Transient nonlinear optical spectroscopy, performed on excitons confined to single GaAs quantum dots, shows oscillations that are analogous to Rabi oscillations in two-level atomic systems. This demonstration corresponds to a one-qubit rotation in a single quantum dot which is important for proposals using quantum dot excitons for quantum computing. The dipole moment inferred from the data is consistent with that directly obtained from linear absorption studies. The measurement extends the artificial atom model of quantum dot excitonic transitions into the strong-field limit, and makes possible full coherent optical control of the quantum state of single excitons using optical pi pulses.

We show how a spin interaction between electrons localized in neighboring quantum dots can be induced and controlled optically. The coupling is generated via virtual excitation of delocalized excitons and provides an efficient coherent control of the spins. This quantum manipulation can be realized in the adiabatic limit and is robust against decoherence by spontaneous emission. Applications to the realization of quantum gates, scalable quantum computers, and to the control of magnetization in an array of charged dots are proposed.Quantum control of an electron spin, either independent of other spins or condition on their states, in a semiconductor nanostructure is a central issue in the emerging fields of spintronics and quantum information processing. The spin of a single electron confined in a semiconductor quantum dot (QD) was proposed [1] as a qubit for the realization of scalable quantum computers. Quantum gates are designed using electric gates to control via overlap the exchange interaction between two electrons in neighboring dots. Optical control was also proposed, in which a cavity mode couples different dots [2], or a dipole-dipole interaction between charged excitons strongly polarized by an external dc field is exploited [3]. Optical control possesses several advantages compared with control by gate voltage. Ultrafast lasers can control quantum systems on the femtosecond time scale, and using shaping techniques the amplitude and phase of the pulses can be designed at will offering a great deal of flexibility and efficiency [4].In this paper we report a theory of an exchange interaction between two electron spins in separate dots in a typical semiconductor QD system by virtual excitation of delocalized exciton states in the host material which interact with the electrons in both dots. This time-dependent effective interaction is driven by the external laser field, and is, thus, controllable. The virtual excitation by an off-resonant laser preserve the coherence of the spin dynamics. This indirect exchange mechanism is analogous to a RKKY interaction [5] between two magnetic impurities mediated by conduction electron or excitons[6], except that the intermediate electron-hole pair is produced by the external light. The optical quantum control of a single exciton in a semiconductor QD has been recently reported in GaAs QDs generated by monolayer fluctuations [7] and InGaAs self-assembled QDs [8,9]. The short radiative recombination lifetime of the exciton (of the order of 100 ps) gives a severe limitation for the application to quantum computation, even with the help of shaping techniques [4]. This can be avoided by doping QDs each with a single conduction electron and by encoding the quantum information in the spin degrees of freedom. Optical control by virtual excitation avoids the fast optical decoherence. Thus, the advantages of a very long spin coherence time in QDs [10] and fast optical control can be combined.Consider two electrons localized in two QDs at R ℓ (ℓ = 1, 2) with wavefunctions φ ℓ (r...

We present a theory of the linear and nonlinear optical characteristics of the insulating phase of the Falicov-Kimball model within the self-consistent mean-field approximation. The Coulomb attraction between the itinerant d-electrons and the localized f -holes gives rise to a built-in coherence between the d-and f -states, which breaks the inversion symmetry of the underlying crystal, leading to: (1) electronic ferroelectricity, (2) ferroelectric resonance, and (3) a nonvanishing susceptibility for second-harmonic generation. As experimental tests of such a built-in coherence in mixed-valent compounds we propose measurements of the static dielectric constant, the microwave absorption spectrum, and the dynamic second-order susceptibility.

We present a theory of quantum optical control of an electron spin in a single semiconductor quantum dot via spin-flip Raman transitions. We show how an arbitrary spin rotation may be achieved by virtual excitation of discrete or continuum trion states. The basic physics issues of the appropriate adiabatic optical pulses in a static magnetic field to perform the single qubit operation are addressed.

This work presents a step furthering a new perspective of proactive control of the spin-exciton dynamics in the quantum limit. Laser manipulation of spin-polarized optical excitations in a semiconductor nanodot is used to control the spin dynamics of two interacting excitons. Shaping of femtosecond laser pulses keeps the quantum operation within the decoherence time. Computation of the fidelity of the operations and application to the complete solution of a basic quantum computing algorithm demonstrate in theory the feasibility of quantum control.Experimental laser control of spin states of excitons has been demonstrated in ensembles of semiconductor quantum dots (QDs) [1]. In a single dot, ultrafast control of spin-excitons [2], and entanglement of the electron-hole complex [3] have been reported. Here, we present a study of the design of laser pulses for the ultrafast control of the spin dynamics of individual excitons in a QD. This is a special case of designing Hamiltonians to bring a system from one state to another [4]. We hope that the theory of control of exciton spin dynamics may help rapid realization of basic quantum operations in nanodots. An exciting application would be the further development of quantum computation [5] using excitons [6][7][8][9][10] or intersubband transitions [11][12][13].In this paper, the control of exciton spin dynamics consists in designing laser pulses to create as a function of time desired multiexciton states of a subsystem of dots. In the ultrafast control of the spin dynamics of excitons, there is the possibility of unintended dynamics due to the presence of close resonances. Sharp resonant pulses can minimize such unintended dynamics, but at the cost of a long operation time. The latter leads to the spontaneous recombination of the excitons and to their dephasing, resulting in uncontrolled deterioration of the amplitude and phase of the coefficients of the desired linear combination of quantum states. We give a solution to these two contradictory requirements by suggesting extending the wellknown laser pulse-shaping technique [14] to the delicate control in the quantum limit. Design of excitations has been applied to quantum computation by NMR [15] and by electron spin dynamics or intersubband transitions in QDs [16][17][18][19]. We rely on the theory of DiVincenzo [20] stating that quantum gates operating on just two qubits at a time are sufficient to construct a general quantum circuit in a system of many dots. As an application to a prototype quantum computation which illustrates the issues raised above, we present the results of numerical simulations of the two exciton dynamics in a sequence of operations to solve the Deutsch-Jozsa (DJ) problem [21,5]. We shall concentrate on the control of the lowest four states formed by two excitons with opposite spins in a single dot. The spin-down and up states can be excited by the left (σ−) and right-handed (σ+) circularly polarized light, respectively. The four basis states are, in order: the lowest biexciton state | + − , ...