Spin decay and quantum parallelism

We study the time evolution of a single spin coupled inhomogeneously to a spin environment. Such a system is realized by a single electron spin bound in a semiconductor nanostructure and interacting with surrounding nuclear spins. We find striking dependencies on the type of the initial state of the nuclear spin system. Simple product states show a profoundly different behavior than randomly correlated states whose time evolution provides an illustrative example of quantum parallelism and entanglement in a decoherence phenomenon.Comment: 6 pages, 4 figures included, version to appear in Phys. Rev.

Electron spin evolution induced by interaction with nuclei in a quantum dot

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei for times smaller than the nuclear spin relaxation time. The decay is caused by the spatial variation of the electron envelope wave function within the dot, leading to a non-uniform hyperfine coupling $A$. We show that the usual treatment of the problem based on the Markovian approximation is impossible because the correlation time for the nuclear magnetic field seen by the electron spin is itself determined by the flip-flop processes. The decay of the electron spin correlation function is not exponential but rather power (inverse logarithm) law-like. 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 $\hbar N/A$, where $N$ is the number of nuclei inside the dot. The amplitude of precession, reached as a result of the decay, is finite. 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.Comment: Revtex, 11 pages, 5 figure

Electron spin relaxation by nuclei in semiconductor quantum dots

We have studied theoretically the electron spin relaxation in semiconductor quantum dots via interaction with nuclear spins. The relaxation is shown to be determined by three processes: (i) -- the precession of the electron spin in the hyperfine field of the frozen fluctuation of the nuclear spins; (ii) -- the precession of the nuclear spins in the hyperfine field of the electron; and (iii) -- the precession of the nuclear spin in the dipole field of its nuclear neighbors. In external magnetic fields the relaxation of electron spins directed along the magnetic field is suppressed. Electron spins directed transverse to the magnetic field relax completely in a time on the order of the precession period of its spin in the field of the frozen fluctuation of the nuclear spins. Comparison with experiment shows that the hyperfine interaction with nuclei may be the dominant mechanism of electron spin relaxation in quantum dots

Nuclear spin relaxation probed by a single quantum dot

We present measurements on nuclear spin relaxation probed by a single quantum dot in a high-mobility electron gas. Current passing through the dot leads to a spin transfer from the electronic to the nuclear spin system. Applying electron spin resonance the transfer mechanism can directly be tuned. Additionally, the dependence of nuclear spin relaxation on the dot gate voltage is observed. We find electron-nuclear relaxation times of the order of 10 minutes

Nuclear Spins in Quantum Dots

The main theme of this thesis is the hyperfine interaction between the many lattice nuclear spins and electron spins localized in GaAs quantum dots. This interaction is an intrinsic property of the material. Despite the fact that this interaction is rather weak, it can, as shown in this thesis, strongly influence the dynamics of electron spins in quantum dots. In chapter 1 some basic features of quantum dots are described and the most important sources for the mixing of spin components in GaAs, i.e. the hyperfine and spin-orbit interaction, are introduced and discussed. The hyperfine mediated transition rate from a triplet state to the ground state singlet is considered in chapter 2. The transition involves changing both the orbital and spin degree of freedom so the phonon scattering alone cannot facilitate the transition. Also, the hyperfine interaction alone can not cause the transition because the nuclear spin system cannot absorb the energy released by the singlet-to-triplet transition. Thus, both a source of inelastic scattering and the hyperfine interaction are required for the transition. The resulting transition involves virtual excited states. Assuming a small exchange splitting a simple expression for the transition rate is obtained that involves only the first excited singlet state. The subject of chapter 3 is the hyperfine mediated transitions between Zeeman split doublet components of the ground state orbital of a single-electron quantum dot. The spin-flip mechanism is the same as for the singlet-triplet case, i.e. the transition goes via higher orbital virtual states and involves both the hyperfine interaction and phonon scattering. A closer look is taken at the relevant electron-phonon coupling mechanism: The piezoelectric phonons. In addition, a semiclassical picture of the nuclear system is formulated. The great number of nuclei in the quantum dot makes it possible to consider them as an effective nuclear magnetic field acting on the electron spin. The transition amplitude between the doublet components due to the hyperfine interaction remains finite even if the external magnetic field goes to zero. This is in contrast to spin-orbit interaction where the transition amplitude vanishes at zero field. Thus, at sufficiently low magnetic field the hyperfine related spin-flip rate will dominate the spin-orbit one. The rates obtained in chapters 2 and 3 are usually much smaller than non-spin-flip transition rates in quantum dots. Transport through a GaAs double quantum dot in the socalled spin-blockade regime is the subject of chapter 4. The current is blocked due to the absence of transitions between singlet and triplet states within the quantum dots. Mo tivated by a recent experiment, we consider the influence of the hyperfine in teraction on transport in the spin-blockade regime. A small transport current will flow if the singlet and triplet states are mixed. In our model the mixing is induced by the different effective nuclear magnetic fields acting the electron spins in the two dots. Not only does the nuclear system affect the electron spins and lift the spin-blockade, there is also a back-action on the nuclear system that is determined by the average electron spin in the two dots. The nuclear system precesses around the average electron spin, leading to a time dependent transport current whose characteristics are in qualitative agreement with the experimental observations. In the last chapter the dynamics induced by the hyperfine coupling of the electron and nuclear spins in a quantum dot are studied. An effective spin Hamiltonian is considered where the spatial dependence of the electron wave- function results in an inhomogenoues hyperfine coupling of the electron spin to different nuclear spins. Generally, it is not possible to solve this Hamiltonian except in the special case of homogeneous coupling. To obtain an approximate solution, we split the nuclear system into Nb subsystems where all nuclei within a given subsystem have equal coupling to the electron spin. An important fea ture of the original Hamiltonian is the separation of the timescales, i.e. the electron spin dynamics are much faster than that of the nuclear spins. This allows us to use the adiabatic approximation when calculating the average elec tron spin which each nuclear spin sees. In this way the electron spin is removed from the problem leaving 3Nb coupled differential equations. These are solved numerically and the results used to calculate certain electron spin correlation functions. Contrary to what one may guess, the dynamics are not chaotic and the correlation functions show no decay in time, only complicated oscillations. This may be be attributed to the fact that the system has many integrals of motion and that it is close to exactly solvable. This behavior persists even for Nb » 1, which is the limit in which our approximation becomes more accurate.Applied Science

Optical out-of-plane spin polarization and charge conductivities in spin-orbit-coupled systems in the presence of an in-plane magnetic field

Out-of-plane spin and charge responses to the terahertz field for a clean two-dimensional electron gas with a Rashba spin-orbit interaction in the presence of an in-plane magnetic field are studied. We show that the characteristic optical spectral behavior is remarkably different from that of the system in the absence of in-plane magnetic fields. It is found that the optical spin polarization normal to the plane is nonzero even for this clean system, in sharp contrast to the static case. Due to the combined effect of spin-orbit coupling and in-plane magnetic field, both diagonal and off-diagonal components of optical charge conductivity tensor are nonvanishing. It is indicated that one can control the spin polarization and the optical current by adjusting the optical frequency. In addition, the out-of-plane spin polarization and conductivities strongly rely on the direction of the external magnetic field. Nevertheless, they meet different angle-dependent relations. This dynamical out-of-plane spin polarization could be measured by the time-resolved Kerr rotation technique. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010