Electrical control of spin relaxation in a quantum dot. S. Amasha et al., condmat/

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Junior Stevenson
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1 Electrical control of spin relaxation in a quantum dot S. Amasha et al., condmat/

2 Spin relaxation In a magnetic field, spin states are split b the Zeeman energ = g µ B B Provides a two-level sstem that can be used as a qubit or the basis of a spin memor

3 Spin relaxation Need to understand the interactions of electron spin with environment, namel hperfine interaction and spin-orbit coupling Spin-orbit: mixes the orbital and spin states, thus couples the spin to electric fluctuations (e. g. piezoelectric phonons)

4 Spin Spin-orbit coupling orbit coupling Spin Spin-orbit: Rashba and Dresselhaus orbit: Rashba and Dresselhaus [ ] ) (,(001) 2 x x R x x D D p p H p p H σ σ α σ σ β + = + =

5 Spin-orbit coupling Rashba and Dresselhaus contributions add up for motion in the x-x direction and oppose each other for the - direction The Hamiltonian then takes the form H SO = ( β α) p σ + ( β + α) p σ x x

6 Experiment Single-electron electron quantum dot in a Al 0.3 Ga 0.7 As/GaAs heterostructure QPC adjacent to the quantum dot used as a charge sensor allows real-time detection of electron tunneling between dot and lead

7 Experiment First step: Ionize the dot Second step: Charge the dot, possible relaxation into the ground state (waiting time t w ) Read out step: count the number of electrons: We expect an exponential deca of N with waiting time t w P e Wt w Γ t ( t ) ( e e t w w )

8 Amasha et al. cond-mat/ Measurements

9 Electrical control B changing the energ of orbital states, tr to control the amount of SOI induced mixing and thus control the spin relaxation rate Manipulation of orbital states via changing the dot shape (using the gate voltages) Manipulating the dot shape means rotating the wavefunction of the single electron

10 Electrical control Expect less confinement in the x-direction x than in the -direction Model the electrostatic potential with U 1 = 2 1 ω x + ω ( x, ) m x m

11 Electrical Control The energ is measured for each V Shape the three step sequence with B=0 using Shape using

12 Electrical control For each V Shape, measure the relaxation rate of the electron spin Zeeman splitting does not change for different V Shape so the observed variation is caused b changes in orbital states

13 Electrical control With higher energ of the excited states, the SOI to the ground state becomes weaker Obviousl, E dominates the spin relaxation rate: onl the first term in H SO can couple different spin states H SO = ( β α) p σ + ( β + α) x p x σ Change in parit needed: x-excited x state does not fullfill this requirement and therefore does not contribute to spin relaxation

14 Electrical control For V Shape > mv, the higher energ state determines W which is contrast to the usual situation Golovach et al. : W AB 5 E 4 λ 2 SO If one takes E x instead of E, the data would be inconsistent with theor. This can be taken as an independent confirmation of the dot orientation

15 T1 measurements Spin relaxation also depends on the magnetic field (longer T1 for lower magnetic fields)

16 T1 measurements Spin relaxation rate for two different sets of gate voltages

17 T1 measurements For low magnetic fields, coupling to electrical fluctuations from the ohmic leads, the surface gates and the QPC ma become important Good agreement to the theoretical predictions of Golovach et al. indicates that spin-orbit mediated coupling to piezoelectric phonons is the dominant spin relaxation mechanism

Quantum Information Processing with Semiconductor Quantum Dots. slides courtesy of Lieven Vandersypen, TU Delft

Quantum Information Processing with Semiconductor Quantum Dots slides courtesy of Lieven Vandersypen, TU Delft Can we access the quantum world at the level of single-particles? in a solid state environment?