### 17 results for qubit oscillator frequency

Contributors: Suter, Dieter, Klieber, Robert, Rippe, Lars, Nilsson, Mattias, Kröll, Stefan

Date: 2005-01-01

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. ... 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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Contributors: Suter, Dieter, Zhang, Jingfu, Peng, Xinhua

Date: 2006-01-01

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. ... 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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Contributors: Surmann, Dirk

Date: 2018-01-01

Energy supply in the European power transmission system undergoes a structural change due to expansion and integration of renewable energy sources on a large scale. Generating renewable energy is more volatile and less predictable because it usually depends on the weather like wind and sun. Furthermore, the increase in power trading as a result of the full integration of national electricity markets into the European transmission system additionally burdens the power network. Higher volatility and increasing power trading consume additional resources of existing transmission lines while construction projects for network extension take a huge amount of time. As a consequence, the available resources within the European network have to be utilised efficiently and carefully. Reducing the security margins of components in power networks leads to higher vulnerability to additional problems. This thesis focuses on two topics with the aim of supporting power transmission systems stability. Firstly, selecting an optimal subset of nodes within a power network with respect to the particular issue of Low-**Frequency** **Oscillation** is addressed. A common application is the optimal placement of measurement devices within a power network. By integrating the modelled **oscillations** as a preprocessor into the algorithm, the constructed subset includes their characteristics and is optimal to measure this type of **oscillation**. Secondly, simulation software is widely applied to power networks generating data or investigating the potential effects of changed device parameters. The state of the art way manually defines test scenarios to investigate effects. Each test scenario challenges the corresponding transmission system by, e. g. changing device parameters, increasing its power consumption, or disconnecting a transmission line. Instead of relying on the manual generation of test scenarios to check the network behaviour for modified or new components, it is advantageous to employ an algorithm for building test scenarios. These mechanisms ensure that the range of operating conditions is covered and at the same time propose challenging test scenarios much better than manually generated test scenarios. Black box optimisation techniques support this ess by exploring the possible space for test scenarios using a specialised criterion. This cumulative dissertation comprises a summary of six papers which deal with modelling of Low-**Frequency** **Oscillations** and with the prediction of corresponding values at unobserved nodes within a power transmission system. I will present two published R packages we implemented to simplify the above process. Applying graph kernels in combination with evolutionary algorithms addresses the node selection task. Issues in multimodal optimisation are addressed using contemporary techniques from model-based optimisation to efficiently identify local minima....Modelling **oscillations** ... Energy supply in the European power transmission system undergoes a structural change due to expansion and integration of renewable energy sources on a large scale. Generating renewable energy is more volatile and less predictable because it usually depends on the weather like wind and sun. Furthermore, the increase in power trading as a result of the full integration of national electricity markets into the European transmission system additionally burdens the power network. Higher volatility and increasing power trading consume additional resources of existing transmission lines while construction projects for network extension take a huge amount of time. As a consequence, the available resources within the European network have to be utilised efficiently and carefully. Reducing the security margins of components in power networks leads to higher vulnerability to additional problems. This thesis focuses on two topics with the aim of supporting power transmission systems stability. Firstly, selecting an optimal subset of nodes within a power network with respect to the particular issue of Low-**Frequency** **Oscillation** is addressed. A common application is the optimal placement of measurement devices within a power network. By integrating the modelled **oscillations** as a preprocessor into the algorithm, the constructed subset includes their characteristics and is optimal to measure this type of **oscillation**. Secondly, simulation software is widely applied to power networks generating data or investigating the potential effects of changed device parameters. The state of the art way manually defines test scenarios to investigate effects. Each test scenario challenges the corresponding transmission system by, e. g. changing device parameters, increasing its power consumption, or disconnecting a transmission line. Instead of relying on the manual generation of test scenarios to check the network behaviour for modified or new components, it is advantageous to employ an algorithm for building test scenarios. These mechanisms ensure that the range of operating conditions is covered and at the same time propose challenging test scenarios much better than manually generated test scenarios. Black box optimisation techniques support this ess by exploring the possible space for test scenarios using a specialised criterion. This cumulative dissertation comprises a summary of six papers which deal with modelling of Low-**Frequency** **Oscillations** and with the prediction of corresponding values at unobserved nodes within a power transmission system. I will present two published R packages we implemented to simplify the above process. Applying graph kernels in combination with evolutionary algorithms addresses the node selection task. Issues in multimodal optimisation are addressed using contemporary techniques from model-based optimisation to efficiently identify local minima.

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Contributors: Surmann, Dirk

Date: 2018-01-01

Modelling **oscillations**...Energy supply in the European power transmission system undergoes a structural change due to expansion and integration of renewable energy sources on a large scale. Generating renewable energy is more volatile and less predictable because it usually depends on the weather like wind and sun. Furthermore, the increase in power trading as a result of the full integration of national electricity markets into the European transmission system additionally burdens the power network. Higher volatility and increasing power trading consume additional resources of existing transmission lines while construction projects for network extension take a huge amount of time. As a consequence, the available resources within the European network have to be utilised efficiently and carefully. Reducing the security margins of components in power networks leads to higher vulnerability to additional problems. This thesis focuses on two topics with the aim of supporting power transmission systems stability. Firstly, selecting an optimal subset of nodes within a power network with respect to the particular issue of Low-**Frequency** **Oscillation** is addressed. A common application is the optimal placement of measurement devices within a power network. By integrating the modelled **oscillations** as a preprocessor into the algorithm, the constructed subset includes their characteristics and is optimal to measure this type of **oscillation**. Secondly, simulation software is widely applied to power networks generating data or investigating the potential effects of changed device parameters. The state of the art way manually defines test scenarios to investigate effects. Each test scenario challenges the corresponding transmission system by, e. g. changing device parameters, increasing its power consumption, or disconnecting a transmission line. Instead of relying on the manual generation of test scenarios to check the network behaviour for modified or new components, it is advantageous to employ an algorithm for building test scenarios. These mechanisms ensure that the range of operating conditions is covered and at the same time propose challenging test scenarios much better than manually generated test scenarios. Black box optimisation techniques support this process by exploring the possible space for test scenarios using a specialised criterion. This cumulative dissertation comprises a summary of six papers which deal with modelling of Low-**Frequency** **Oscillations** and with the prediction of corresponding values at unobserved nodes within a power transmission system. I will present two published R packages we implemented to simplify the above process. Applying graph kernels in combination with evolutionary algorithms addresses the node selection task. Issues in multimodal optimisation are addressed using contemporary techniques from model-based optimisation to efficiently identify local minima. ... Energy supply in the European power transmission system undergoes a structural change due to expansion and integration of renewable energy sources on a large scale. Generating renewable energy is more volatile and less predictable because it usually depends on the weather like wind and sun. Furthermore, the increase in power trading as a result of the full integration of national electricity markets into the European transmission system additionally burdens the power network. Higher volatility and increasing power trading consume additional resources of existing transmission lines while construction projects for network extension take a huge amount of time. As a consequence, the available resources within the European network have to be utilised efficiently and carefully. Reducing the security margins of components in power networks leads to higher vulnerability to additional problems. This thesis focuses on two topics with the aim of supporting power transmission systems stability. Firstly, selecting an optimal subset of nodes within a power network with respect to the particular issue of Low-**Frequency** **Oscillation** is addressed. A common application is the optimal placement of measurement devices within a power network. By integrating the modelled **oscillations** as a preprocessor into the algorithm, the constructed subset includes their characteristics and is optimal to measure this type of **oscillation**. Secondly, simulation software is widely applied to power networks generating data or investigating the potential effects of changed device parameters. The state of the art way manually defines test scenarios to investigate effects. Each test scenario challenges the corresponding transmission system by, e. g. changing device parameters, increasing its power consumption, or disconnecting a transmission line. Instead of relying on the manual generation of test scenarios to check the network behaviour for modified or new components, it is advantageous to employ an algorithm for building test scenarios. These mechanisms ensure that the range of operating conditions is covered and at the same time propose challenging test scenarios much better than manually generated test scenarios. Black box optimisation techniques support this process by exploring the possible space for test scenarios using a specialised criterion. This cumulative dissertation comprises a summary of six papers which deal with modelling of Low-**Frequency** **Oscillations** and with the prediction of corresponding values at unobserved nodes within a power transmission system. I will present two published R packages we implemented to simplify the above process. Applying graph kernels in combination with evolutionary algorithms addresses the node selection task. Issues in multimodal optimisation are addressed using contemporary techniques from model-based optimisation to efficiently identify local minima.

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Contributors: Suter, Dieter, Neuhaus, Rudolf, Sellars, Matthew J., Bingham, Stephen J.

Date: 1998-01-01

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. ... 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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Contributors: Suter, Dieter, Fustmann, S., Eickhoff, M.

Date: 2005-01-01

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. ... 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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Contributors: Stolze, Joachim, Bortz, Michael

Date: 2007-01-01

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. ... 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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Contributors: Böhmer, Roland, Kircher, O., Diezemann, G.

Date: 2001-01-01

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. ... 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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Contributors: Krull, Holger

Date: 2014-01-01

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., ... 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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Contributors: Suter, Dieter, Börger, Birgit, Bingham, Stephen J., Gutschank, Jörg, Schweika, Marc-Oliver, Thomson, Andrew J.

Date: 1999-01-01

Electron paramagnetic resonance (EPR) can be detected optically, with a laser beam propagating perpendicular to the static magnetic field. As in conventional EPR, excitation uses a resonant microwave field. The detection process can be interpreted as coherent Raman scattering or as a modulation of the laser beam by the circular dichroism of the sample **oscillating** at the microwave **frequency**. The latter model suggests that the signal should show the same dependence on the optical wavelength as the MCD signal. We check this for two different samples [cytochrome c-551, a metalloprotein, and ruby (Cr3 + :Al2O3)]. In both cases, the observed wavelength dependence is almost identical to that of the MCD signal. A quantitative estimate of the amplitude of the optically detected EPR signal from the MCD also shows good agreement with the experimental results. ... Electron paramagnetic resonance (EPR) can be detected optically, with a laser beam propagating perpendicular to the static magnetic field. As in conventional EPR, excitation uses a resonant microwave field. The detection process can be interpreted as coherent Raman scattering or as a modulation of the laser beam by the circular dichroism of the sample **oscillating** at the microwave **frequency**. The latter model suggests that the signal should show the same dependence on the optical wavelength as the MCD signal. We check this for two different samples [cytochrome c-551, a metalloprotein, and ruby (Cr3 + :Al2O3)]. In both cases, the observed wavelength dependence is almost identical to that of the MCD signal. A quantitative estimate of the amplitude of the optically detected EPR signal from the MCD also shows good agreement with the experimental results.

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