Search Results (45 total)

By exciting a BCS superconductor with ultrashort pulses in the frequency range of the superconducting gap a nonadiabatic regime can be reached. In this regime the modulus of the order parameter oscillates in time. Although its average value can be identified with the gap in the absorption spectrum, the oscillation itself remains invisible in pump-probe spectra. In this Brief Report we demonstrate that by employing a coherent control-type scheme of excitation by two phase-locked pump pulses this oscillation can be unveiled in the probe spectrum. We find that the reaction of the superconductor to a second pump pulse depends strongly on its instantaneous state at the time of the impact of the second pulse. Based on numerical calculations performed on the mean-field level it is shown that by varying the delay time between the two pump pulses the transient oscillation of the order parameter can be transformed into an oscillation of its long-time value, which shows up in the absorption spectrum of a subsequent weak probe pulse as an oscillation of the gap when plotted as a function of the delay time.

The influence of strain waves traveling across a semiconductor quantum dot on the optical spectra of the lowest quantum dot transition is analyzed. Pure dephasing interactions between electronic and phononic degrees of freedom in quantum dot systems are considered, which represent the most important type of electron-phonon interaction in strongly confined quantum dots. For the case of excitation by ultrafast laser pulses, a generating function formalism provides analytical results, which are exact within the framework of the model. Two situations are compared: (i) a phonon wave packet is generated by the optical excitation of a single-quantum dot near a surface, which after reflection at the surface reenters the quantum dot and (ii) a phonon wave packet is generated by the excitation of a nearby second dot and then travels across the quantum dot. Although the displacement fields passing the dot are almost identical in these two situations, we find that the real time responses as well as the corresponding spectra exhibit qualitative differences and thus allow for a discrimination of phonon wave packets from different origins.

The density matrix formalism is employed to calculate pump-probe spectra of BCS superconductors in the coherent regime. Two dynamical regimes, one adiabatic and one nonadiabatic, can be clearly distinguished. In the adiabatic regime, the modulus of the BCS order parameter can be identified with half the gap in the probe spectra. In the nonadiabatic regime, the order parameter oscillates in real time, whereas the gap observed in the spectra reflects its temporal average. The transition between these regimes is accompanied by a qualitative change of the intensity dependence of the dynamical gap renormalization. Furthermore, a hole-burning effect occurs if the spectral shape of the pump pulse is sufficiently sharp. A probe pulse preceding the pump pulse leads to spectral oscillations, and both the gap before and after the pump pulse are visible in the probe spectra.

We study the phonon influence on the spin of an exciton confined in a quantum dot. A process causing the transition of an initial bright heavy hole exciton spin state to dark states is identified. For a set of parameters typical for InAs∕GaAs self-assembled quantum dots the corresponding decay times are over two orders of magnitude faster than for the previously studied transition between bright states and are comparable to exciton lifetimes already at temperatures of several tens of Kelvins.

Pump-probe (PP) and four-wave mixing (FWM) signals from a single quantum dot are presented which are based on a four-level quantum dot model, accounting for the fine structure splitting as well as for the biexciton binding and phonon-induced pure dephasing. We have derived closed form analytical expressions for the PP and FWM polarization components in the time domain after excitation with a pair of ultrafast laser pulses. The solutions are exact within this model. We discuss the dependence of the signals on the polarization of the exciting pulses. We show that for PP spectra after excitation with collinearly polarized pulses and for FWM spectra after cocircular excitation changes in the line shape are entirely due to the polaron formation leading to a fixed shape when this process is completed. For PP spectra after cocircular excitation and FWM spectra after collinear excitation in general periodic modulations of the shape are superimposed which persist even on long time scales and reflect quantum beats due to the fine structure splitting or the biexciton binding energy.

The dynamics of strongly confined laser driven semiconductor quantum dots coupled to phonons is studied theoretically by calculating the time evolution of the reduced density matrix using a numerical path integral method. We explore the cases of long pulses, strong dot-phonon and dot-laser coupling, and high temperatures, which, up to now, have been inaccessible. We find that the phonon-induced damping of Rabi rotations is a nonmonotonic function of the laser field that is increasing at low fields and decreasing at high fields. This results in a reappearance of Rabi rotations at high fields. This phenomenon is of a general nature which occurs for all temperatures and carrier-phonon coupling strengths.

It is shown that quantum information stored in a two-level system coupled to a super-Ohmic bosonic bath is coherently distributed between the system and the environment. A different two-level subsystem, including a proper coherent state of the environment, satisfies all control, reset, and measurement conditions required for a qubit, including two-qubit conditional gates. Such a dressed qubit is decoupled from the remaining environmental degrees of freedom but its control imposes specific adiabaticity conditions. The dressed qubit is the actual physical medium in which quantum information is encoded whenever control operations are slower than the environment dynamics.

Transitions of optically excited carriers between delocalized states in a quantum wire and localized states in a quantum dot are studied on a quantum kinetic level. These transitions are mediated by the emission or absorption of longitudinal optical phonons. Three different excitation scenarios are considered: The capture of a traveling wave packet results in occupations of the bound states and, under suitable conditions, in coherent superpositions. Both occupations and coherences decay due to thermal escape processes resulting from the absorption of phonons. A spatially homogeneous excitation in the quantum wire below the threshold for optical phonon emission leads to capture processes associated with the buildup of a wave front in the carrier density between regions which are already influenced by the capture and regions where this influence is not yet present. A selective excitation of the quantum dot exciton is at elevated temperatures followed by thermal escape processes with a subsequent spreading of the carriers in the quantum wire. We find that for a physically meaningful description of the spatiotemporal dynamics a consistent treatment of both diagonal and off-diagonal density matrix elements is essential in all three scenarios.

An analysis of the control of capture processes from a traveling wave packet in a semiconductor quantum wire into localized states of a quantum dot is presented. On ultrafast time scales this capture in general leads to occupations of the discrete states as well as to coherences among these states. We show that both occupations and coherences can be efficiently controlled by excitation with a pair of spatially localized laser pulses which are spatially, temporally, or spectrally displaced with respect to each other. The coherences between discrete dot states are controlled by spatially nonoverlapping pulses by varying either their spatial or their temporal displacement. For spatially overlapping pulses an effective pulse shaping occurs which modifies both occupations and coherences. By using two-color laser pulses the dot states can be selectively addressed which may result in particularly pronounced coherences.

By use of an optical coherent-control technique we demonstrate and analyze the control of transitions involved in the generation of four-wave-mixing signals in a semiconductor quantum well for the two different four-wave-mixing directions and for different sequences of the excitation pulses. Results are presented for frequency- as well as for time-resolved signals. A doubling of the coherent switching frequency is found which occurs if the laser pulses performing the control process contribute quadratically to the wave-mixing signal. A direct comparison between experiment and microscopic theory reveals how the coherent-control process acts on the coherent polarization of the exciton-biexciton system in all different configurations. An additional interpretation of the experimental results based on a simplified few-level model is able to provide an intuitive understanding of the relevant processes which govern the coherent control of the excitonic and biexcitonic wave-mixing polarizations.

We report on Rabi oscillations of the biexciton in a single In_xGa_1−xAs∕GaAs quantum dot, induced via a coherent two-photon process. In contrast to single-exciton Rabi oscillations the measured population oscillation is not purely sinusoidal in excitation pulse area. The experimental results are well reproduced by a theoretical calculation that relies only on the pulse shape and biexciton binding energy. Dephasing times of the biexciton are similar to those of the single exciton under the applied measurement conditions reaching up to 220 ps.

The dynamics in a GaAs-type quantum dot induced by excitation with Gaussian laser pulses of arbitrary duration are calculated in the density matrix formalism using the correlation expansion. In particular the back-action of nonequilibrium phonons, i.e., the coherent phonon amplitude and the nonequilibrium phonon occupation, on the electronic two-level system are studied. We find that especially for long pulses and low temperatures nonequilibrium phonons play an important role and cannot be neglected.

An analysis of the pure dephasing of a single quantum dot embedded in a half-space or a free-standing slab due to the interaction of the carriers with confined acoustic phonons is presented. We discuss the time dependence of the polarization and the relative volume change based on exact expressions which hold for ultrafast excitation. We find that the proximity of the quantum dot to a surface leaves distinct traces in the polarization and in the case of the half-space leads to an additional decay. In the case of the slab the polarization shows a pronounced periodic structure depending on the width of the slab.

A semiconductor quantum dot model accounting for single exciton as well as biexciton states coupled to phonons and laser light is investigated in the limit of strong electronic confinement. For an arbitrary sequence of excitations with ultrafast pulses analytical solutions are obtained for all density-matrix elements. The results are nonperturbative with respect to both the carrier-phonon and the carrier-light coupling. Numerical results for a single pulse excitation are presented illustrating spectral features of our solution as well as pulse area and temperature dependences.

Capture processes of an electronic wave packet traveling in a quantum wire into localized states of an embedded quantum dot by means of phonon emission are studied in a quantum kinetic approach. It turns out that due to the ultrashort length and time scales involved the capture processes exhibit a variety of quantum kinetic features which cannot be described by a simple semiclassical capture rate. We find in general a nonmonotonic rise of the occupation of bound states even at low temperatures where no phonon absorption is possible. This is related to the finite collision duration and the presence of coherent superpositions between initial and final states in the scattering process giving rise to phonon Rabi oscillations between free and trapped states. In the case of more than one bound state in the dot typically a linear combination of these bound states is populated, which leads to a nontrivial dynamics of the trapped carrier density. For potential profiles with large reflection probability it turns out that also the transmission and reflection behavior is modified by the capture process. Finally the theory is applied to a two-band model including optical excitation and excitonic effects. For the scenarios studied in the paper these phenomena lead to some quantitative modifications but they do not change the characteristic quantum features of the capture dynamics.

The pure dephasing of excitons in quantum dot structures due to their interaction with acoustic phonons as well as the spatiotemporal dynamics of the created nonequilibrium phonon population is studied theoretically. The theory is applied to GaAs- as well as GaN-based heterostructures. A detailed analysis of the interplay between different material parameters, different quantum dot geometries, and different electric fields is presented. The optical polarization induced by an ultrashort laser pulse exhibits a characteristic nonexponential behavior: it decays on a pico- or subpicosecond time scale to a value that strongly depends on temperature, structure, and material parameters and is then retained until, on a typically much longer time scale, it finally decays because of electron-hole recombination or transitions to other states. We find that, in general, the remnant optical polarization is much higher in the GaAs-based structures than in the GaN-based structure mainly because of the strongly enhanced piezoelectric coupling in GaN quantum dots. The optical excitation also leads to the buildup of a phonon population consisting of a polaron part that remains localized in the region of the quantum dot and a traveling part that leaves the dot region at the speed of sound. This traveling part exhibits characteristic anisotropies reflecting both the anisotropy of the quantum dot structure and of the coupling matrix elements.

We study the phonon-induced dephasing of the exciton state in a quantum dot excited by a sequence of ultrashort pulses. We show that the multiple-pulse control leads to a considerable improvement of the coherence of the optically excited state. For a fixed control time window, the optimized pulsed control often leads to a higher degree of coherence than the control by a smooth, single Gaussian pulse. The reduction of dephasing is considerable already for 2–3 pulses.

We have analyzed the initial decoherence of strongly confined semiconductor quantum dots by performing four-wave-mixing experiments and comparing with theory. The measurements are in quantitative agreement with analytical results accounting for the pure dephasing induced by acoustic phonons. The experiments confirm the recent prediction of an unusual nonmonotonous temperature dependence of the initial decoherence time.

We investigate theoretically the nonlinear optical response of a semiconductor for excitation conditions where simultaneously all kinds of correlated two-pair transitions contribute to the dynamics. This includes transitions to biexcitons, exciton-exciton scattering states, two free electron-hole pairs as well as two-pair states involving an exciton and a free electron-hole pair. For certain excitation conditions two-pair correlations give rise to a complex line shape of four-wave-mixing spectra with an emission spread over the whole range between the exciton line and the band-edge. Even a strong suppression of the signal at the exciton line can be achieved while the emission is still concentrated between the exciton and the band-edge. The dependence of these features on the excitation conditions and on the strength of the Coulomb interaction is discussed. Comparing a nonperturbative treatment of the Coulomb interaction with the Born approximation and the mean-field theory clearly reveals the importance of nonperturbative Coulomb correlations even for excitations involving the continuum of free electron-hole pairs.

It is shown that lower bounds for the effective memory time induced by two-pair correlations can be estimated by monitoring changes of the shape of excitonic four-wave-mixing spectra. Experimentally we demonstrate a memory time of at least 540 fs for a ZnSe single quantum well. Microscopic calculations reveal that this lower bound is not sharp. Interactions retarded by more than 800 fs are shown to influence the dynamics, reflecting the presence of a long time tail in the memory kernel.

The dynamics of optically generated carriers interacting with longitudinal optical phonons in spatially inhomogeneous systems is analyzed on a quantum kinetic level. A microscopic density-matrix theory is formulated accounting for arbitrary spatial inhomogeneities in the semiconductor structure and the excitation conditions. The physical origin of the various contributions entering the dynamical equations is discussed. The theory is applied to the dynamics of a wave packet optically generated locally in a quantum wire. We study quantum kinetic features due to the interaction with phonons in the expansion process both in a one-band and a two-band model as well as the generation and dynamics of coherent phonon amplitudes.

A Reply to the Comment by M. Joffre.

The nonlinear optical response to ultrafast laser pulses of semiconductor quantum dots coupled to acoustic phonons is discussed on the basis of closed-form analytical results valid for dots in the strong confinement regime. General properties of four-wave-mixing (FWM) signals are derived from the analytical formulas. Numerical results are presented for two-pulse FWM signals from single quantum dots and from dot ensembles in the time and the frequency domains. Interestingly, the initial decay time of the signal is found to depend nonmonotonously on temperature and delay time. In general, the phonon coupling leads to a modulated decay of the time domain optical response which is neither exponential nor Gaussian. The strength of the modulations is influenced by inhomogeneous broadening and temperature as well as by the relative localization lengths of electrons and holes. FWM spectra of single dots evolve from asymmetric functions for coinciding pulses into symmetric spectra for large delays. Nonlinear signals are compared with linear signals revealing striking similarities but also significant differences, e.g., concerning the depth of the initial drop.