 Tunneling Measurement of a Single Quantum Spin
M. Hru\u{s}ka, L.N. Bulaevskii and G. Ortiz
Los Alamos National Laboratory, US
Keywords: tunneling, spin, quantum measurement,qubit
Abstract: We consider tunneling between electrodes via a microscopic system
which can be modeled by the twolevel Hamiltonian
(a localized spin 1/2 probed by STM or a quantum dot).
Measurements of the tunneling current $I(t)$ in such a system provide
information on the orientation and dynamics of the spin and they
constitute an example of indirectcontinuous quantum measurements.
We assume that a) coupling of the spin with electrodes is
much stronger than that with environment, b) the DC magnetic field ${\bf B}$
acts on the spin, c) electrons in the electrodes are polarized, and d)
distribution function of electrons in the electrodes corresponds to the
thermal equilibrium at the
temperature $T$. By using the nonequilibrium Keldysh method and Majorana
representation for
spin [1] we find conditions under which the tunneling current leads to the
steady state with spin
precession seen as a peak at the Larmor frequency in the spectral density
of the currentcurrent correlation function
$\langle I(\omega)I(\omega)\rangle$. This occurs, for example, when
electrons in the electrodes are fully polarized in the direction ${\bf P}\perp
{\bf B}$, but does not occur if electrons are weakly polarized or are
polarized with ${\bf P}\parallel {\bf B}$. The height and the width of the
peak in the spectral density $\langle I(\omega)I(\omega)\rangle$ at the
Larmor frequency depend on the electron temperature $T$, on the strength of
the magnetic field $B$ and on the voltage applied to the electrodes. The
width of the peak increases with the tunneling current and in the limit of high
current
the spin dynamics (spin precession) is suppressed
because the width of the peak becomes much larger than the Larmor frequency
(quantum Zeno effect).
We describe how the tunneling current may be used to read a qubit represented
by a single quantum spin 1/2. We discuss also the experimental results
obtained by STM dynamic probes of spins [2,3]. \\
1. O. Parcollet and C. Hooley, condmat/0202425. \\
2. Y. Manassen, {\it et al.}, Phys. Rev. Lett. {\bf 62}, 2531 (1989); J.
Magn. Reson. {\bf 126}, 133 (1997); Phys. Rev. B {\bf 61}, 16223
(2000).\\
3. C. Durkan and M.E. Welland, Appl. Phys. Lett. {\bf 80}, 458 (2002).
NSTI Nanotech 2003 Conference Technical Program Abstract
