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  • In optically controlled quantum computers it may be favorable to address different qubits using light with different frequencies, since the optical diffraction does not then limit the distance between qubits. Using qubits that are close to each other enables qubit-qubit interactions and gate operations that are strong and fast in comparison to qubit-environment interactions and decoherence rates. However, as qubits are addressed in frequency space, great care has to be taken when designing the laser pulses, so that they perform the desired operation on one qubit, without affecting other qubits. Complex hyperbolic secant pulses have theoretically been shown to be excellent for such frequency-addressed quantum computing [I. Roos and K. Molmer, Phys. Rev. A 69, 022321 (2004)]—e.g., for use in quantum computers based on optical interactions in rare-earth-metal-ion-doped crystals. The optical transition lines of the rare-earth-metal-ions are inhomogeneously broadened and therefore the frequency of the excitation pulses can be used to selectively address qubit ions that are spatially separated by a distance much less than a wavelength. Here, frequency-selective transfer of qubit ions between qubit states using complex hyperbolic secant pulses is experimentally demonstrated. Transfer efficiencies better than 90% were obtained. Using the complex hyperbolic secant pulses it was also possible to create two groups of ions, absorbing at specific frequencies, where 85% of the ions at one of the frequencies was shifted out of resonance with the field when ions in the other frequency group were excited. This procedure of selecting interacting ions, called qubit distillation, was carried out in preparation for two-qubit gate operations in the rare-earth-metal-ion-doped crystals. The techniques for frequency-selective state-to-state transfer developed here may be also useful also for other quantum optics and quantum information experiments in these long-coherence-time solid-state systems.
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  • Universal quantum information processing requires single-qubit rotations and two-qubit interactions as minimal resources. A possible step beyond this minimal scheme is the use of three-qubit interactions. We consider such three-qubit interactions and show how they can reduce the time required for a quantum state transfer in an XY spin chain. For the experimental implementation, we use liquid-state nuclear magnetic resonance, where three-qubit interactions can be implemented by sequences of radio-frequency pulses.
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  • Modelling oscillations
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  • Modelling oscillations
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  • Coherent Raman scattering can generate Stokes and anti-Stokes fields of comparable intensities. When the Raman shift is due to a magnetic resonance transition (usually in the MHz to GHz range), the Raman fields are generally detected by optical heterodyne detection, using the excitation laser as the local oscillator. In this case, the two sidebands generate beat signals at the same frequency and are therefore indistinguishable. Separation of the two contributions becomes possible, however, by superheterodyne detection with a frequency-shifted optical local oscillator. We compare the two scattering processes, and show how the symmetry between them can be broken in Pr3+:YAlO3.
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  • The coupling between quantum-confined electron spins in semiconductor heterostructures and nuclear spins dominates the dephasing of spin qubits in III/V semiconductors. The interaction can be measured through the electron-spin dynamics or through its effect on the nuclear spin. Here, we discuss the resulting shift of the NMR frequency (the Knight shift) and measure its size as a function of the charge-carrier density for photoexcited charge carriers in a GaAs quantum well.
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  • We study the dynamics of a single spin 1/2 coupled to a bath of spins 1/2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. For initially completely polarized bath spins and small magnetic field, we find persistent oscillations of the central spin about a nonzero mean value. For a large number of bath spins Nb, the oscillation frequency is proportional to Nb, whereas the amplitude behaves as 1/Nb, to leading order. No asymptotic decay of the oscillations due to the nonuniform couplings is observed, in contrast to some recent studies.
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  • Nonresonant dielectric hole-burning experiments were performed on the titanium-modified relaxor ferroelectric lead magnesium niobate around the diffuse maximum in the dielectric permittivity. After applying large alternating electric pump fields we monitored the polarization response to small field steps for times between 0.3 ms and 100 s. Depending on the frequency of the pump oscillation a speedup of the polarization response was observed with a maximum located around times corresponding to the inverse pump frequency. The refilling of the dielectric holes was investigated for several temperatures, pump frequencies, and pump field amplitudes. It proceeded always slower than the time scale set by the pump frequencies. Additionally, we observe a significant increase of the refilling times for increasing pump field amplitudes. This finding can be interpreted to indicate that increasingly large pump fields enable the domain walls to cross larger and larger pinning barriers. The subsequent recovery process, which leads back to the equilibrium domain size distribution, proceeds in the absence of an external electrical field. This rationalizes that recovery is slowed down significantly by application of large pump field amplitudes since then the pinning barriers that have to be traversed back are larger.
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  • The study of nonequilibrium physics is of great interest, because one can capture novel phenomena and properties which are hidden at equilibrium, e.g., one can study relaxation processes. A common way to study the nonequilibrium dynamics of a sample is a pump-probe experiment. In a pump probe experiment an intense laser pulse, the so called pump pulse, excites the sample and takes it out of equilibrium. After a certain delay time a second pulse, the probe pulse, measures the actual state of the sample. In this thesis, we theoretically study the pump-probe response of superconductors. On the one hand we are interest in the effect of a pump pulse and on the other hand we want to provide the pump-probe response, such that experimental measurement can be easily interpreted. In order to do this, we use the density matrix formalism to compute the pump-probe response of the system. In the density matrix formalism equations of motion are set up for expectation values of interest. In order to study the dynamics induced by a pump pulse, we compute the temporal evolution of the quasiparticle densities and the mean phonon amplitude. We find that the induced dynamics of the system depends on characteristics of the pump pulse. For short pulses, the system is pushed into the nonadiabatic regime. In this regime, the order parameter is lowered during the pump pulse and shows a decaying oscillation afterwards. In addition, coherent phonons are generated, which is resonantly enhanced if the frequency of the order parameter oscillation is equal to the phonon frequency. For long pulses, the system is pushed into the adiabatic regime. In this regime, the order parameter is lowered during the pulse and remains almost constant afterwards. Further, there is almost no generation of coherent phonons. For the pump-probe response we compute the conductivity induced by the probe pulse. The conductivity is a typical observable in real pump-probe experiments. Hence, it is possible to compare the theoretical conductivity with a measured one. We find that the dynamics of the superconductor is reflected in oscillation of the conductivity as function of delay time between pump and probe pulse. This oscillation provides information of the frequency and decay time of the algebraically decaying order-parameter oscillations. Further, the dynamics of the coherent phonons is reflected by an oscillation of conductivity as function of delay time at the phonon frequency.,Die Physik jenseits vom Gleichgewicht ist ein sehr spannendes Forschungsfeld, weil man neuartige Phänomene und Eigenschaften erfassen kann, die im Gleichgewicht nicht beobachtbar sind. Zum Beispiel können Relaxationsprozesse untersucht werden. Eine gängige Methode zur Untersuchung von Systemen im Nicht-Gleichgewicht ist das sogenannte "pump-probe-Experiment". In solchen Experimenten bringt ein Laserpuls, der sogenannte "pump pulse" die Probe aus dem Gleichgewicht. Nach einer Verzögerungszeit misst ein zweiter Laserpuls, der sogenannte "probe pulse" den aktuellen Zustand der Probe. In der vorliegenden Arbeit wird das Ergebnis eines solchen Experimentes an einem Supraleiter theoretisch untersucht. Zum einen wird die vom "pump pulse" erzeugte Dynamik berechnet, zum anderen wird eine typische Messgröße, die Leitfähigkeit, berechnet. Mit dieser Größe ist es möglich die theoretischen Resultate mit denen eines Experiments zu vergleichen. Zur Berechnung wird der Dichtematrixformalismus verwendet. In dieser Methode wird die zeitliche Entwicklung von Erwartungswerten, welche von Interesse sind, berechnet. Um den Effekt des "pump pulse" zu untersuchen, wird die zeitliche Entwicklung der Quasiteilchendichten und der mittleren Phononamplitude bestimmt. Die Dynamik dieser Größen hängt von den Eigenschaften des Laserpulses ab. Kurze Laserpulse bringen den Supraleiter ins nichtadiabatische Regime. In diesem Regime wird der Wert des Ordnungsparameters während des Laserpulses abgesenkt und oszilliert danach mit einer abfallenden Schwingung. Zusätzlich werden kohärente Phononen erzeugt. Wenn die Phononfrequenz gleich der Frequenz der Ordnungsparameterschwingung ist, wird die kohärente Erzeugung der Phononen verstärkt. Lange Laserpulse hingegen bringen das System ins adiabatische Regime, in welchem der Ordnungsparameter nach dem Puls nicht oszilliert. Des Weiteren werden kaum kohärente Phononen erzeugt. Zusätzlich wird die Leitfähigkeit, die durch den "probe pulse" induziert wird, berechnet. Die Leitfähigkeit ist eine typische Messgröße eines Experiments und damit ist ein direkter Vergleich zwischen theoretischen und experimentellen Resultaten möglich. Es wird gezeigt, dass die Leitfähigkeit die Dynamik des Systems in Schwingungen als Funktion der Verzögerungszeit wiederspiegeln. Diese Schwingungen geben Aufschluss über die Frequenz und den Abfall der Ordnungsparameterschwingung. Zusätzlich beinhaltet die Leitfähigkeit Hinweise auf die Dynamik der Gitterionen. Schwingungen in der Leitfähigkeit als Funktion der Verzögerungszeit bei der Absorptionsfrequenz, die gleich der Phononfrequenz ist, spiegeln die Dynamik des Gitters wieder.,
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  • In this work experiments on the interaction of picosecond strain wave packets with semiconductor quantum wells and optical microcavities are presented. The focus is on the transient change of the semiconductors optical properties due to the applied dynamical strain. The strain pulses are injected into the sample structures using laser heating of a thin aluminum film, which was deposited on the backside of each sample. After propagating through a GaAs substrate, these strain pulses impact on the structured semiconductors at the front side of the sample. The induced changes in the optical properties are monitored by optical reflectance and photoluminescense spectroscopy. At first optical reflectance spectra of the cavity mode in a II-VI semiconductor based planar microcavity are presented. The modulation occurs when the strain pulse passes interfaces of the layered cavity structure at which the electric field has an antinode. Maximum modulation is reached when the pulse enters or leaves the central cavity layer. The mode energy shifts in the cavity with a finesse of about 2000 are comparable to its mode linewidth, which shows that the proposed technique is prospective for ultrafast optical switching. Further the effect of high amplitude strain waves on a II-VI quantum well is investigated. Acoustic solitons formed during the propagation of the picosecond strain wave in the GaAs substrate lead to exciton resonance energy shifts of up to 10 meV in the quantum well as well as to ultrafast frequency modulation, i.e., chirping, of the exciton transition. Both kind of semiconductor structures have been combined in a III-V semiconductor quantum well microcavity in the strong-coupling regime. A domain can be obtained in which large variations in the optical frequency are induced on time scales shorter than the polariton decoherence. Under these conditions characteristic sidebands which are spectral fingerprints of the terahertz modulation process appear in the reflectance spectra near the polariton resonance. In extreme cases of the polariton resonance energy modulation the strong coupling regime effectively is left. Thereby antiphase oscillations are observed concerning the intensity of the polariton modes and the photonic cavity mode. These oscillations occur on a timescale corresponding to the minimum normal mode splitting of the coupled system. Additionally ultrafast modulation of the photoluminescence intensity from the lower polariton branch is observed.
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