<title>Optical memory using photonic crystals without external driving lasers for quantum computation</title>

Abstract

ABSTRACT In real photonic band gap (PBG) materials, the PBG is highly anisotropic. In this paper, we propose an opticalmemory composed of a three-level atom embedded in the realistic anisotropic PBG structures without external drivinglasers, which can be considered as essential components for a novel class of computation including an optical quantumcomputation.Keywords: Quantum optics, photonic crystal, optical memory, quantum computation 1. INTRODUCTION The recent progress of nanotechnologies makes it possible to fabricate an atomic scale device. Among the atomicscale devices, an optical memory is of special interest because such a device is considered as essential components for anovel class of computation including an optical quantum computation [1]. In the optical memory, quantuminformation is encoded by quantum states of materials for the optical memory. In order to keep the quantuminformation for a long time, it is necessary to maintain the quantum state. However, it has been difficult to maintainquantum states in optical frequency ranges, because of significant loss in materials [2]. More recently, feasibleapproaches to reduce the loss have been proposed [1], where photonic crystals attract a great deal of considerableattentions. The photonic crystal is used for a platform [3] in which an impurity three-level atom is embedded. Thethree-level atom is used for the optical memory applications including a quantum bit (qubit) that is an essential devicefor quantum computing [4]. For the three-level atom, a photonic band gap (PBG) provided by the photonic crystalplatform acts as a high-Q cavity in the optical frequency ranges. Due to the presence of the PBG, a localized field isformed in spontaneous emission from the atom, and then the quantum state of the atom is maintained for a long time [5].In this case, the steady-state inversion of the atom is formed, which leads to the formation of population trapping in thetwo upper levels of the atom. Amounts of the trapped populations encode the quantum information. However, it isimpossible to trap 100% of populations on the upper levels, even if we use a full PBG and external driving lasers. Theamount of the trapped populations depends on the type of the atom, the PBG and the external driving lasers.In order to carry out a high S/N ratio, it is essential to enhance the amount of the trapped populations [6]. The amountsof the trapped populations for several models have been reported [4-10]. Here, it has been reported that the amount ofthe trapped populations is enhanced by using the external driving lasers [4]. However, the model without drivinglasers is simpler rather than the model with driving lasers, so that consideration of the former model is important fromthe viewpoint of its fabrication. Furthermore, it has been reported that, even if we do not use the driving lasers, anisotropic PBG provides a large amount of population trapping [7]. More than 80% of populations can be trapped forthe three-level atom embedded in the isotropic PBG structure. However, a more realistic picture of the band edgebehavior requires the incorporation of the anisotropy. Therefore, in the realistic viewpoint, it is important to consideranisotropic PBG structures. For the realistic anisotropic PBG, the population trapping has been investigated only whenthe transition frequency of the atom is close to the edge of the PBG [4]. This investigation has revealed that thepopulations trapped in the upper levels are reduced to 50% for the anisotropic PBG.In this paper, we find that more than 80% of populations can be trapped in the upper levels of the atom, even in therealistic anisotropic PBG model. This modification is a direct consequence of the consideration for a large detuning ofthe upper levels from the band edge frequency, which reveals that the reduction of the trapping effect in the anisotropicPBG is improved by means of the large detuning. First, we introduce our mathematical approach to calculate statevectors of the atom for the large detuning. Next, we calculate spontaneous emission from the atom using the atomic