We develop a free-carrier theory of the optical absorption of light carrying orbital angular momentum (twisted light) by bulk semiconductors. We obtain the optical transition matrix elements for Bessel-mode twisted light and use them to calculate the wave function of photo-excited electrons to first-order in the vector potential of the laser. The associated net electric currents of first and second-order on the field are obtained. It is shown that the magnetic field produced at the center of the beam for the ℓ = 1 mode is of the order of a millitesla, and could therefore be detected experimentally using, for example, the technique of time-resolved Faraday rotation. PACS numbers: 78.20.Bh,78.20.Ls,78.40.Fy,42.50.Tx It is well known from classical electromagnetism that light can carry spin and orbital angular momentum. While the former was detected for the first time in the 1930s [1], the latter became widely available for experimental study only recently after the work of Allen et al.[2] In a seminal paper, those authors showed that light carrying an integer amount of orbital angular momentum ( l, with l an integer) may be generated in the laboratory using conventional laser beams. Since then, research on the subject of light carrying orbital angular momentum (OAM), or twisted light (TL) [3,4,5] has spanned a large number of areas, namely, generation of beams [4], interaction with mesoscopic particles (optical tweezers) [6,7,8], entanglement with spins for potential applications in quantum information processing [9], interaction with atoms and molecules [10,11], cavity-QED [12], and interaction with Bose-Einstein condensates [13,14]. Nevertheless, the interaction with solid state systems, although potentially important for technological applications, has not been explored so far. In this Letter, we present the first theoretical predictions about the interaction of TL with bulk semiconductors. We consider band-to-band transitions, i.e. optical transitions with light frequencies above the bandgap, so that free carriers rather than excitons are produced. We show that there is a transfer of OAM between the light and the photoexcited electrons so that a net electric current initially confined to the beam area appears. The magnetic field induced by these photocurrents is estimated.A beam of TL presents an azimuthal phase dependence -helical wavefront -responsible for the OAM, and a radial dependence of the Laguerre-Gaussian(LG) or Bessel mode type. We will focus on the Bessel modes, but our results are applicable to the LG-mode with slight changes. The vector potential in the Coulomb gauge with cylindrical coordinates {r , φ, z} is [15]with polarization vectors ǫ ± =x ± iŷ, Bessel functions J l , and parameters q ≪ q z . Semiconductors are solids which at zero temperature have the highest occupied (valence) and lowest empty (conduction) energy bands separated by a gap E g . In this respect, they are closer to insulators than to metals. However, in typical semiconductors E g ≃ 1 eV, making possible the transitions bet...
Quantum control of the wave function of two interacting electrons confined in quasi-onedimensional double-well semiconductor structures is demonstrated. The control strategies are based on the knowledge of the energy spectrum as a function of an external uniform electric field. When two low-lying levels have avoided crossings our system behaves dynamically to a large extent as a two-level system. This characteristic is exploited to implement coherent control strategies based on slow (adiabatic passage) and rapid (diabatic Landau-Zener transition) changes of the external field. We apply this method to reach desired target states that lie far in the spectrum from the initial state.PACS numbers: 78.67.Hc The control of quantum systems is a fundamental challenge in physical chemistry, nanoscience, and quantum information processing [1,2]. Quantum control is the manipulation of the temporal evolution of a system in order to obtain a desired target state or value of a certain physical observable. From the experimental point of view, the techniques of quantum control are highly developed in the area of magnetic resonance, and more recently great progress has been made in quantum chemistry thanks to the development of ultrafast laser pulses [3].Coherent control in semiconductor quantum dots has become an active field of research in the last 15 years. Early works on electron localization in double well systems spurred intense theoretical activity. In a seminal paper, Grossmann et al. [4] showed that, by applying an appropriate AC electric field, the tunneling of the electron between the wells could be coherently destroyed, thereby maintaining an existing localization in one of the wells. Shortly after, Bavli and Metiu [5] found ways to, starting from the delocalized ground state, localize the electron wave function and then to preserve the localization with a precisely taylored time-dependent electric field. A large body of literature followed these pioneering works. A decade later, the first steps in the theoretical exploration of localization and control of two interacting electrons in quantum dots were made [6,7,8]. Whereas Zhang and Zhao studied a model two-level system, Tamborenea and Metiu studied a more realistic multi-level system inspired by quasi-one-dimensional semiconductor nanorods. The study of two-electron localization and control in double dots has remained active ever since [9,10,11,12,13].In this Letter we propose an efficient method to control the wave function of two interacting electrons confined in quasi-one-dimensional nanorods [8,14]. The control method is based on the knowledge of the energy spectrum as a function of an external uniform electric field. The method requires that the system behaves locallynear avoided level crossings-as the Landau-Zener (LZ) two-level model [15]. This fact is exploited to navigate the spectrum using slow (adiabatic) and rapid (diabatic) changes of the external control parameter. Although this characteristic may seem rather restrictive, it is, in fact, a general ...
The starting point of this paper is the equation of motion (5) for the carrier spin component perpendicular to the impurity magnetization, which has been derived in Ref. [1]. In Eq. (5), a cross-product sign is not printed accurately. Furthermore, in the derivation of this equation in Ref. [1], it was assumed that the effective magnetic field ω M for the carrier spins caused by the impurity magnetization is parallel to the total impurity spin, i.e., the coupling constant J sd is positive. In the present paper, however, this equation has been applied to the conduction band of CdTe where this condition is not fulfilled. To correct this error, the corresponding equation of motion needs to be derived for an arbitrary sign of J sd . Toward that end, it is useful to define the quantization axis (z) as pointing in the direction of ω M . Then, also the spin-up and spin-down occupations n ↑ k and n ↓ k as well as the parallel impurity spin operator S =Ŝ · ω M |ω M | in the definition of the factors b i in Eq. (5) should be defined with respect to the direction of ω M . In this coordinate system, Eq. (5) should be replaced by [2]As a consequence, using the equation derived in Ref.[1] with a negative value of J sd led to the wrong sign of the relative frequency renormalization ω ω M in Figs. 1 and 3. Actually, the correlation-induced renormalization enhances the precession frequency instead of decreasing it, independently of the sign of J sd . The magnitude of the renormalization, however, is not influenced.Also, Eq. (6) has an error with parentheses. It should readFurthermore, a factor 1 2 is missing in Eq. (21). The corrected version of Eq. (21) isAlso, due to an error in the computer program, the evaluation of the correlation energy according to Eq. (21) led to a wrong value. For the situation described in this paper, the value of the average correlation energy per electron, H cor sd /( k n k ), is not −1.8 μeV, but rather −0.34 meV, which corresponds to a temperature of T ≈ 4 K.The above errors have little influence on the conclusion about the frequency renormalization. While the sign of the frequency renormalization has to be changed, the magnitude remains the same. However, the relatively large corrected value of the correlation energy indicates that the carrier-impurity correlations are strong in low-temperature experiments and should therefore not be neglected, as is usually done by invoking a semiclassical approximation [3-7]. [1] M. Cygorek and V. M. Axt, Semicond. Sci. Technol. 30, 085011 (2015). [2] M. Cygorek, P. I. Tamborenea, and V. M. Axt, Phys. Rev. B 93, 205201 (2016). [3] H.
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