Awschalom Group

All-Optical NMR

Nuclear spins can be manipulated with optical femtosecond pulses. Using circularly polarized light, spin-polarized electrons are pumped into the conductance band of a semiconductor. Due to the hyperfine interaction, the electron spins interact with the nuclear spin. This leads to dynamic nuclear polarziation with several orders of magnitude larger spin polarization than the thermal value. The nuclei act back on the electrons in form of an effective magnetic field (mediated through the hyperfine interaction). With time-resolved Faraday rotation techniques, we monitor the modified precession of the electron spin in the spin-oriented nuclear lattice.

Nuclear polarization changes the electron Larmor frequency. The greyscale plot shows the electron spin precession 2.66 to 2.70 ns after pumping a spin-polarized electron population into the conduction band of bulk GaAs (shown is the measured Faradayrotation qF). Such pumping was done continously with a repetition rate of 76 MHz. The vertical axis in the grayscale plot denotes the laboratory time. When the sample was translated, the Larmor frequency abruptly decreased and recovered within a time scale of 1000 seconds. The relative magnetic field change DB can be fitted by an exponentially saturating function.

Each time the optical pump pulse generates oriented electrons in the conduction band, the nuclei feel a hyperfine magnetic field from those spins. If the pump pulses are applied resonantly with the nuclear spin precession frequency, this field leads to a tipping of the nuclear spins, which can again be monitored by the electron spin precession frequency. In this scheme only optical pulses are used to induce and detect nuclear magnetic resonance. This opens the door for controlled and spatially resolved manipulation of the nuclear spin.

Nuclear magnetic resonance at B=5.25T: Spin precession between 2.66 and 2.70 ns after the pump pulse displays abrupt change when the slowly varied magnetic field B (0.01 T/min) passes through 5.25 T. This is explained by a tipping field generated by the Laser pulse train (repetition rate 76MHz), which is in resonance with the precession of one of the nuclear spins.

Hyperfine Interaction

Manipulation of the nuclear spin states in semiconductors is possible through the hyperfine interaction with electron spins. With I and S being the spin operators of the nuclear and electron spins, respectively, the hyperfine interaction contributes to the Hamiltonian as

In the presence of a magnetic field B, this term adds to the Zeeman energy of the two spins, I and S. Depending on the point of view, the electrons or the nuclei see a modified magnetic field due to the hyperfine interaction with the other spin species:

Effect on Electrons

If the nuclear spin is oriented along the field B, the electron precession frequency is modified. This effect is well-known in electron spin resonance and is called Overhauser shift.

Effect on Nuclei

On the other hand, if the electron spins are oriented, the nuclear precession frequency is altered, which is known as the Knight shift in nuclear spin resonance.

Flip-flop Spin Scattering

In addition to the modified precession frequencies, the hyperfine interaction allows for flip-flop spin scattering. This means that an electron can flip its spin by simultaneously flipping a nuclei into the other direction. This leads to a dynamic polarization of the nuclear spins. If the electron spin levels are saturated by a driving field (i.e. the population of the upper spin state is made equal to that of the lower state), such flip-flop processes try to reestablish thermal equilibrium, resulting in a nuclear spin polarization which is described by a Boltzman factor where the electron Zeeman splitting enters. Because the electron splitting is typically 1000 times larger than the nuclear splitting, the nuclei end up in an up to 1000 times enhanced polarization compared to their thermal equilibrium value. This is the so-called Overhauser effect (not to be confused with the Overhauser shift, see above).