We analyze decoherence of an electron in a double-dot due to the interaction with acoustic phonons. For large tunneling rates between the quantum dots, the main contribution to decoherence comes from the phonon emission relaxation processes, while for small tunneling rates, the virtual-phonon, dephasing processes dominate. Our results show that in common semiconductors, such as Si and GaAs, the latter mechanism determines the upper limit for the double-dot charge qubit performance measure.PACS numbers: 03.67. Lx, 85.35.Be, 73.20.Hb Recently, there has been a lot of interest in implementation of quantum logic gates by manipulating two-level electron systems in semiconductor quantum dots (artificial atoms) [1]. Several designs for solid state quantum information processing have been suggested [2,3,4]. Quantum-dot architecture of a quantum computer is very attractive because it is possibly scalable and the most compatible with the recent microelectronics technology. However, it is a great challenge to maintain a satisfactory level of coherence of an electron in semiconductor to perform even elementary quantum gates [5]. Hopefully, coherence can be enhanced by encoding of the logical qubit states into a subspace of the electron states in a large quantum dot array (artificial crystal) [6]. It is also noted that in a gate-engineered structure of two coupled identical quantum dots one can control decoherence rates by several orders of magnitude [3]. Recent advances in technology of fabrication of double-dot [7,8] and doubledonor [4] qubits have been reported. Coherent oscillations in double-dot qubit are observed [9]. It have been demonstrated that scattering by phonons can significantly influence electron transport through double-dot system [10] and qubit dynamics during measurement [11].In this work, we analyze decoherence of an electron in a double-dot potential due to acoustic phonons during one qubit gate cycle.We consider a single electron in the double well potential shown schematically in Fig. 1. Such a structure can be fabricated as two gate-engineered quantum dots [7,8,9], whose geometry is determined by the pattern of external metallic gates and electric potential at them, or by the coupling the two nearby phosphorus donors embedded in silicon [4]. The resulting qubit is supposed to evolve in the basis spanned by the states |0 and |1 which describe the electron localized around the left and right minima of the potential, respectively. We assume that the parameters of the double-dot qubit structure are selected appropriately and the temperature is low enough such that the effects of the electron transitions to the higher energy levels can be neglected. Inves- tigation of decoherence due to acoustic phonons is the primary goal of our work. Below, we will present the model and describe the two main mechanisms of decoherence. We will introduce the appropriate approximations schemes, quantify the overall error rate and discuss the ways to minimize it.The Hamiltonian of the electron and the phonon bath isHere q...
We consider a qubit interacting with its environment and continuously monitored by a detector represented by a point contact. Bloch-type equations describing the entire system of the qubit, the environment and the detector are derived. Using these equations we evaluate the detector current and its noise spectrum in terms of the decoherence and relaxation rates of the qubit. Simple expressions are obtained that show how these quantities can be accurately measured. We demonstrate that due to interaction with the environment, the measurement can never localize a qubit even for infinite decoherence rate. : 73.50.-h, 73.23.-b, 03.65.X. PACSAn account of decoherence and relaxation in quantum evolution of a two-level system (qubit), interacting with an environment and a measurement device, has become a problem of crucial importance in quantum computing. Numerous publications have appeared on this subject dealing with interactions either with a measurement device (detector) [1][2][3] or with the environment (a thermal bath) [4,5]. Generally, the simultaneous influence of an environment and a detector on a qubit is very important for understanding qubit measurements because the environment and the detector act on the qubit in different ways. For instance, the environment at zero temperature relaxes the qubit to its ground state. As a result the qubit finally appears in a pure state, even though it was initially in a statistical mixture. On the other hand, the measurement device puts the qubit in a statistical mixture, even if it was initially in a pure state.One of the most striking measurement effects in which the role of relaxation has not been investigated is the socalled Zeno paradox [6]. It consists of total freezing of a qubit in the limit of continuous measurement. Usually, it is associated with the projection postulate in the theory of quantum measurements. Indeed, it follows from the Schrödinger equation that the probability of a quantum transition from an initially occupied state of a qubit is P (∆t) = a(∆t) 2 , where a is a factor which depends on the system [6]. If we assume that ∆t is the measurement time which determines the timescale on which the system is projected into the initial state, then after N successive measurements the probability of finding the qubit in its initial state, at time t = N ∆t, is P (t) = [1−a(∆t) 2 ] (t/∆t) . Thus P (t) → 1 for ∆t → 0, N → ∞ and t=const. Including the environment into the Schrödinger equation for the entire system one would expect from the above arguments that the relaxation processes could only affect the coefficient a, but cannot destroy the qubit localization in the limit of ∆t → 0.This conclusion, however, is not correct. We demonstrate in this Letter that any weak relaxation delocalizes the qubit even in the limit of continuous measurement. It is shown by using new Bloch-type quantum rate equations for the description of a qubit interacting with a detector and its environment. These rate equations are derived from the microscopic Schrödinger equation for the e...
We investigated using as basic elements of the quantum computerquantum bits (qubits) semiconductor quantum dots containing one electron and consisting each of two tunnelconnected parts, as shown in Fig. 1. The numerical solution of a Schrodinger equation with the account of Coulomb field of adjacent electrons shows, that in such structures the realization of a full set of basic logic operations which are necessary for fulfillment of quantum computations is possible. Decoherence rates due to spontaneous emission of phonons and acoustic phonons (both piezoelectric and deformational) are evaluated. Durations of one-and two-qubit operations versus qubit geometry are obtained.
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