Quantum Interference in Electron-Hole Generation in Noncentrosymmetric Semiconductors

Abstract

We show that, when fundamental optical beams are present in a noncentrosymmetric medium simultaneously with their sum-frequency beam, quantum interference between single-and two-photon transitions modifies the net absorption, if the sum frequency corresponds to an energy greater than the band gap. At a macroscopic level this effect can be related to the imaginary part of a second-order susceptibility and can be used to coherently control carrier populations and optical absorption. We illustrate this novel effect using phased 1550 and 775 nm, 120 fs pulses incident on GaAs at 295 K. PACS numbers: 78.47.+ p, 78.55.Cr The field of nonlinear laser optics dates from the observation of second-harmonic generation in crystalline quartz [1]. Although a myriad of nonlinear optical processes have been discovered since then [2-4], second-order ͑x 2 ͒ processes such as sum-and difference-frequency mixing continue to capture most of the interest. Of necessity x 2 is nonzero only in noncentrosymmetric media, such as certain crystals. When such a crystal is transparent at all frequencies involved, x 2 is real and the crystal can act as an optical "catalyst" to convert incident energy into new optical frequencies. If, however, the crystal is absorbing for at least one of the frequencies, the imaginary component of x 2 ͑Im͓x 2 ͔͒ is nonzero. In the case of sum-frequency generation, it is generally believed [5] that Im͓x 2 ͔ plays no role in energy absorption. Here we demonstrate that when coherent fundamental and sum-frequency beams are simultaneously present in a crystal, and if the sum frequency falls in a region of band absorption, Im͓x 2 ͔ can contribute to the removal of energy from all beams. This is due to the interference of single-and two-photon absorption pathways. This effect can be used in an active sense to coherently control optical transmission and band populations through the relative phase of the fields. We experimentally demonstrate this new effect in bulk GaAs at 295 K, and explicitly discriminate its origin and nature from the coherent control of current injection in semiconductors [6].

Excitonic effects on the two-color coherent control of interband transitions in bulk semiconductors

“…90 However, close to the band edge, where allowed-allowed transitions dominate two-photon absorption, excitonic effects increase these ratios by a factor C over their value in the independent particle approximation. In contrast, as a consequence of (58), excitonic effects do not affect the maximum control ratio for population and spin control (ξ (I) / ξ (1) ξ (2) and ζ (I) / ξ (1) ξ (2) respectively) 19,21,22 close to the band edge and decrease them by a factor C at higher photon energies for which allowed-forbidden transitions dominate two-photon absorption.…”

“…19,20 Expressions such as (4) and (8) can also be written for carrier spin polarization and spin current. 22 The interference terms of these describe '1+2' spin control 21 and '1+2' spin current injection, 13 which can be written in terms of material response pseudotensors ζ ijkl…”

“…43,69 However, we neglect such nonlocal corrections, as has been the practice in previous calculations of coherent control effects. 11,13,19 The initial state is the "vacuum" |0 ; it corresponds to completely filled valence bands and empty conduction bands. If the Coulomb interaction were neglected in a two-band model consisting of valence (v) and conduction (c) bands, the final states would be of the form a † ck a vk |0 , where the operator a † nk creates an electron in an eigenstate of H B , a Bloch state |n, k with band index n and wavevector k. The photon momentum has been neglected, consistent with the long wavelength approximation.…”

“…10 Interband '1 + 2' interference in unbiased semiconductors, which is our interest here, allows independent control of electrical current injection 11,12 and spin current injection. 13,14,15,16,17,18 Furthermore, in noncentrosymmetric semiconductors, it allows independent control of carrier populations (i.e., absorption) 19,20 and carrier spin polarization. 21, 22 In each scenario, the experimenter can control the interference by adjusting the phases of the two colors.…”

“…28,29 Nevertheless, microscopic theories for the interband '1 + 2' processes in bulk semiconductors have until now predicted trivial intrinsic phases. 11,13,19,21 The photocurrent, for example, was predicted to be proportional to the sine of the relative phase parameter for all final energies. 11 Each of these theories use the independent particle approximation, in which the Coulomb attraction between the injected electron and hole is neglected.…”