ABSTRACT
The basic idea of two-beam interference control [7,10] is shown in Figure 1 for a generic III-V semiconductor crystal where details of the band structure, such as the presence of heavy and light hole bands, have been suppressed for clarity. We consider
single photon absorption of a photon of energy 2hco along with two-photon absorption of photons of energy hco where hco< Eg<2hco and Eg is the band gap of the semiconductor. If the perturbations causing these transitions act coherently, then quantum mechanics tells us that we must first add the transition amplitudes and then take the modulus squared of the total amplitude to determine the transition probability. While the transition probabilities for the two absorption channels acting independently lead to the usual population generation rates for single and two photon transitions, the interference terms brings about new physics. Figure 1 illustrates just one of the possibilities for a two photon absorption process with the intermediate and final states both being conduction band states. For a minimal coupling Hamiltonian ocA • p where A is the vector potential and p is the momentum operator, the matrix element of p for a conduction band state is proportional to the crystal momentum, k. The interference term will therefore change sign for momentum states of opposite sign. Hence a constructive interference process increases the transition amplitude in one region of k-space and decreases it in another, leading to a polar distribution of carriers in both the valence and conduction bands. This would lead to a charge current in real space-and in the absence of any external bias! Because the interference process generates the current, its strength is also related to cos{(p2(0-2(pQ)) where the phases refer to the two harmonic beams. Hence one can use the relative phase of the two beams to control the magnitude and direction of the current.
