We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei. The decay is caused by the spatial variation of the electron wave function within the dot, leading to a nonuniform hyperfine coupling A. We evaluate the spin correlation function and find that the decay is not exponential but rather power (inverse logarithm) lawlike. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by (planck)N/A, where N is the number of nuclei inside the dot, and the amplitude of precession decays to a finite value. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.

We study spin relaxation and decoherence in a GaAs quantum dot due to spin-orbit interaction. We derive an effective Hamiltonian which couples the electron spin to phonons or any other fluctuation of the dot potential. We show that the spin decoherence time T2 is as large as the spin relaxation time T1, under realistic conditions. For the Dresselhaus and Rashba spin-orbit couplings, we find that, in leading order, the effective magnetic field can have only fluctuations transverse to the applied magnetic field. As a result, T2 = 2T1 for arbitrarily large Zeeman splittings, in contrast to the naively expected case T2 ≪ T1. We show that the spin decay is drastically suppressed for certain magnetic field directions and values of the Rashba coupling constant. Finally, for the spin coupling to acoustic phonons, we show that T2 = 2T1 for all spin-orbit mechanisms in leading order in the electron-phonon interaction.PACS numbers: 72.25. Rb, 73.21.La, 03.67.Lx Phase coherence of spin in quantum dots (QDs) is of central importance for spin-based quantum computation in the solid state [1,2]. Sufficiently long coherence times are needed for implementing quantum algorithms and error correction schemes. If the qubit is operated as a classical bit, its decay time is given by the spin relaxation time T 1 , which is the time of a spin-flip process. For quantum computation, however, the spin decoherence time T 2 -the lifetime of a coherent superposition of spin up and spin down states -must be sufficiently long. In semiconductor QDs, the spin coherence is limited by the dot intrinsic degrees of freedom, such as phonons, spins of nuclei, excitations on the Fermi surface (e.g. in metallic gates), fluctuating impurity states nearby the dot, electromagnetic fields, etc. It is well known (and experimentally verified) that the T 1 time of spin in QDs is extremely long, extending up to 100 µs. The decoherence time T 2 , in its turn, is limited by both spin-flip and dephasing processes, and can be much smaller than T 1 , although its upper bound is T 2 ≤ 2T 1 . Knowledge of the mechanisms of spin relaxation and decoherence in QDs can allow one to find regimes with the least spin decay.Recently, the spin relaxation time T 1 in a singleelectron GaAs QD was measured [3] by means of a pulsed relaxation measurement technique (PRMT) [4]. This technique was previously applied to measure the triplet-to-singlet spin relaxation in a two-electron quantum dot [5], yielding a spin relaxation time of 200 µs. The application of the PRMT to Zeeman sublevels became possible with resolving the Zeeman splitting in dc transport spectroscopy [3,6], which required a magnetic field B > 5 T. The results of Ref. 3 show that T 1 > 50 µs at B = 7.5 T and 14 T, with no indication of a B-field dependence. Experimental values for the spin T 2 time in a single QD are not available yet, but an ESR scheme for its measurement has been proposed [7]. The ensemble spin decoherence time T * 2 was measured in n-doped GaAs bulk semiconductors [8], demonstrating coherent spin...

We have studied spin-flip transitions between Zeeman sublevels in GaAs electron quantum dots. Several different mechanisms which originate from spin-orbit coupling are shown to be responsible for such processes. It is shown that spin-lattice relaxation for the electron localized in a quantum dot is much less effective than for the free electron. The spin-flip rates due to several other mechanisms not related to the spin-orbit interaction are also estimated.

We have studied spin-flip processes in GaAs electron quantum dots that accompany transitions between different discrete energy levels. Several different mechanisms that originate from spin-orbit coupling are shown to be responsible for such processes. We have evaluated the rates for all mechanisms with and without a magnetic field. We have shown that the spin relaxation of the electrons localized in the dots differs strikingly from that of the delocalized electrons. The most effective spin-flip mechanisms related to the absence of the inversion symmetry appear to be strongly suppressed for localized electrons. This results in unusually low spin-flip rates.Quantum dots ͑QD's͒ are small conductive regions in semiconductor structures that contain a tunable number of carriers. The shape and size of quantum dots can be controlled by the gate voltage. The localized electronic states in QD's can be significantly modified by a magnetic field. All this provides a valuable opportunity to study the properties of the electron quantum states in detail and manipulate the electrons in these artificial atoms in a controllable way ͑see Refs. 1 and 2 for review͒.The spin states in quantum dots are considered to be promising for physical realization of the quantum computation algorithm.3 Quantum computation requires coherent coupling between the dots, the coherence to be preserved on sufficiently long time scales. That makes it relevant to provide a complete theoretical estimation of the typical spin dephasing time of the electron in the QD. Transport experiments with QD's have revealed that the current through a quantum dot can be influenced by the spin effects. 4 It opens up a possibility to estimate spin relaxation rates by means of transport measurement. 5 The origin of this effect is that the spin-flip process can provide a bottleneck for the energy relaxation in the dot, i.e., for transitions between the excited and ground states. Indeed, in the absence of the spin flip the total spin of the dot is a good quantum number and no transition is allowed between the states of different total spins. To illustrate, let us consider a QD with two electrons which can be placed in two levels. The ground state corresponds to two electrons in the lowest level having opposite spins (S ϭ0). One of the excited states corresponds to two electrons in different levels having the same spin direction (Sϭ1). Due to the Pauli principle, the electron in the upper level cannot get to the lower level without changing its spin. Therefore, the relaxation to the ground state of the dot has to be accompanied by a spin flip.In contrast to the situation in two-dimensional ͑2D͒ electron gas the electrons confined in the dot experience no electron-electron scattering ͑see Ref. 6͒. The only source of dissipation is the interaction with phonons. Moreover, although the electron-electron interaction is quite important in determining the energies of the states and the number of electrons in the dot, it is less important for the structure of the wave functions. To ...

We review and summarize recent theoretical and experimental work on electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with surrounding nuclear spins. This topic is of particular interest with respect to several proposals for quantum information processing in solid state systems. Specifically, we investigate the hyperfine interaction of an electron spin confined in a quantum dot in an s-type conduction band with the nuclear spins in the dot. This interaction is proportional to the square modulus of the electron wavefunction at the location of each nucleus leading to an inhomogeneous coupling, i.e. nuclei in different locations are coupled with different strengths. In the case of an initially fully polarized nuclear spin system an exact analytical solution for the spin dynamics can be found. For not completely polarized nuclei, approximation-free results can only be obtained numerically in sufficiently small systems. We compare these exact results with findings from several approximation strategies.