Photon-to-electron quantum information transfer

Optical excitation and control of electron spins in semiconductor quantum wells

We use spontaneous (two-pulse) and stimulated (three-pulse) photon echoes for studying the coherent evolution of optically excited ensemble of trions which are localized in semiconductor CdTe/CdMgTe quantum well. Application of transverse magnetic field leads to the Larmor precession of the resident electron spins, which shuffles optically induced polarization between optically accessible and inaccessible states. This results in several spectacular phenomena. First, magnetic field induces oscillations of spontaneous photon echo amplitude. Second, in three-pulse excitation scheme, the photon echo decay is extended by several orders of magnitude. In this study, short-lived optical excitation which is created by the first pulse is coherently transferred into a long-lived electron spin state using the second optical pulse. This coherent spin state of electron ensemble persists much longer than any optical excitation in the system, preserving information on initial optical field, which can be retrieved as a photon echo by means of third optical pulse.

The study of electronic spin dynamics and coherence is central to gaining insights into a variety of contemporary problems in condensed matter physics. In particular, there is substantial current interest in understanding spin-dependent phenomena in materials systems that involve interfacial and confined geometries such as semiconductor quantum wells [1], metallic magnetic multilayers [2], granular magnetic materials [3], and magnetic semiconductor (MS) quantum structures [4]. For instance, a detailed understanding of electronic spin scattering in low dimensional systems can provide important clues about the fundamental origins of the giant magneto-resistance observed in multilayered and granular magnets. Furthermore, investigations of spin coherence in quantum semiconductor structures are important for exploring coherent spin behavior in solid state systems as a basis for quantum computation and for new generations of magneto-electronic devices [5,6]. In this chapter, we focus on experiments that probe the fundamental spin dynamical properties of a low dimensional (i.e. d < 3) electron or exciton gas that is strongly exchange coupled to a controlled distribution of local moments. We have recently carried out a systematic and detailed study of dynamical spin interactions in such systems by exploiting the concurrent development of sophisticated magnetic nanostructures (e.g. digital magnetic heterostructures and magnetic two-dimensional electron gases) and spatio-temporally resolved spin dynamical probes (e.g. ultrafast Faraday rotation and near-field scanning optical microscopy).

The dependence of the excitonic two-photon absorption on the quantum correlations (entanglement) of exciting biphotons by a semiconductor quantum well is studied. We show that entangled photon absorption can display very unusual features depending on space-time-polarization biphoton parameters and absorber density of states for both bound exciton states as well as for unbound electron-hole pairs. We report on the connection between biphoton entanglement, as quantified by the Schmidt number, and absorption by a semiconductor quantum well. Comparison between frequency-anti-correlated, unentangled and frequency-correlated biphoton absorption is addressed. We found that exciton oscillator strengths are highly increased when photons arrive almost simultaneously in an entangled state. Two-photon-absorption becomes a highly sensitive probe of photon quantum correlations when narrow semiconductor quantum wells are used as two-photon absorbers.

In this paper, we review our recent experimental studies on electromagnetically induced transparency (EIT) from electron spin coherences in semiconductor quantum wells. Coherent Raman resonances, manifestations of EIT from electron spin coherences at relatively low pump intensities, were demonstrated in both V-type and Λ-type three-level systems via heavy-hole exciton and trion transitions in undoped and doped quantum wells, respectively. Coherent Raman resonances from electron spin coherences via light-hole transitions were also demonstrated in a waveguide geometry that enables a long optical interaction length as well as a large absorption coefficient. Experimental approaches that can avoid or reduce detrimental many-body effects in quantum wells are suggested for the realization of nearly ideal EIT processes.

Four-wave mixing via electron spin coherence in a quantum well waveguide

The electron-spin/nuclear-spin interactions in semiconductors are summarized by putting emphasis on dynamical nuclear-spin polarization and detection achieved by using electrical means. These have been demonstrated in quantum dots in the spin-blockade regime, edge channel in the integer quantum-Hall-effect regime and bulk in the fractional quantum-Hall-effect regime. The electron-spin/nuclear-spin interactions, especially at the spin transition point of ν = 2/3 fractional filling, result in an almost linear relationship between nuclear-spin magnetization and the resistance value. As the nuclear-spin magnetization can be measured for a single layer and even for nanostructures by just measuring the resistance, the powerful features of nuclear magnetic resonance can be successfully applied to semiconductor quantum wells, bilayers and point-contact structures where characteristics are well controlled by gates. In GaAs point-contact devices, full coherent control of a quantum four-level system has been demonstrated for I = 3/2 As and Ga nuclei toward nuclear-spin-based quantum information processing. Multiple quantum coherence was clearly observed reflecting the direct detection of nuclear-spin magnetization. In quantum wells and bilayer systems, novel electron-spin features, such as spin texture, a canted spin state and related low-frequency spin fluctuations arising from the breakdown of planar symmetry, have been sensitively detected by using nuclear-spin-based measurements. We also discuss electron-spin fluctuations originating from spin–orbit interactions observed via a nuclear relaxation experiment and the characterization of the nanoscale strain obtained through quadrupolar splitting. Finally, a possible extension of nuclear-spin manipulation and nuclear-spin-based measurements is briefly discussed.

A fully microscopic theory of electron spin relaxation by the D'yakonov-Perel' type spin-orbit coupling is developed for a semiconductor quantum well with a magnetic field applied in the growth direction of the well. We derive the Bloch equations for an electron spin in the well and define microscopic expressions for the spin relaxation times. The dependencies of the electron spin relaxation rate on the lowest quantum well subband energy, magnetic field and temperature are analyzed.

We provide a microscopic theory for the Doppler velocimetry of spin\npropagation in the presence of spatial inhomogeneity, driving electric field\nand the spin orbit coupling in semiconductor quantum wells in a wide range of\ntemperature regime based on the kinetic spin Bloch equation. It is analytically\nshown that under an applied electric field, the spin density wave gains a\ntime-dependent phase shift $\\phi(t)$. Without the spin-orbit coupling, the\nphase shift increases linearly with time and is equivalent to a normal Doppler\nshift in optical measurements. Due to the joint effect of spin-orbit coupling\nand the applied electric field, the phase shift behaviors differently at the\nearly and the later stages. At the early stage, the phase shifts are the same\nwith or without the spin-orbit coupling. While at the later stage, the phase\nshift deviates from the normal Doppler one when the spin-orbit coupling is\npresent. The crossover time from the early normal Doppler behavior to the\nanomalous one at the later stage is inversely proportional to the spin\ndiffusion coefficient, wave vector of the spin density wave and the spin-orbit\ncoupling strength. In the high temperature regime, the crossover time becomes\nlarge as a result of the decreased spin diffusion coefficient. The analytic\nresults capture all the quantitative features of the experimental results,\nwhile the full numerical calculations agree quantitatively well with the\nexperimental data obtained from the Doppler velocimetry of spin propagation\n[Yang {\\it et al.}, Nat. Phys. {\\bf 8}, 153 (2012)]. We further predict that\nthe coherent spin precession, originally thought to be broken down at high\ntemperature, is robust up to the room temperature for narrow quantum wells. We\npoint out that one has to carry out the experiments longer to see the effect of\nthe coherent spin precession at higher temperature due to the larger crossover\ntime.\n

Semiconductor heterostructures for spintronics and quantum information

In this paper, we present an analytical solution to the Maxwell–Bloch equations of the two-level semiconductor quantum well, G a A s / A l G a A s . In addition, we discuss the effects of coherent Rabi oscillations Ω ( t ) and the frequency of the semiconductor system ν ( t ) on atomic occupation probabilities, ρ 11 ( t ) and ρ 22 ( t ) , population inversion, ρ z ( t ) , and information entropies, H ( σ x ) , H ( σ y ) , and H ( σ z ) . We observe clearly the emergence of long-lived quantum coherence and the decay in curves for some special cases of Ω ( t ) and ν ( t ) . Also, we show that the dynamic nonlinear properties of the system can be controlled by changing the values of the coherent Rabi oscillations Ω ( t ) and the frequency of the semiconductor system ν ( t ) . Due to the lack of mathematical treatment of such systems, our study promises significant advantages for a large number of nonlinear dynamic systems, opening up a wide range of applications for semiconductor quantum wells.

Femtosecond-resolved measurements of induced Faraday rotation reveal exchange coupling between the spin angular momenta of charge carriers and a sublattice of magnetic ions in semiconductor quantum wells. In transverse magnetic fields, we observe terahertz spin precession of photoinjected electrons, rapid spin relaxation of holes, and the coherent transfer of angular momentum to the magnetic sublattice via the ultrafast rotation of the local moments. The perturbed ions undergo free-induction decay, enabling time-domain all-optical electron-spin-resonance measurements in single magnetic planes.

A new technique for the measurement of the intersubband lifetime in semiconductor quantum wells is demonstrated. Electrons are optically excited from the ground state to the first excited state of a doped quantum well. From measurements of the absorption cross section between excited states, we find a lifetime equal to τs=0.65±0.15 ps for a 85 Å GaAs quantum well and τs=0.8±0.2 ps for a 100 Å Ga0.47In0.53As quantum well, in good agreement with the theoretical predictions of Ferreira and Bastard [Phys. Rev. B 40, 1074 (1989)]. In addition, our experiments unambiguously show that the intersubband absorption line is homogeneously broadened at cryogenic temperatures (≤100 K).

The spin orientation of electrons is studied in ferromagnet (FM)–semiconductor (SC) hybrid structures composed of a (Ga,Mn)As ferromagnetic layer, which is placed in the direct vicinity of a non‐magnetic SC quantum well (QW). It is shown that the polarization of carriers in the SC QW is achieved by spin‐dependent tunnelling into the magnetized ferromagnetic layer. This leads to dynamical spin polarization of the electrons, which can be directly observed by means of time‐resolved photoluminescence. We find that the electron spin polarization grows in time after excitation with an optical pulse and may reach values as large as 30%. The rate of spin‐dependent capture grows exponentially steeply with decreasing thickness of the spacer between ferromagnetic layer and QW, and it persists up to the Curie temperature of the (Ga,Mn)As layer. From time‐resolved pump–probe Kerr rotation data, we evaluate a value of only a few eV for the energy splitting between the electron Zeeman sublevels due to interaction with the ferromagnetic (Ga,Mn)As layer, indicating that the equilibrium spin polarization is negligible.Schematic presentation of electron spin orientation in a semiconductor quantum well (QW) under linearly polarized excitation due to spin‐dependent capture of electrons in the ferromagnetic layer (FM). The arrows in the FM box indicate the orientation of the magnetization . The effect is detected by appearance of a circular polarization degree of photoluminescence after pulsed optical excitation (right). The data are shown for a spacer thickness of 5 nm.

Polaron dephasing processes are investigated in InAs/GaAs dots using far-infrared transient four wave mixing (FWM) spectroscopy. We observe an oscillatory behaviour in the FWM signal shortly (< 5 ps) after resonant excitation of the lowest energy conduction band transition due to coherent acoustic phonon generation. The subsequent single exponential decay yields long intraband dephasing times of 90 ps. We find excellent agreement between our measured and calculated FWM dynamics, and show that both real and virtual acoustic phonon processes are necessary to explain the temperature dependence of the polarization decay. PACS numbers: 78.67.Hc, 78.47.+p, 42.50.Md, 71.38.-k The strong spatial confinement of carriers in semiconductor quantum dots (QDs) leads to striking differences in the carrier-phonon interaction compared with systems of higher dimensionality. In particular, the discrete energy level s tructure in QDs results in long exciton and electron dephasing times [1, 2, 3, 4], making these semiconductor nanostructures highly attractive for implementation in quantum information processing applications. The study of dephasing mechanisms in QDs is commonly carried out using transient four wave mixing (FWM) spectroscopy. Using resonant interband excitation, FWM measurements have revealed the absorption lineshape of single QDs to consist of a narrow zero phonon line (ZPL) and an acoustic phonon-related broadband centred at the same energy. The only intraband FWM study [5] involved resonant excitation of high energy transitions in th e valence band of p-doped QDs yielding dephasing times ∼ 15 ps. However it was not possible to determine the dephasing mechanisms in this case. Intraband studies of the well-resolved lowest energy conduction band electron transitions in InAs/GaAs QDs have provided deep insight into the electron-phonon interaction and carrier relaxation processes in n-doped samples. Clear evidence of strong coupling between electrons and phonons, resulting in polaron formation, has been demonstrated using magneto-transmission measurements [6]. Ultrafast studies [7, 8] of polaron decay have shown that the previously assumed ’phonon bottleneck’ picture is not valid. Compared with semiconductor quantum wells, the intraband population relaxation time in QDs is long (∼ 50 ps) suggesting relatively long dephasing times. However there have been no reports of direct dephasing measurements to date. In the present letter we present the first investigations of i ntraband dephasing in n-doped QDs using degenerate FWM. Our calculations of the absorption lineshape in this case sh ow marked differences in comparison with the interband absorption [9]. The intraband lineshape consists of peaked acoustic phonon sidebands separated by ∼ 1.5 meV from the ZPL, which corresponds to phonons with wavelength close to the dot size, and is reminiscent of the lineshape associated wit h impurity-bound electron transitions [10]. Using pulse durations short enough to excite both the ZPL and acoustic phonon sidebands we find damped oscillations in the FWM signal, indicative of coherent acoustic phonon generation, followed by a single exponential decay. In contrast with the interband case, where the origin of the strong temperature dependence of the excitonic linewidth is still subject to debate, the simple 3 -level structure of the lowest energy conduction band states in InAs QDs permits an accurate simulation of the temperature dependence of the FWM signal. The excellent agreement found between experiment and theory, shows that virtual transitions between the p-states is the dominant dephasing mechanism at high temperature. At low temperature, we have measured an intersublevel dephasing time of T2 ∼ 90 ps. It is also interesting to compare our results with previous intraband dephasing measurements in higher dimensional (quantum well) systems [11]. Here phonon-mediated processes are not significant with the intraband dephasing instead determined by electronelectron interactions, yielding typical dephasing times ∼ 0.3 ps which are approximately 2 orders of magnitude faster than for the QD samples studied here. The relatively long intraband dephasing time in QDs is key to the efficient operation of new types of mid-infrared QD-based devices, such as intersublevel polaron lasers [12] and may be relevant for potential device applications such as qubits for quantum information processors [13]. The investigated samples were grown on (100) GaAs substrates by molecular beam epitaxy in the Stranski-Krastranow mode. They comprise 80 layers of InAs self-assembled QDs separated by 50 nm wide GaAs barriers, thus preventing both structural and electronic coupling between QD layers. The polaron transitions were studied between s-like ground (s) and p-like first excited ( p) states within the conduction band. To populate the s state, the samples were delta-doped with Si 2 nm below each QD layer. The doping density was controlled in such a way that the average doping did not exceed 1 electron per dot (see Ref. [14] for more details). Absorp