Time-dependent growth of nuclear spin polarization under periodic optical pumping

Consecutive circularly polarized optical pulses generate and rotate electron spin polarization through optical orientation and the optical Stark effect. We perform time- and magnetic-field-dependent optical pump-probe measurements on gallium arsenide and observe a variable Overhauser field growth that depends on the external magnetic field and laser wavelength. We show that the time dependence of the nuclear spin polarization can be attributed to the time-averaged electron spin polarization produced along the external magnetic field direction.

Figure 1

Relationship between $\langle S_x\rangle$ and steady-state Overhauser field. (a) Calculated time-averaged $\langle S_x\rangle$ component for negative detuning (819.5 nm) in blue and positive detuning (818.2 nm) in orange. (b) Simulated steady-state total effective magnetic field for both detunings, showing that the positive detuning (orange) results in integer multiples of $\frac{h}{g{\mu }_B{T}_{\mathrm{rep}}}$, denoted by the gray dashed horizontal lines, while the negative detuning (blue) exhibits plateaus at the half-integer values. (c)–(f) The blue and green vertical lines correspond to the integer and half-integer values, respectively. The orange and red vertical lines are example external fields, and the orange and red arrows demonstrate the magnitude and direction the Overhauser field builds for the total field to reach the integer or half-integer values.

Figure 2

Simulated Overhauser field growth profiles for different external field values and (a) negative detuning and (c) positive detuning. Each curve is labeled with its external magnetic field value. In the case of positive detuning, we observe that the curves for 129 and 130 mT result in the largest Overhauser fields, but have an initial slow delayed growth before the Overhauser field increases more rapidly. (b), (d) The Overhauser field profile plotted as a function of external field for different elapsed laboratory times.

Figure 3

Two-dimensional (2D) Kerr data and plots of Kerr rotation as a function of time delay for different laboratory times. (a) Experimental 2D TRKR data for external field of 133 mT and wavelength of 818.2 nm. The vertical axis is the pump-probe delays, and the horizontal axis is the laboratory time. (b) TRKR data at select laboratory times plotted with respect to the pump-probe time delay. The data correspond to vertical slices of the 2D data, denoted by the vertical white dashed lines in (a).

Figure 4

Larmor frequency curve fits for all laboratory times, different external fields, and both spectral detunings. (a), (b) Larmor frequencies for negative detuning. The magenta and red horizontal dashed lines correspond to the predicted NIFF half-integer values of 10.5 and 11.5 of $n*2\pi /T_{\mathrm{rep}}$. The Larmor frequency rapidly changes to approach one of these half-integer values depending on the external field. (c), (d) Larmor frequencies for positive detuning. The blue and green horizontal dashed lines correspond to the predicted NIFF integer values of 10 and 11 of $n*2\pi /T_{\mathrm{rep}}$. The predicted delayed growth behavior for fields with a larger predicted Overhauser field is observed.