Dynamics of the linear chain with arbitrary potential applied to quantum crystals

In one dimension, many-body matrix elements can be calculated exactly by the transfer integral (TI) method if the wave functions are assumed to be products of single-particle functions and nearest-neighbor correlation functions. In the frame of this TI approximation the phonons can be calculated without any further approximation. The theory is first developed for the case of a harmonic potential. Here the TI phonons are an excellent approximation of the well-known exact results, except for very long wavelengths. However, a Bogoliubov transformation finally yields the exact phonons. The whole procedure can be generalized for arbitrary two-body interactions, including those containing a hard core. In the generalized theory the hard-core problem has vanished completely.     

New derivation of a theory of quantum crystals

A new variational cluster-expansion derivation of Guyer's theory of the ground state of a quantum crystal is presented. The results are identical with his in the two-body correlation approximation except that the variational approach provides a justification of the minimization technique used to choose the unperturbed Hamiltonian. The treatments differ in the higher correlation terms because of the use of a Jastrow trial function.Supported in part by Office of Naval Research contract No. N0001467-A-0230-003.     

Three-dimensional Si/Ge quantum dot crystals

Modern nanotechnology offers routes to create new artificial materials, widening the functionality of devices in physics, chemistry, and biology. Templated self-organization has been recognized as a possible route to achieve exact positioning of quantum dots to create quantum dot arrays, molecules, and crystals. Here we employ extreme ultraviolet interference lithography (EUV-IL) at a wavelength of lambda = 13.5 nm for fast, large-area exposure of templates with perfect periodicity. Si(001) substrates have been patterned with two-dimensional hole arrays using EUV-IL and reactive ion etching. On these substrates, three-dimensionally ordered SiGe quantum dot crystals with the so far smallest quantum dot sizes and periods both in lateral and vertical directions have been grown by molecular beam epitaxy. X-ray diffractometry from a sample volume corresponding to about 3.6 x 10(7) dots and atomic force microscopy (AFM) reveal an up to now unmatched structural perfection of the quantum dot crystal and a narrow quantum dot size distribution. Intense interband photoluminescence has been observed up to room temperature, indicating a low defect density in the three-dimensional (3D) SiGe quantum dot crystals. Using the Ge concentration and dot shapes determined by X-ray and AFM measurements as input parameters for 3D band structure calculations, an excellent quantitative agreement between measured and calculated PL energies is obtained. The calculations show that the band structure of the 3D ordered quantum dot crystal is significantly modified by the artificial periodicity. A calculation of the variation of the eigenenergies based on the statistical variation in the dot dimensions as determined experimentally (+/-10% in linear dimensions) shows that the calculated electronic coupling between neighboring dots is not destroyed due to the quantum dot size variations. Thus, not only from a structural point of view but also with respect to the band structure, the 3D ordered quantum dots can be regarded as artificial crystal.     

Dynamics of the Jaynes-Cummings model in the presence of photonic crystals

The three-level atom Jaynes-Cummings model is solved exactly and its dynamics investigated in photonic crystals that exhibit band gaps. The atom-field coupling and the probability amplitudes are evaluated as functions of the mode frequency and for different cavity parameters. Besides band-gap effects, the system exhibits novel local field effects. These show as peaks in the atom-field coupling and hence peaks or dips in the probability functions.     

Dynamics of quantum steerability for two atoms in coupled cavities

We study the dynamics of quantum steerability between two non-interacting atoms, each of which is trapped inside one of two coupled cavities. Compared with entanglement, quantum steerability manifests sudden birth and sudden death phenomenon during the time evolution. We find that the cavity decay plays a destruction role for both steerability and entanglement. It is also shown that the survival time as well as the maximal value of steerability are sensitive to the asymmetry of the cavities. Moreover, it is found the sudden death of steerability can be controlled by the hopping rate of the coupled cavities.     

Short-range and long-range forces on a common basis in quantum crystals

A theory is developed which allows the determination of the ground-state energy and the phonons of quantum crystals on an equal footing in the collective picture. The central quantity required to dress the lines of the diagrams of the phonons as well as those of the kinetic and potential energy is the phonon self-energyM(). It is approximated in a systematic way, giving the force constants:M()M. This theory is in contrast to those using theT-matrix theory. We show that use of theT-matrix as an effective interaction in phonon calculations leads to an inconsistency.     

Self-consistent phonons in configurationally disordered quantum crystals. I. Theory

A generalization of the coherent potential approximation (CPA) to strongly anharmonic systems is presented that takes into account the static relaxations in the vicinity of each defect and the changes in the averaged mean lattice constant and in the mean square fluctuations. In the limits of a perturbed classical, harmonic crystal or an ideal, anharmonic crystal the theory reduces to the conventional CPA and the self-consistent phonon results, respectively. For the numerical solution an approximation is used that starts from the renormalized harmonic phonons in ideal crystals. As an example, some characteristic results are discussed for the systems ofoD₂ orpH₂ in Ne.Deceased.     

Self-consistent phonons in configurationally disordered quantum crystals. II. Group-theoretic considerations

In a foregoing publication a self-consistent phonon theory for configurationally disordered crystals was discussed by W. Biem and the author. In this article some simplifications concerning the coherent potential approximation (CPA) equations and the static relaxations are derived with the help of group-theoretic methods. Besides the familiar reduction of the relevant matrices to block-diagonal form, a very fast Fourier transformation between thek space and the space spanned by symmetry-adapted coordinates is discussed. This allows a solution of the CPA equations without using the real lattice.     

Spontaneous emission from a four-level atom embedded in photonic crystals via quantum interference

The spontaneous emission of a four-level atom embedded in a one-dimensional photonic crystal is investigated. The atom has two upper levels coupled by the same vacuum modes to a common lower level and is driven by a coherent field to an auxiliary level. Spontaneous emission can be suppressed significantly due to the combinational influences of the interference effect and the band edge effect. The radiation field emitted by the atom is also studied. Spontaneous emission can be modified by controlling the Rabi frequency of the driving.     

Pre-selection of optical transitions in rare-earth ions in crystals perspective for quantum information processing

A systematic analysis of decoherence rates due to electron–phonon interactions for optical transitions of rare-earth dopant ions in crystals is presented in the frame of the point charge model. For this model, the large value of any one of the matrix elements of the unit tensor operator U ^{( k )} of rank k for transitions within the 4f-electronic configuration, viz. U2, U4 or U6, is enough to ensure the strong optical transition between different levels, while the Stark–Stark transitions within the multiplet can be characterized by the matrix element U2 alone, the influence of elements U4, U6 being of much smaller order of magnitude and neglected. The circumstance that exactly such Stark–Stark transitions within the multiplet define the efficiency of electron–phonon interaction and, consequently, the decoherence rate (except for the case of lowest, less than approximately 2–4?K, temperatures), enables selection of optical transitions which are strong enough and at the same time are characterized by relatively small decoherence rates. Correspondingly, these optical transitions, provided that they lie in an appropriate spectral range and the gap to the nearest neighboring energy level is large enough (>500?cm^?1) to prevent eventual fast phonon-assisted relaxation, should be considered as prospective for subsequent use in quantum informatics processing and communication. The list of such pre-selected transitions is given; the applicability area and limitations of our approach are discussed.     

Dynamics and the statistics of three-photon cascade emissions from single semiconductor quantum dots with pulse excitation

We analyse the population dynamics and the photon emission statistics of a single semiconductor quantum dot with an exciton–biexciton–triexciton multilevel driven by a pulse field, in which the quantum regression theorem and optical Bloch equations are employed. The populations of the three states are comparable under resonant excitation with the input pulse area around 1.5π. Three second-order cross-correlation functions demonstrate the correlated three-photon emissions at a given order from triexciton, biexciton and exciton states driven by single pulses, while the probability of the bunched three-photon cascaded emissions decreases to the minimum as the input pulse area increases to 2π in every period.     

The luminescent quantum efficiency of Cr ions in Cs2NaAlF6 single crystals

The luminescent quantum efficiency of Cr³⁺ ions in single fluoride crystal Cs₂NaAlF₆ was determined by using the simultaneous multiple-wavelength photoacoustic and luminescent experiments method, based on the generation of photoacoustic and luminescence signals after pulsed laser excitation. The luminescent quantum yield for the most important transition between the ⁴T₂→⁴A₂ vibronic levels was found to be 68±3%. This value agrees with that obtained from the ratio of the lifetimes of the corresponding transition at different temperatures.     

Luminescence quantum efficiency of F2 and F3 centers in LiF crystals

F^-₂ color center in LiF crystals is a unique specie of color centers concerning its photothermal stability, its broad absorption band, centered at 0.96 μm, and its broad emission band peaking at 1.12 μm, being a tunable laser operating in the range from 1.08 μm to 1.22 μm. The luminescence quantum efficiency of the main transition in the laser optical cycle was determined, at room temperature, and its value is 0.5 ± 0.1. This value was obtained using a method correlating the absorption, excitation and photoacoustic spectra. Besides, the luminescence quantum efficiency of the fundamental transition of the F^-₃ color center was determined. Also was estimated the energy transfer efficiency due to the overlapping of the F^-₃ center emission and the F^-₂ center absorption bands. Possible nonradiative deexcitation mechanisms accounting for the small luminescence quantum efficiency of the F^-₂ color centers in LiF are also discussed.     

The one-way quantum computer--a non-network model of quantum computation

A one-way quantum computer (QC _C ) works by performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the QC _C . On the other hand, the network model of quantum computation cannot explain all ways of processing quantum information possible with the QC _C . In this paper, two examples of the non-network character of the QC _C are given. First, circuits in the Clifford group can be performed in a single time step. Second, the QC _C -realization of a particular circuit—the bit-reversal gate—has no network interpretation.