Nuclear spin coherence in a quantum wire

We have observed millisecond-long coherent evolution of nuclear spins in a quantum wire at 1.2 K. Local, all-electrical manipulation of nuclear spins is achieved by dynamic nuclear polarization in the breakdown regime of the integer quantum Hall effect combined with pulsed nuclear magnetic resonance. The excitation thresholds for the breakdown are significantly smaller than what would be expected for our sample and the direction of the nuclear polarization can be controlled by the voltage bias. As a four-level spin system, the device is equivalent to two qubits.

Figure 1

(Color online) (a) Schematic view of the device (not to scale). Two split gates define the one-dimensional channel. A layer of PMMA isolates the split gates from the antenna overgate used to apply the RF magnetic field; (b) one-dimensional subbands as a function of gate voltage $V_{\text{SG}}$ at 50 mK and zero magnetic field. The conductance is shown in $\mu \text{S}$ (left-hand vertical axis) and in units of $2{\text{e}}^2/\text{h}$ (right-hand vertical axis)

Figure 2

(Color online) (a) Hysteresis curve for $V_{\text{SG}}=-0.8\text{V}$ (light traces, left-hand axis) and conductance-relaxation measurements (grayscale plot, right-hand axis) as a function of magnetic field. The inset shows a blow up of the hysteresis region just below ${\nu }_{\text{w}}=1$; (b) conductance relaxation at $V_{\text{SG}}=-0.8\text{V}$ and $B=5.2\text{T}$ [dotted line in (a)]; (c) ${}^{75}\text{A}\text{s}$ NMR signals for $V_{\text{SG}}=-0.8\text{V}$. Magnetic field varies in steps of 0.1 T from 2 (lowermost curve) to 6.9 (uppermost curve) T. Data have been shifted vertically for clarity. Insets show blow ups of the regions just below 3 and just above 5 T, where the NMR signals can be seen; (d) derivative of the NMR signals shown in (c) as a function of magnetic field.

Figure 3

(Color online) (a) and (b) Onset of DNP with increasing excitation voltage as observed in conductance relaxation (a) and NMR $\left({}^{75}\text{A}\text{s}\right)$ (b) measurements at $V_{\text{SG}}=-0.8\text{V}$ and $B=5.2\text{T}$. Excitation voltage varies in steps of $10\mu \text{V}$ from $10\mu \text{V}$ (uppermost curves) to $100\mu \text{V}$ (lowermost curves). NMR lines have been shifted vertically for clarity; (c) values of unpolarized (empty) and equilibrium (full) conductance values at 50 mK (circles) and 800 mK (triangles) (see text for explanation).

Figure 4

(Color online) (a) Conductance as a function of dc and ac excitation voltages; [(b) and (c)] horizontal cuts of (a) at (b) $V_{\text{ac}}=10$ and (c) $95\mu \text{V}$ [dotted lines in (a)], showing the equilibrium (line) and unpolarized (dots) conductance as a function of dc Hall voltage; [(d) and (e)] (d) relaxation and (e) NMR traces for $V_{\text{dc}}$ values of (I) 0 and (II) 0.3 mV in (c).

Figure 5

(a) Rabi oscillations of ${}^{75}\text{A}\text{s}$ at 50 mK for $f_{\text{RF}}=37.685\text{MHz}$ and $V_{\text{RF}}=0.16$, 0.22, 0.32, and 0.47 V; (b) $f_{\text{Rabi}}$ vs $V_{\text{RF}}$; (c) energy levels diagram for a 3/2 spin with quadrupolar splitting, showing single- (I, II, and III), two- (IV and V) and three- (VI) photon transitions.

Figure 6

(Color online) (a) Frequency spectrum of ${}^{75}\text{A}\text{s}$ at $T=1.2\text{K}$ using $312\mu \text{s}$ long pulses and $B_{\text{RF}}=1.53\text{mT}$ with (triangles) and without (circles) electron-nuclear coupling, showing a 4 kHz Knight shift. Resonance frequencies for the different transitions in Fig. 5c are indicated; (b) Rabi oscillations corresponding to the frequencies 1, 2, and 3 in (a).