Optimal quantum control in nanostructures: Theory and application to generic three-level system

Coherent carrier control in quantum nanostructures is studied within the framework of Optimal Control. We develop a general solution scheme for the optimization of an external control (e.g., lasers pulses), which allows to channel the system's wavefunction between two given states in its most efficient way; physically motivated constraints, such as limited laser resources or population suppression of certain states, can be accounted for through a general cost functional. Using a generic three-level scheme for the quantum system, we demonstrate the applicability of our approach and identify the pertinent calculation and convergence parameters.Comment: 7 pages; to appear in Phys. Rev.

Quantum Entanglement of Excitons in Coupled Quantum Dots

Optically-controlled exciton dynamics in coupled quantum dots is studied. We show that the maximally entangled Bell states and Greenberger-Horne-Zeilinger (GHZ) states can be robustly generated by manipulating the system parameters to be at the avoided crossings in the eigenenergy spectrum. The analysis of population transfer is systematically carried out using a dressed-state picture. In addition to the quantum dot configuration that have been discussed by Quiroga and Johnson [Phys. Rev. Lett. \QTR{bf}{83}, 2270 (1999)], we show that the GHZ states also may be produced in a ray of three quantum dots with a shorter generation time.Comment: 16 pages, 7 figures, to appear in Phys. Rev.

Size-dependent decoherence of excitonic states in semiconductor microcrystallites

The size-dependent decoherence of the exciton states resulting from the spontaneous emission is investigated in a semiconductor spherical microcrystallite under condition $a_{B}\ll R_{0}\leq\lambda$. In general, the larger size of the microcrystallite corresponds to the shorter coherence time. If the initial state is a superposition of two different excitonic coherent states, the coherence time depends on both the overlap of two excitonic coherent states and the size of the microcrystallite. When the system with fixed size is initially in the even or odd coherent states, the larger average number of the excitons corresponds to the faster decoherence. When the average number of the excitons is given, the bigger size of the microcrystallite corresponds to the faster decoherence. The decoherence of the exciton states for the materials GaAs and CdS is numerically studied by our theoretical analysis.Comment: 4 pages, two figure

Decoherence and Relaxation of a Quantum Bit in the Presence of Rabi Oscillations

Dissipative dynamics of a quantum bit driven by a strong resonant field and interacting with a heat bath is investigated. We derive generalized Bloch equations and find modifications of the qubit's damping rates caused by Rabi oscillations. Nonequilibrium decoherence of a phase qubit inductively coupled to a LC-circuit is considered as an illustration of the general results. It is argued that recent experimental results give a clear evidence of effective suppression of decoherence in a strongly driven flux qubit.Comment: 14 pages; misprints correcte

Resonant nature of phonon-induced damping of Rabi oscillations in quantum dots

Optically controlled coherent dynamics of charge (excitonic) degrees of freedom in a semiconductor quantum dot under the influence of lattice dynamics (phonons) is discussed theoretically. We show that the dynamics of the lattice response in the strongly non-linear regime is governed by a semiclassical resonance between the phonon modes and the optically driven dynamics. We stress on the importance of the stability of intermediate states for the truly coherent control.Comment: 4 pages, 2 figures; final version; moderate changes, new titl

Strong-field terahertz-optical mixing in excitons

Driving a double-quantum-well excitonic intersubband resonance with a terahertz (THz) electric field of frequency \omega_{THz} generated terahertz optical sidebands \omega=\omega_{THz}+\omega_{NIR} on a weak NIR probe. At high THz intensities, the intersubband dipole energy which coupled two excitons was comparable to the THz photon energy. In this strong-field regime the sideband intensity displayed a non-monotonic dependence on the THz field strength. The oscillating refractive index which gives rise to the sidebands may be understood by the formation of Floquet states, which oscillate with the same periodicity as the driving THz field.Comment: 4 pages, 6 figure

Experimental realization of the one qubit Deutsch-Jozsa algorithm in a quantum dot

We perform quantum interference experiments on a single self-assembled semiconductor quantum dot. The presence or absence of a single exciton in the dot provides a qubit that we control with femtosecond time resolution. We combine a set of quantum operations to realize the single-qubit Deutsch-Jozsa algorithm. The results show the feasibility of single qubit quantum logic in a semiconductor quantum dot using ultrafast optical control.Comment: REVTex4, 4 pages, 3 figures. Now includes more details about the dephasing in the quantum dots. The introduction has been reworded for clarity. Minor readability fixe

Generation of maximum spin entanglement induced by cavity field in quantum-dot systems

Equivalent-neighbor interactions of the conduction-band electron spins of quantum dots in the model of Imamoglu et al. [Phys. Rev. Lett. 83, 4204 (1999)] are analyzed. Analytical solution and its Schmidt decomposition are found and applied to evaluate how much the initially excited dots can be entangled to the remaining dots if all of them are initially disentangled. It is demonstrated that the perfect maximally entangled states (MES) can only be generated in the systems of up to 6 dots with a single dot initially excited. It is also shown that highly entangled states, approximating the MES with a good accuracy, can still be generated in systems of odd number of dots with almost half of them being excited. A sudden decrease of entanglement is observed by increasing the total number of dots in a system with a fixed number of excitations.Comment: 6 pages, 7 figures, to appear in Phys. Rev.

Spin-based all-optical quantum computation with quantum dots: understanding and suppressing decoherence

We present an all-optical implementation of quantum computation using semiconductor quantum dots. Quantum memory is represented by the spin of an excess electron stored in each dot. Two-qubit gates are realized by switching on trion-trion interactions between different dots. State selectivity is achieved via conditional laser excitation exploiting Pauli exclusion principle. Read-out is performed via a quantum-jump technique. We analyze the effect on our scheme's performance of the main imperfections present in real quantum dots: exciton decay, hole mixing and phonon decoherence. We introduce an adiabatic gate procedure that allows one to circumvent these effects, and evaluate quantitatively its fidelity

Multi-scale ordering of self-assembled InAs/GaAs(001) quantum dots

Ordering phenomena related to the self-assembly of InAs quantum dots (QD) grown on GaAs(001) substrates are experimentally investigated on different length scales. On the shortest length-scale studied here, we examine the QD morphology and observe two types of QD shapes, i.e., pyramids and domes. Pyramids are elongated along the [1-10] directions and are bounded by {137} facets, while domes have a multi-facetted shape. By changing the growth rates, we are able to control the size and size homogeneity of freestanding QDs. QDs grown by using low growth rate are characterized by larger sizes and a narrower size distribution. The homogeneity of buried QDs is measured by photoluminescence spectroscopy and can be improved by low temperature overgrowth. The overgrowth induces the formation of nanostructures on the surface. The fabrication of self-assembled nanoholes, which are used as a template to induce short-range positioning of QDs, is also investigated. The growth of closely spaced QDs (QD molecules) containing 2–6 QDs per QD molecule is discussed. Finally, the long-range positioning of self-assembled QDs, which can be achieved by the growth on patterned substrates, is demonstrated. Lateral QD replication observed during growth of three-dimensional QD crystals is reported