Semiconductor Quantum Structures and Physics of New Information Technologies

Optically active quantum dots (QD) and quantum wires (QWR) are compound semiconductor structures that confine both electrons and holes in a potential box having a dimension of few tens of nanometers. These semiconductor structures have exceptionally high optical quality on special transport properties, which makes them ideal for both fundamental research and technological applications. In the enclosed project descriptions we describe few topics that have been in focus during 2002.

This work includes extensive domestic and international collaboration with the following laboratories: Optoelectronics Laboratory, HUT, VTT Electronics, Instituto Nazionale di Fisica della Materia, University of Lecce, MegaGauss Laboratory, University. of Tokyo, Inst. of Industrial Science, University of Tokyo. Center for Teraherz Science, USCB.

The ever-decreasing size of the basic components of information processing will give quantum effects an important role in future technologies. Recent developments such as quantum cryptography and the idea of a quantum computer have shown that, rather than being only harmful, these effects can probably be utilized to a great extent. In communications technologies, optical transmission is setting the trend in the development of the networks. The full harnessing of the huge bandwidth provided by light still requires for replacing the switching, routing and processing electronics by all-optical components. Research on nonlinear optical materials and light-induced quantum effects will be crusial in the development of future all-optical processing technologies. Some of our latest work is described below by J. Oksanen and J. Tulkki and A. Huttunen and P. Törmä.

We have investigated cold atomic Fermi-gases which can be used for studing important quantum many-body effects such as superconductivity. Cold atomic gases may also serve as a source of atoms in quantum information processing applications. This research is done in collaboration with the University of Innsbruck, Austria, with Nordita, Denmark, and with the Loomis Laboratory, University of Illinois, USA. We have also participated in the University of Jyväskylä -based experimental research on the idea of using superconducting Josephson junctions as the basic processing element of a quantum computer. Related to optical communications technology, we have started a project investigating the possibilities of all-optical swithing and processing using nonlinear materials, combined with novel material structures such as photonic crystals. For more detail see A. Huttunen et al. and M. Rodriguez et al.

Modelling of Nanoscale Semiconductor Devices

Researchers: Fredrik Boxberg, Roman Terechonkov and Jukka Tulkki

During the year 2001 the research has been focused on the electronic and optical properties of complex III-V compound semiconductor devices (eg GaAs). We have developed very general tools for strain analysis and band structure calculations.

We have been working on different types of quantum wires and quantum dots. Figure 31a shows schematically a modelled structure. The shaded layer is a corrugated InGaAs quantum well were the periodic corrugation and strain induce aligned quantum wires. Figure 31b shows the model of a buried InAs quantum dot. The InAs quantum dot is covered by both GaAs and InGaAs. The charge carriers are localized in the InAs. Both of these structures are being analysed using band structure calculations including full strain picture. Possible applications of these device are low-threshold current lasers, radiation detectors and some quantum information devices.

Figure 31a

Figure 31a: A Corrugated quantum well were the periodic corrugation and strain induce aligned quantum wires.

Figure 31b

Figure 31b: A model of a buried InAs quantum dot in a structure of GaAs and InGaAs.

Strain Calculations

Researchers: Fredrik Boxberg, Roman Terechonkov and Jukka Tulkki

The strain in the modelled structures is of the order 10-2 and is due to different lattice constants of the epitaxially combined materials. Hence, the devices can be built with hardly any dislocations and we now that the strain is completely elastic. However, the strain affects the electronic structure remarkably and it cannot be omitted from the electronic and optical model. The assumption of a dislocation-free structure is one of the corner-stones of our model. The strain and the piezoelectric field in these structures shifts and mixes the electron energy bands.

The strain calculations are based on elastic continuum theory which is numerically modelled using the finite element method. The full threatment of strained compound semiconductors leads to a coupled problem where the elastic strain is coupled to the piezoelectric field. This coupling is due to the atmoic structure of III-V compound materials and the different electronegativity of the compounds. This effect is not present in purely one material semiconductors like silicon or germanium. A thorough strain simulation for e.g the quantum dot of Fig. 31b requires more than 104 nodes. The calculations have been carried out using commercial softwares like Ansys and Abacus in collaboration with the Centre of Scientific Computing.

Calculation of Electronic Confined States

Researchers: Fredrik Boxberg, Roman Terechonkov and Jukka Tulkki

The electronic structure of semiconductors governs it transport and optical properties. From optical properties one can estimate the emission wavelength and material gain I na semiconductor laser. As well as the dynamical laser characteristics. This has prompted us to develop a very general electronic structure code for calculations of electronic states in various semiconductor quantum structures.

In our project we consider quantum wells, wires and dots. We are interested in the electronic states near the bandedge. To treat this case, the k · p -method is used being more efficient. In k · p -method the interaction of the conduction and valence bands is treated using diagonalization procedure while the coupling of the 8 bands to the remote or weakly coupled bands is treated by perturbation theory. In the bases composed of s- and p-orbitals this gives us an eigenvalue problem with the matrix of the size 8x8 in so called Luttinger-Kohn form. This hamiltonian has to be solved numerically. First of all, the discretization is made in such a way that our discretized hamiltonian is symmetrical thereby provides good convergence.

If we start to calculate the band structure of quantum wire, for example, we have to find eigenvalues of the matrix of size 160000x160000 at least to get reliable results. We have to use PARPACK library to diagonalize the discretized Hamiltonian in parallel computers like CLUX. It is important to write an efficient source code. One has to be very careful in splitting the task between different processors.

To do it we have to take into account that the time of calculation is decreased exponentially when number of processors is increased Fig. 32. That is caused by the existence the network interaction between different processors.

Figure 32

Figure 32: The dependence of the time of calculation on the number processors used.

That is why we have to split our eigenvalue problem in such a way that the number of data transfers to be the smallest one.

Modelling Optical Components for Access Networks

Researchers: Jani Oksanen and Jukka Tulkki

With the long haul network backbone transformed into an optical information highway, the transfer capacity is mostly limited by the electronic bottlenecks in the access and metropolitan area networks. The undisputed success of the optical fibres in the network backbone encourages to resolve the bottlenecks by passing to optical solutions in the other parts of the networks as well. This solution, however, requires all-optical components which do not exist commercially (or at all) at present. Metropolitan area networks include a large number of separate connections, which makes fast switching devices and inexpensive laser transceivers essential. The goal of this project is to create models and new ideas for the components needed in expanding the optical network.

We have investigated the differences of the quantum well and dot lasers with respect to their chirp under direct current modulation. This is done by evaluating the changes caused by the current modulation to the refractive index of the laser waveguide. The basic mechanism causing the chirp is the relation between the refractive index and the absorption of the medium. When a laser is modulated with current, the carrier concentration in the lasers changes in time. The changes in carrier density alter the gain, which further induces changes in the refractive index. And as the refractive index changes the wavelength of the optical field that 'fits' in the laser cavity changes.

The refractive index changes corresponding to a change in the carrier density can be tracked using the Kramers-Kronig relation stating that the the refractive index at a given wavelength depends on an integral of the absorption spectrum of the material. It has been shown that the quasi-equilibrium is a good approximation of the carrier distribution under lasing conditions, and if the carrier distribution in the material is known, also the absorption spectrum can be calculated. This enables to evaluate the linewidth enhancement factor at a given carrier density and wavelength even without a dynamical model.

To evaluate the actual chirp, it is necessary to use dynamical equations to find out just how much the current modulation changes the carrier density of the laser. The simplest model is the two-level rate equations describing the relation between carrier density and the laser field. After the amplitude of the carrier density fluctuation is known it becomes a simple task to evaluate the chirp, provided the linewidth enhancement factor is known. It turns out that, in addition of having a low threshold current, the quantum dot lasers add very low chirp - an order of magnitude lower than corresponding quantum well lasers - to the signal, even when modulated directly with current. In practice this might remove the need of costly external modulators in the laser transmitters.

At the present the interest is directed at a new kind of semiconductor amplifiers that have a stabilizing laser field perpendicular to the amplified signal. The analysis is based on a set partial differential equations coupled through the carrier density of the laser. These differential equations are to be solved numerically to see the final effects of the stabilizing field to the amplification, and the differences to the traditional semiconductor amplifiers. Due to the compact size, customizable amplification spectrum, integrability and current operation, semiconductor amplifiers would be ideal for signal amplification, if their signal degradation is small enough. Also the effects of selecting the active material (quantum dots or wells) is of much interest.

Future topics include switching, adjustable wavelength lasers and other related components. Also the electronic structure calculations of the material research group are to be used in the future simulations.

Figure 33

Figure 33: a) A schematic representation of a quantum dot laser with a vertical cavity b) Calculated absorption spectrum of a quantum dot laser's active material accounting for the quantum dot layers, barrier layers and optical confinement regions.

All-optical Switching with Non-linear Photonic Crystals

Researchers: Anu Huttunen and Päivi Törmä

Photonic crystals are periodic structures of dielectric media with alternating dielectric constants. The periodicity causes bandgaps for light to appear, i.e., light with a certain wavelength cannot travel in the crystal. Photonic crystals are a very attractive solution to various problems in telecommunications. The periodicity, and thus the bandgap, can be in either one, two or three dimensions. A widely used example of a one-dimensional photonic crystal is the Bragg grating. Two-dimensional photonic crystals embedded with defects could be used, e.g., as a waveguide for integrated optics and three-dimensional photonic crystals as a microcavity. Photonic crystals may become the key material for integrated optics.

We study photonic crystals made of Kerr-nonlinear materials, which means that the material properties are dependent on the local light intensity. Thus the bandstructure of the photonic crystal, i.e., the transmission as a function of the frequency, can be changed dynamically by applying a high-intensity control pulse. This phenomenon could be used for fast all-optical switching in optical telecommunications. Nowadays the switching of light signals in optical networks is done mainly electronically, which imposes a bottleneck for the data transmission.

We are modelling one- and two-dimensional photonic crystals and intensity distributions and studying the effects of interfaces (see Fig. 34 ) and defects. To calculate the bandstructures for nonlinear photonic crystals, we have developed an iterative Fourier-method.

Figure 34a Figure 34b

Figure 34: Two electric field distributions Ez for the same photonic crystal geometry and at corresponding band structure points in the second energy band, for metallic (left figure) and air (right figure) interfaces. The inclusion of interfaces has a noticeable effect to the band structure, which cannot be neglected in the design of applications.

Microtrap for Neutral Atoms

Researchers: Anu Huttunen, Mirta Rodriguez and Päivi Törmä1
A. Schevchenko2 and M. Kaivola2
T. Lindvall 3 and I. Tittonen 3
1Department of Physics, University of Jyväskylä
2Optics and Molecular Materials Laboratory, HUT
3Metrology Research Institute HUT.

By bringing atoms close to electric and magnetic structures, one can achieve high gradients to create microscopic potentials with size comparable to the de-Broglie wavelength of the atoms. One can design quantum wires and wells by combining magnetic fields created by current-carrying wires and external electric fields. The wires can be mounted on a surface and an ultracold atom cloud can be guided along the surface. This is called "atom chip" for its analogy with the corresponding electronic device.

While the experimental work is being done in the Metrology Research Institute of this University, we are working on the theory part of the project.

We are analyzing numerically the preservation of quantum coherence in a Y-shaped atom guide in the presence of the noise created by the surface.

Figure 35a Figure 35b Figure 35c

Figure 35: Projection of the Wigner function of the atom in the x-y plane. Atoms are propagating in the x-direction while a double well potential forms in the y-axis. Initial state, solution after propagation with and without noise from the chip surface.

Cold Degenerate Atomic Fermi Gases

Researchers: Mirta Rodriguez, Gheorghe-Sorin Paraoanu 1 and Päivi Törmä2
1Department of Physics, University of Illinois
2Department of Physics, University of Jyväskylä

The remarkable achievement of Bose-Einstein condensation (BEC) in alkali gases has stimulated the trapping and cooling of also the Fermionic isotopes. The regime of quamtum degeneracy has been achieved for 40K and 6Li by several experimental groups.

Atomic gases can be efficiently and accurately manipulated. They are dilute and weakly interacting thus offering the ideal tool for studying fundamental quantum statistical and many-body physics.

The most prominent phenomena for the fermionic samples would be the superfluid BCS transition. When fermionic atoms in two different hyperfine states are trapped they may have an attractive interaction between them caused by s-wave scattering. According to theoretical predictions, the system then lowers its energy by the formation of atomic Cooper-pairs and becomes a superfluid.

Vortices are a macroscopic signature of the superfluidity, and the vortex core size reflects the typical coherence lengths of the system. We have analyzed the single vortex solution for the order parameter very close to the transition temperature, and studied how the trapping potential affects the healing length of the system. We found that the healing length differs essentially from that of metallic superconductors due to the trapping effects.

We have proposed the use of on-resonant or near-resonant light to probe the order parameter in order to detect the superfluid transition and the Cooper-pair coherence across different regions of the superfluid. The possibility of exciting collective modes by the probing laser light has also been considered.

Figure 36

Figure 36: Vortex solutions for the order parameter. Solid, dashed, and dot-dashed lines correspond to different parameter choices. The * are our estimates for the healing length (vortex core size) and + are corresponding ones based on the theory of metallic superconductors. The fit of * with the numerical results and the deviation of + is evident. The figure is from M. Rodriguez et al., PRL 87, 100402 (2001).