We study control of electron-nuclear spin dynamics at magnetic field strengths where the Larmor frequency of the nucleus is comparable to the hyperfine coupling strength. The quantization axis for the nuclear spin differs from the static ${B}_{0}$ field direction and depends on the state of the electron spin. The quantization axis can be switched by flipping the state of electron spin, allowing for universal control of nuclear spin states. We show that by performing a sequence of flips (each followed by a suitable delay), we can perform any desired rotation of the nuclear spin, which can also be conditioned on the state of the electron spin. These operations, combined with electron spin rotations, can be used to synthesize any unitary transformation of the coupled electron-nuclear spin system. We discuss how these methods can be used for design of experiments for transfer of polarization from the electron to the nuclear spins.We study control of electron-nuclear spin dynamics at magnetic field strengths where the Larmor frequency of the nucleus is comparable to the hyperfine coupling strength. The quantization axis for the nuclear spin differs from the static ${B}_{0}$ field direction and depends on the state of the electron spin. The quantization axis can be switched by flipping the state of electron spin, allowing for universal control of nuclear spin states. We show that by performing a sequence of flips (each followed by a suitable delay), we can perform any desired rotation of the nuclear spin, which can also be conditioned on the state of the electron spin. These operations, combined with electron spin rotations, can be used to synthesize any unitary transformation of the coupled electron-nuclear spin system. We discuss how these methods can be used for design of experiments for transfer of polarization from the electron to the nuclear spins.

arXiv:0707.1572Physical Review ASep 26, 200760 citations

Entanglement of an impurity and conduction spins in the Kondo model

Sangchul Oh, Jaewan Kim

Based on Yosida's ground state of the single-impurity Kondo Hamiltonian, we study three kinds of entanglement between an impurity and conduction electron spins. First, it is shown that the impurity spin is maximally entangled with all the conduction electrons. Second, a two-spin density matrix of the impurity spin and one conduction electron spin is given by a Werner state. We find that the impurity spin is not entangled with one conduction electron spin even within the Kondo screening length ${\ensuremath{\xi}}_{K}$, although there is the spin-spin correlation between them. Third, we show the density matrix of two conduction electron spins is nearly the same as that of a free electron gas. The single impurity does not change the entanglement structure of the conduction electrons in contrast to the dramatic change in electrical resistance.Based on Yosida's ground state of the single-impurity Kondo Hamiltonian, we study three kinds of entanglement between an impurity and conduction electron spins. First, it is shown that the impurity spin is maximally entangled with all the conduction electrons. Second, a two-spin density matrix of the impurity spin and one conduction electron spin is given by a Werner state. We find that the impurity spin is not entangled with one conduction electron spin even within the Kondo screening length ${\ensuremath{\xi}}_{K}$, although there is the spin-spin correlation between them. Third, we show the density matrix of two conduction electron spins is nearly the same as that of a free electron gas. The single impurity does not change the entanglement structure of the conduction electrons in contrast to the dramatic change in electrical resistance.

arXiv:quant-ph/0601166Physical Review BFeb 21, 200622 citations

The Electron Spin

Valerio Magnasco

Elsevier eBooksJan 1, 20070 citations

Electron spin

Jeff Greensite

Institute of Physics eBooksFeb 1, 20170 citations

Collective state of electrons and impurities with a spin

É. G. Batyev

The problem of states of an electron system interacting with impurities that have a spin of 1/2 is considered. It is shown that in the calculation of the energy of the system, the electron spin-flip processes and the formation of electron–hole–impurity flip spin (hole against the background of electrons with another spin projection) play the major role. Such complexes are accumulated in the system (a sort of Bose condensate of complexes is formed); this reduces the energy of the system, which is a linear function of the initial interaction of an electron with the impurity spin (in contrast, for example, to the result obtained in perturbation theory). The hole-type excitation and the spin excitation have a gap in the spectrum. Small parameters of the problem are the interaction of electrons with impurity spins and the number of impurities. The electron–electron interaction is not taken into account. Impurities are assumed to be distributed at random, and calculations are performed using the known averaging over the positions of impurities.The problem of states of an electron system interacting with impurities that have a spin of 1/2 is considered. It is shown that in the calculation of the energy of the system, the electron spin-flip processes and the formation of electron–hole–impurity flip spin (hole against the background of electrons with another spin projection) play the major role. Such complexes are accumulated in the system (a sort of Bose condensate of complexes is formed); this reduces the energy of the system, which is a linear function of the initial interaction of an electron with the impurity spin (in contrast, for example, to the result obtained in perturbation theory). The hole-type excitation and the spin excitation have a gap in the spectrum. Small parameters of the problem are the interaction of electrons with impurity spins and the number of impurities. The electron–electron interaction is not taken into account. Impurities are assumed to be distributed at random, and calculations are performed using the known averaging over the positions of impurities.

Journal of Experimental and Theoretical PhysicsNov 1, 20170 citations

{B}_{0}

field direction and depends on the state of the electron spin. The quantization axis can be switched by flipping the state of electron spin, allowing for universal control of nuclear spin states. We show that by performing a sequence of flips (each followed by a suitable delay), we can perform any desired rotation of the nuclear spin, which can also be conditioned on the state of the electron spin. These operations, combined with electron spin rotations, can be used to synthesize any unitary transformation of the coupled electron-nuclear spin system. We discuss how these methods can be used for design of experiments for transfer of polarization from the electron to the nuclear spins.