoms and solid matter in a quantum mechanical way. In particular, a quantum memory, the principal difficulty for linear-optical quantum computing, can be created. In this chapter we will take the first steps towards a full understanding of a photon's interaction with atoms. We will show how to describe the interactions within a system consisting of photons and few-level atoms and show how this interaction can be manipulated and exploited to provide quantum information processors based on both atomic and photonic qubits. We will also show that photon emission from atoms can degrade the quantum information contained within atoms, and we will present a formalism to model this effect. We begin with a general discussion of atom-photon interactions. Atomic systems as qubits Let us first consider an electron in an isolated atom. It is bound there by the Coulomb force due to the charge distribution of all the other electrons and the nucleus. The potential that describes this coupling is given by V ( r ).