IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 4, NO. 1, JANUARY 2005 65 Study of Temperature Dependence of Electron–Phonon Relaxation and Dephasing in Semiconductor Double-Dot Nanostructures Leonid Fedichkin and Arkady Fedorov Abstract—This paper examines mechanisms of relaxation and dephasing of electrons in double-dot nanostructures due to inter- action with acoustic phonon modes. The effect of temperature of phonon bath on decay on electron quantum evolution is obtained. Our results set the temperature ranges outside of which the quantum dynamics of electrons will be significantly suppressed. Index Terms—Nanotechnology, phonons, quantum dots, quantum theory. I. INTRODUCTION O VER THE last decade, a great deal of attention has been paid to information processing by using coherent quantum dynamics [1]. Quantum devices based on solid-state nanostructures are considered to be among the major candidates for large-scale quantum computation because they can draw on existing large investments in nanotechnology and materials studies [2]. Several designs of semiconductor quantum bits (qubits) were proposed [3]–[7]. In particular, the encoding of quantum information into spatial degrees of freedom of electrons placed in a quantum dot was considered in [8]–[12]. The relatively fast decay of coherence of the electron state in ordinary quantum dots, mentioned in [13], can be efficiently suppressed by encoding quantum information into the subspace of electron states in specially constructed arrays of quantum dots (artificial crystals) proposed by Zanardi and Rossi [14]. Actually, under certain conditions, even double-dot systems in semiconductors can be relatively well protected against decoherence processes due to the interaction with the phonon environment and electromagnetic fields [15]. This observation was confirmed in recent experiments by Hayashi et al., who demonstrated coherent quantum oscillations of an electron position in the double-dot structure [16]. Various specific designs of double-dot qubits are studied in recent experiments [17]–[21] in the temperature ranges of tens Manuscript received May 20, 2004; revised June 30, 2004. This work was supported by the National Security Agency and Advanced Research and Devel- opment Activity under Army Research Office Contract DAAD-19-02-1-0035 and by the National Science Foundation under Grant DMR-0121146. The authors are with the Center for Quantum Device Technology, Department of Electrical and Computer Engineering and Department of Physics, Clarkson University, Potsdam, NY 13699-5721 USA (e-mail: leonid@clarkson.edu; fedorova@clarkson.edu). Digital Object Identifier 10.1109/TNANO.2004.840156 Fig. 1. Single electron within a double-well potential. and hundreds of millikelvins. Evaluations of temperature influ- ence on the first-order transition rates in Si charge qubits were obtained in [22] and [23], although it is not well understood what is the major factor limiting decoherence under these conditions. In a previous paper [24], we showed that, at a zero temperature limit and for conventional double-dot structures, the account for higher order processes of electron–phonon interactions changes the electron state significantly. In this study, we study the effects of lattice temperature on electron decoherence and qubit performance. We consider the action of phonon environment within the frameworks of an inde- pendent boson model [25] which were extensively used, in par- ticular, for the study of coherent electron dynamics in optically excited quantum dots (see, e.g., [26] and references therein). In Section II, we describe the model of qubit. The derivation of the electron–phonon interaction Hamiltonian for the specific double-dot geometry is given in Section III. The relaxation pro- cesses are considered in Section IV. Section V is devoted to the study of dephasing of qubit without energy exchange with the acoustic phonon bath. Finally, in Section VI, we derive qubit error rates due to both dephasing and relaxation mechanisms. II. MODEL We consider a double-dot structure that consists of two quantum dots coupled to each other via a tunneling barrier and a single electron traveling from one dot to another and back, as shown in Fig. 1. We limit our consideration by double-dot structures in which energy required to transfer to upper levels is much higher than lattice temperature and energy spacing between ground levels of two dots. Accordingly, we take into account only ground energy levels of each dot. 1536-125X/$20.00 © 2005 IEEE