Nonequilibrium stabilization of charge states in double quantum dots

We analyze the decoherence of charge states in double quantum dots due to cotunneling. The system is treated using the Bloch-Redfield generalized master equation for the Schrieffer-Wolff transformed Hamiltonian. We show that the decoherence, characterized through a relaxation t r and a dephasing time t f , can be controlled through the external voltage and that the optimum point, where these times are maximum, is not necessarily in equilibrium. We outline the mechanism of this nonequilibrium-induced enhancement of lifetime and coherence. We discuss the relevance of our results for recent charge qubit experiments. The loss of quantum coherence is a central paradigm of modern physics. It not only governs the transition between the quantum-mechanical and the classical world, but has recently also gained practical importance in the context of engineering quantum computing devices. Decoherence naturally occurs in small quantum systems coupled to macroscopic heat baths. A huge class of such baths generates Gaussian noise and can hence be mapped on an ensemble of harmonic oscillators as in the spin-boson model. 1 This can even apply, if the fundamental degrees of freedom of the bath are fermions, as it is, e.g., the case if the bath is a linear electrical circuit, 2,3 which is producing Gaussian JohnsonNyquist noise. In this Rapid Communication, we study a generically different system: a double quantum dot coupled to electronic leads. Such systems are studied as realizations of quantum bits. 4‐6 The position ~either left or right dot! of an additional spin-polarized electron is used as the computational basis of a charge qubit as realized in Ref. 6. For another proposal of a charge qubit in semiconductors, see Ref. 7. Our system simultaneously couples to two distinct reservoirs of real fermions. Other than oscillator bath models, this allows for the application of a voltage between these reservoirs as a new parameter for controlling decoherence. The voltage creates nonequilibrium between the baths, which to the best of our knowledge has not been studied yet in the literature on open quantum systems. We study the dynamics of the reduced density matrix and identify the usual two modes of decoherence, dephasing and relaxation: Dephasing is the loss of phase information, manifest as the decay of coherent oscillations. This corresponds to the time evolution of the off-diagonal elements of the reduced density matrix in the energy basis. Relaxation is the process during which a quantum system exchanges energy with the environment and ends up in a stationary state. This is described through the evolution of the diagonal density matrix elements. We are going to show that, surprisingly, the charge states can be stabilized by external nonequilibrium, i.e., the relaxation time is longest at a well-defined finite voltage. We will show, that this working point is also very favorable in terms of dephasing but competes with another local maximum at zero voltage. Our theory should also have applications in other systems. We consider a double quantum dot system with an appreciable tunnel coupling between the dots allowing for coherent molecular states in these systems. 8 The computational basis is formed by the position states of an additional spinpolarized electron. 6,7 A superposition can be created by variation of the interdot coupling. In order to stabilize the charge, the coupling of the dots to the two leads is driven to weak values and the dot is tuned to the Coulomb blockade regime 9 where sequential tunneling is suppressed through the addition energy. Even then, the system couples to the environment through cotunneling, 10 the correlated exchange of two electrons with the external leads which ends up in a state