Both the Integer-and Fractional Quantum Hall Effects (IQHE and FQHE) are anticorrelation effects.... more Both the Integer-and Fractional Quantum Hall Effects (IQHE and FQHE) are anticorrelation effects. During each plateau of both effects a two-dimensional face centered square crystal of the electrons exists with a minimum of correlation energy. The IQHE is characterized by one face centered magnetic flux quantum per primitive cell which is occupied by one face centered electron yielding an integer filling factor ν. IQHE-plateaus occur when the population Nν of ν Landau-levels with energies below the Fermi energy increases linearly with the magnetic field B Nν(B)=ν•const•B. The ν th plateau ends when the energy Eν(B)=f(ν)•B of the ν th Landau-level crosses the Fermi energy. The FQHE is due to the integer m of flux quanta per primitive cell of which only the integer n≤m are occupied by electrons yielding a fractional filling factor of κ=n/m. In order to allow a face centered square crystal of the n electrons m has to be an odd integer. The κ=n/m-plateau of the FQHE occurs at the field Bn/m when the correlation energy of the κ=n/m Landau-crystal is smaller within the width ΔBn/m of the plateau than the correlation energy outside this width with disordered positions of the electrons. The population Nκ of the 2DEG then increases linearly with the magnetic field B Nκ(B)=κ•const•B within ΔBn/m. The population N e of the 2DEG outside the plateaus is constant and allows the classical Hall effect to occur. The high precision and reproducibility of the QHE-plateaus is due to all so-called noble electrons with energies below EFermi-kT in the 2DEG. These noble electrons don't suffer from any perturbation (including an acceleration in an electric field) since all quantum-mechanical final states of such perturbations are occupied by other electrons. For this reason, they cannot take part in the normal conduction through the 2DEG. But they are responsible for the QHE-Jx-current with Rxx=0 during plateaus through the 2DEG due to a common drift velocity vDx=Ey/Bz which they experience in the crossed electric field Ey and the magnetic field Bz.
Both the Integer-and Fractional Quantum Hall Effects (IQHE and FQHE) are anticorrelation effects.... more Both the Integer-and Fractional Quantum Hall Effects (IQHE and FQHE) are anticorrelation effects. During each plateau of both effects a two-dimensional face centered square crystal of the electrons exists with a minimum of correlation energy. The IQHE is characterized by one face centered magnetic flux quantum per primitive cell which is occupied by one face centered electron yielding an integer filling factor ν. IQHE-plateaus occur when the population Nν of ν Landau-levels with energies below the Fermi energy increases linearly with the magnetic field B Nν(B)=ν•const•B. The ν th plateau ends when the energy Eν(B)=f(ν)•B of the ν th Landau-level crosses the Fermi energy. The FQHE is due to the integer m of flux quanta per primitive cell of which only the integer n≤m are occupied by electrons yielding a fractional filling factor of κ=n/m. In order to allow a face centered square crystal of the n electrons m has to be an odd integer. The κ=n/m-plateau of the FQHE occurs at the field Bn/m when the correlation energy of the κ=n/m Landau-crystal is smaller within the width ΔBn/m of the plateau than the correlation energy outside this width with disordered positions of the electrons. The population Nκ of the 2DEG then increases linearly with the magnetic field B Nκ(B)=κ•const•B within ΔBn/m. The population N e of the 2DEG outside the plateaus is constant and allows the classical Hall effect to occur. The high precision and reproducibility of the QHE-plateaus is due to all so-called noble electrons with energies below EFermi-kT in the 2DEG. These noble electrons don't suffer from any perturbation (including an acceleration in an electric field) since all quantum-mechanical final states of such perturbations are occupied by other electrons. For this reason, they cannot take part in the normal conduction through the 2DEG. But they are responsible for the QHE-Jx-current with Rxx=0 during plateaus through the 2DEG due to a common drift velocity vDx=Ey/Bz which they experience in the crossed electric field Ey and the magnetic field Bz.
Electrical conduction in Free Electron Gases (FEG) only relies on electrons with energies close t... more Electrical conduction in Free Electron Gases (FEG) only relies on electrons with energies close to the Fermi energy. All other electrons are free of any kind of perturbation, since all final states of such perturbations in a fully filled FEG conduction band are occupied by other electrons. A drift velocity can be imposed on these perturbation-free electrons with crossed electric and magnetic fields, resulting in very high, drag-free drift currents through a 2-dimensional electron gas (2DEG), which comes closest to a FEG. These zero-resistance drift currents are the basis for the development of a new concept of an Infinite Electron MobilityTransistor (IEMT) for electrical powers in the range of kWatts and low losses in the range of Watts.
Electrical conduction in Free Electron Gases (FEG) relies only on electrons with energies close t... more Electrical conduction in Free Electron Gases (FEG) relies only on electrons with energies close to the Fermi energy. All other electrons are free of any kind of perturbation, since all final states of such perturbations in a fully filled FEG conduction band are occupied by other electrons. A drift velocity can be imposed on these perturbation-free electrons with crossed electric and magnetic fields, resulting in very high, drag-free drift currents through a 2-dimensional electron gas (2DEG), which comes closest to a FEG. These zero-resistance drift currents are the basis for the development of a new concept for high-current drift transistors with electrical powers in the range of kWatts and low losses in the range of Watts.
A common description of both the Integer(I)-and the Fractional(F)-Quantum Hall Effect (QHE) is pr... more A common description of both the Integer(I)-and the Fractional(F)-Quantum Hall Effect (QHE) is presented. It allows the description of the transition from the IQHE to the FQHE in very good agreement with
... FINE STRUCTURE EFFECTS 348 HJ ANDR;i I (H)f Fig ... Even after eliminating all stray-fields i... more ... FINE STRUCTURE EFFECTS 348 HJ ANDR;i I (H)f Fig ... Even after eliminating all stray-fields in the experiment the interpretation of the data has to include a ... 5, HA Bethe and EE Salpeter,Quantum mechanics of one-and two-electron atoms (Academic Press, Inc., New York, 1957 ...
We report on distinct peaks arising on the low-energy side of KLL Auger spectra which are observe... more We report on distinct peaks arising on the low-energy side of KLL Auger spectra which are observed during the Ž. Ž. interaction of slow highly charged ions at Al 111 and Si 100 surfaces under grazing observation. The energy offset of these structures, with respect to the dominant spectral feature, corresponds to an energy loss of electrons escaping the bulk which can uniquely be connected to surface plasmon excitations. Describing the bulk interaction of outgoing electrons within the framework of a scattering model, we estimate the electron bulk penetration length following a subsurface K-Auger decay. For high impact energies, we also provide experimental evidence for the ionization of target core levels by these outgoing electrons.
Nuclear Instruments and Methods in Physics Research, 1982
... [61] M. Baumann, Z. Naturforsch. 24A (1969) 1049. [62] RW Schmieder, A. Lurio, W. Happer and ... more ... [61] M. Baumann, Z. Naturforsch. 24A (1969) 1049. [62] RW Schmieder, A. Lurio, W. Happer and A. Khadjavi, Phys. Rev. ... Charlotte (Fischer) has shown that there are some subtleties which have to be included, but they can be computed with reasonable certainty. ...
We have measured mean lives of five levels in three different configurations in Sri by exciting t... more We have measured mean lives of five levels in three different configurations in Sri by exciting them selectively in fast beams of neutralized ions by light from an argon-ion laser, and following their timeresolved decay downstream. The mean lives of these levels are 5s5d 3 D 3 , 16.29±0.24 ns; 5s5d 3 D 2 , 16.34±0.13 ns; 5s5d 3D,, 16.49-0.10 ns; 5p 2 3P 2 , 7.89-0.05 ns; and 5s4f 1 F3, 34.2±0.4 ns.
The quantum physics of light is a most fascinating field. Here I present a very personal viewpoin... more The quantum physics of light is a most fascinating field. Here I present a very personal viewpoint, focusing on my own path to quantum entanglement and then on to applications. I have been fascinated by quantum physics ever since I heard about it for the first time in school. The theory struck me immediately for two reasons: (1) its immense mathematical beauty, and (2) the unparalleled precision to which its predictions have been verified again and again. Particularly fascinating for me were the predictions of quantum mechanics for individual particles, individual quantum systems. Surprisingly, the experimental realization of many of these fundamental phenomena has led to novel ideas for applications. Starting from my early experiments with neutrons, I later became interested in quantum entanglement, initially focusing on multi-particle entanglement like GHZ states. This work opened the experimental possibility to do quantum teleportation and quantum hyper-dense coding. The latter became the first entanglement-based quantum experiment breaking a classical limitation. One of the most fascinating phenomena is entanglement swapping, the teleportation of an entangled state. This phenomenon is fundamentally interesting because it can entangle two pairs of particles which do not share any common past. Surprisingly, it also became an important ingredient in a number of applications, including quantum repeaters which will connect future quantum computers with each other. Another application is entanglement-based quantum cryptography where I present some recent long-distance experiments. Entanglement swapping has also been applied in very recent so-called loophole-free tests of Bell's theorem. Within the physics community such loophole-free experiments are perceived as providing nearly definitive proof that local realism is untenable. While, out of principle, local realism can never be excluded entirely, the 2015 achievements narrow down the remaining possibilities for local realistic explanations of the quantum phenomenon of entanglement in a significant way. These experiments may go down in the history books of science. Future experiments will address particularly the freedom-of-choice loophole using cosmic sources of randomness. Such experiments confirm that unconditionally secure quantum cryptography is possible, since quantum cryptography based on Bell's theorem can provide unconditional security. The fact that the experiments were loophole-free proves that an eavesdropper cannot avoid detection in an experiment that correctly follows the protocol. I finally discuss some recent experiments with single-and entangled-photon states in higher dimensions. Such experiments realized quantum entanglement between two photons, each with quantum numbers beyond 10 000 and also simultaneous entanglement of two photons where each carries more than 100 dimensions. Thus they offer the possibility of quantum communication with more than one bit or qubit per photon. The paper concludes discussing Einstein's contributions and viewpoints of quantum mechanics. Even if some of his positions are not supported by recent experiments, he has to be given credit for the fact that his analysis of fundamental issues gave rise to developments which led to a new information technology. Finally, I reflect on some of the lessons learned by the fact that Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
COLLISION-INDUCED ABSORPTION IN ALKALI-METAL-ATOM-.. . 1609 300'K were calculated in the quantum-... more COLLISION-INDUCED ABSORPTION IN ALKALI-METAL-ATOM-.. . 1609 300'K were calculated in the quantum-mechanical formulation. To compare the two methods of calculation, we have evaluated the classical-path expressio~for NaHe it 300'K at several frequencies. The results are included in Fig. 1. The classical approximation is very accurate at low frequencies, but at high frequencies it overestimates the absorption. At high frequencies the classical turning points 8& and 8& in the initial and final states are considerably different and in the quantum-mechanicaltreatment the region 8; &8 &R& contributes little to the matrix elements of D (R). The dependence of the absorption coefficient on the interaction potential is similar to that of the elastic scattering cross section, but the thermal averaging tends to suppress detailed information of the kind that can be obtained from cross-section measurements.
This is the somewhat extended version of the presentation given at the spring meeting of the Deut... more This is the somewhat extended version of the presentation given at the spring meeting of the Deutsche Physikalische Gesellschaft, held at Regensburg, Germany on March 6-11, 2016. It is the extremely compacted part on the Fractional Quantum Hall Effect (FQHE) of the paper " The Physics of the Integer and Fractional Quantum Hall Effects "
ABSTRACT An acceleration of twin A puts him into a relativistic energy state (RES) of kinetic ene... more ABSTRACT An acceleration of twin A puts him into a relativistic energy state (RES) of kinetic energy with respect to twin B where his clock A runs slower than the clock B of twin B who stays at rest. This description of the clock " paradox " is valid for all relativistic energies and for all types of trajectories including circular orbits. In conservative force fields kinetic energy and potential energy become convertible. This allows the description of the rate A of clock A as a function of the potential energy of twin A with respect to twin B. In the limit of small kinetic or potential energies with respect to m 0 c 2 a linear dependence of the rate A on these energies is obtained. This allows the description of rate A with respect to rate B when twin A is subject of all kinds of linear combinations of kinetic and potential energies with respect to twin B. Eight experimental examples are discussed to develop these new interpretations step by step. Since the derivation of the effect of potential energies on the rate A of twin A is not restricted to gravitational potential energies an experiment in electric fields is suggested. A positive result of this experiment would not only provide convincing proof for all interpretations presented here but would have considerable impact in all domains where electric or other type of potential energies play a role.
This paper replaces all my former work on the Quantum Hall Effects. It has the DOI: 10.13140/RG.2... more This paper replaces all my former work on the Quantum Hall Effects. It has the DOI: 10.13140/RG.2.1.3864.7766
A framework is presented for the understanding of both the Integer(I)- and the Fractional(F)-Quan... more A framework is presented for the understanding of both the Integer(I)- and the Fractional(F)-Quantum Hall Effect (QHE), including the widths of their plateaus. It is based on the condition of neutrality which enforces any change in the population of the 2-Dimensional Electron System (2DES) to also occur in an adjacent positive 2-Dimensional Hole Layer (2DHL). The near perfect exchange between the 2DES and the 2DHL allows the description of the IQHE independent of any potential distribution across the 2DES. When on the contrary the 2DHL is nearly constant for all magnetic fields then also the number of electrons in the 2DES has to be nearly constant for all mag-netic fields. This is the condition for the description of the FQHE as the result of a spatial electron and magnetic flux quantization.
The quantum physics of light is a most fascinating field. Here I present a very personal viewpoin... more The quantum physics of light is a most fascinating field. Here I present a very personal viewpoint, focusing on my own path to quantum entanglement and then on to applications. I have been fascinated by quantum physics ever since I heard about it for the first time in school. The theory struck me immediately for two reasons: (1) its immense mathematical beauty, and (2) the unparalleled precision to which its predictions have been verified again and again. Particularly fascinating for me were the predictions of quantum mechanics for individual particles, individual quantum systems. Surprisingly, the experimental realization of many of these fundamental phenomena has led to novel ideas for applications. Starting from my early experiments with neutrons, I later became interested in quantum entanglement, initially focusing on multi-particle entanglement like GHZ states. This work opened the experimental possibility to do quantum teleportation and quantum hyper-dense coding. The latter became the first entanglement-based quantum experiment breaking a classical limitation. One of the most fascinating phenomena is entanglement swapping, the teleportation of an entangled state. This phenomenon is fundamentally interesting because it can entangle two pairs of particles which do not share any common past. Surprisingly, it also became an important ingredient in a number of applications, including quantum repeaters which will connect future quantum computers with each other. Another application is entanglement-based quantum cryptography where I present some recent long-distance experiments. Entanglement swapping has also been applied in very recent so-called loophole-free tests of Bell's theorem. Within the physics community such loophole-free experiments are perceived as providing nearly definitive proof that local realism is untenable. While, out of principle, local realism can never be excluded entirely, the 2015 achievements narrow down the remaining possibilities for local realistic explanations of the quantum phenomenon of entanglement in a significant way. These experiments may go down in the history books of science. Future experiments will address particularly the freedom-of-choice loophole using cosmic sources of randomness. Such experiments confirm that unconditionally secure quantum cryptography is possible, since quantum cryptography based on Bell's theorem can provide unconditional security. The fact that the experiments were loophole-free proves that an eavesdropper cannot avoid detection in an experiment that correctly follows the protocol. I finally discuss some recent experiments with single-and entangled-photon states in higher dimensions. Such experiments realized quantum entanglement between two photons, each with quantum numbers beyond 10 000 and also simultaneous entanglement of two photons where each carries more than 100 dimensions. Thus they offer the possibility of quantum communication with more than one bit or qubit per photon. The paper concludes discussing Einstein's contributions and viewpoints of quantum mechanics. Even if some of his positions are not supported by recent experiments, he has to be given credit for the fact that his analysis of fundamental issues gave rise to developments which led to a new information technology. Finally, I reflect on some of the lessons learned by the fact that Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
A common description of both the Integer(I)-and the Fractional(F)-Quantum Hall Effect (QHE) is pr... more A common description of both the Integer(I)-and the Fractional(F)-Quantum Hall Effect (QHE) is presented. It allows the description of the transition from the IQHE to the FQHE in very good agreement with
Both the Integer-and Fractional Quantum Hall Effects (IQHE and FQHE) are anticorrelation effects.... more Both the Integer-and Fractional Quantum Hall Effects (IQHE and FQHE) are anticorrelation effects. During each plateau of both effects a two-dimensional face centered square crystal of the electrons exists with a minimum of correlation energy. The IQHE is characterized by one face centered magnetic flux quantum per primitive cell which is occupied by one face centered electron yielding an integer filling factor ν. IQHE-plateaus occur when the population Nν of ν Landau-levels with energies below the Fermi energy increases linearly with the magnetic field B Nν(B)=ν•const•B. The ν th plateau ends when the energy Eν(B)=f(ν)•B of the ν th Landau-level crosses the Fermi energy. The FQHE is due to the integer m of flux quanta per primitive cell of which only the integer n≤m are occupied by electrons yielding a fractional filling factor of κ=n/m. In order to allow a face centered square crystal of the n electrons m has to be an odd integer. The κ=n/m-plateau of the FQHE occurs at the field Bn/m when the correlation energy of the κ=n/m Landau-crystal is smaller within the width ΔBn/m of the plateau than the correlation energy outside this width with disordered positions of the electrons. The population Nκ of the 2DEG then increases linearly with the magnetic field B Nκ(B)=κ•const•B within ΔBn/m. The population N e of the 2DEG outside the plateaus is constant and allows the classical Hall effect to occur. The high precision and reproducibility of the QHE-plateaus is due to all so-called noble electrons with energies below EFermi-kT in the 2DEG. These noble electrons don't suffer from any perturbation (including an acceleration in an electric field) since all quantum-mechanical final states of such perturbations are occupied by other electrons. For this reason, they cannot take part in the normal conduction through the 2DEG. But they are responsible for the QHE-Jx-current with Rxx=0 during plateaus through the 2DEG due to a common drift velocity vDx=Ey/Bz which they experience in the crossed electric field Ey and the magnetic field Bz.
Both the Integer-and Fractional Quantum Hall Effects (IQHE and FQHE) are anticorrelation effects.... more Both the Integer-and Fractional Quantum Hall Effects (IQHE and FQHE) are anticorrelation effects. During each plateau of both effects a two-dimensional face centered square crystal of the electrons exists with a minimum of correlation energy. The IQHE is characterized by one face centered magnetic flux quantum per primitive cell which is occupied by one face centered electron yielding an integer filling factor ν. IQHE-plateaus occur when the population Nν of ν Landau-levels with energies below the Fermi energy increases linearly with the magnetic field B Nν(B)=ν•const•B. The ν th plateau ends when the energy Eν(B)=f(ν)•B of the ν th Landau-level crosses the Fermi energy. The FQHE is due to the integer m of flux quanta per primitive cell of which only the integer n≤m are occupied by electrons yielding a fractional filling factor of κ=n/m. In order to allow a face centered square crystal of the n electrons m has to be an odd integer. The κ=n/m-plateau of the FQHE occurs at the field Bn/m when the correlation energy of the κ=n/m Landau-crystal is smaller within the width ΔBn/m of the plateau than the correlation energy outside this width with disordered positions of the electrons. The population Nκ of the 2DEG then increases linearly with the magnetic field B Nκ(B)=κ•const•B within ΔBn/m. The population N e of the 2DEG outside the plateaus is constant and allows the classical Hall effect to occur. The high precision and reproducibility of the QHE-plateaus is due to all so-called noble electrons with energies below EFermi-kT in the 2DEG. These noble electrons don't suffer from any perturbation (including an acceleration in an electric field) since all quantum-mechanical final states of such perturbations are occupied by other electrons. For this reason, they cannot take part in the normal conduction through the 2DEG. But they are responsible for the QHE-Jx-current with Rxx=0 during plateaus through the 2DEG due to a common drift velocity vDx=Ey/Bz which they experience in the crossed electric field Ey and the magnetic field Bz.
Electrical conduction in Free Electron Gases (FEG) only relies on electrons with energies close t... more Electrical conduction in Free Electron Gases (FEG) only relies on electrons with energies close to the Fermi energy. All other electrons are free of any kind of perturbation, since all final states of such perturbations in a fully filled FEG conduction band are occupied by other electrons. A drift velocity can be imposed on these perturbation-free electrons with crossed electric and magnetic fields, resulting in very high, drag-free drift currents through a 2-dimensional electron gas (2DEG), which comes closest to a FEG. These zero-resistance drift currents are the basis for the development of a new concept of an Infinite Electron MobilityTransistor (IEMT) for electrical powers in the range of kWatts and low losses in the range of Watts.
Electrical conduction in Free Electron Gases (FEG) relies only on electrons with energies close t... more Electrical conduction in Free Electron Gases (FEG) relies only on electrons with energies close to the Fermi energy. All other electrons are free of any kind of perturbation, since all final states of such perturbations in a fully filled FEG conduction band are occupied by other electrons. A drift velocity can be imposed on these perturbation-free electrons with crossed electric and magnetic fields, resulting in very high, drag-free drift currents through a 2-dimensional electron gas (2DEG), which comes closest to a FEG. These zero-resistance drift currents are the basis for the development of a new concept for high-current drift transistors with electrical powers in the range of kWatts and low losses in the range of Watts.
A common description of both the Integer(I)-and the Fractional(F)-Quantum Hall Effect (QHE) is pr... more A common description of both the Integer(I)-and the Fractional(F)-Quantum Hall Effect (QHE) is presented. It allows the description of the transition from the IQHE to the FQHE in very good agreement with
... FINE STRUCTURE EFFECTS 348 HJ ANDR;i I (H)f Fig ... Even after eliminating all stray-fields i... more ... FINE STRUCTURE EFFECTS 348 HJ ANDR;i I (H)f Fig ... Even after eliminating all stray-fields in the experiment the interpretation of the data has to include a ... 5, HA Bethe and EE Salpeter,Quantum mechanics of one-and two-electron atoms (Academic Press, Inc., New York, 1957 ...
We report on distinct peaks arising on the low-energy side of KLL Auger spectra which are observe... more We report on distinct peaks arising on the low-energy side of KLL Auger spectra which are observed during the Ž. Ž. interaction of slow highly charged ions at Al 111 and Si 100 surfaces under grazing observation. The energy offset of these structures, with respect to the dominant spectral feature, corresponds to an energy loss of electrons escaping the bulk which can uniquely be connected to surface plasmon excitations. Describing the bulk interaction of outgoing electrons within the framework of a scattering model, we estimate the electron bulk penetration length following a subsurface K-Auger decay. For high impact energies, we also provide experimental evidence for the ionization of target core levels by these outgoing electrons.
Nuclear Instruments and Methods in Physics Research, 1982
... [61] M. Baumann, Z. Naturforsch. 24A (1969) 1049. [62] RW Schmieder, A. Lurio, W. Happer and ... more ... [61] M. Baumann, Z. Naturforsch. 24A (1969) 1049. [62] RW Schmieder, A. Lurio, W. Happer and A. Khadjavi, Phys. Rev. ... Charlotte (Fischer) has shown that there are some subtleties which have to be included, but they can be computed with reasonable certainty. ...
We have measured mean lives of five levels in three different configurations in Sri by exciting t... more We have measured mean lives of five levels in three different configurations in Sri by exciting them selectively in fast beams of neutralized ions by light from an argon-ion laser, and following their timeresolved decay downstream. The mean lives of these levels are 5s5d 3 D 3 , 16.29±0.24 ns; 5s5d 3 D 2 , 16.34±0.13 ns; 5s5d 3D,, 16.49-0.10 ns; 5p 2 3P 2 , 7.89-0.05 ns; and 5s4f 1 F3, 34.2±0.4 ns.
The quantum physics of light is a most fascinating field. Here I present a very personal viewpoin... more The quantum physics of light is a most fascinating field. Here I present a very personal viewpoint, focusing on my own path to quantum entanglement and then on to applications. I have been fascinated by quantum physics ever since I heard about it for the first time in school. The theory struck me immediately for two reasons: (1) its immense mathematical beauty, and (2) the unparalleled precision to which its predictions have been verified again and again. Particularly fascinating for me were the predictions of quantum mechanics for individual particles, individual quantum systems. Surprisingly, the experimental realization of many of these fundamental phenomena has led to novel ideas for applications. Starting from my early experiments with neutrons, I later became interested in quantum entanglement, initially focusing on multi-particle entanglement like GHZ states. This work opened the experimental possibility to do quantum teleportation and quantum hyper-dense coding. The latter became the first entanglement-based quantum experiment breaking a classical limitation. One of the most fascinating phenomena is entanglement swapping, the teleportation of an entangled state. This phenomenon is fundamentally interesting because it can entangle two pairs of particles which do not share any common past. Surprisingly, it also became an important ingredient in a number of applications, including quantum repeaters which will connect future quantum computers with each other. Another application is entanglement-based quantum cryptography where I present some recent long-distance experiments. Entanglement swapping has also been applied in very recent so-called loophole-free tests of Bell's theorem. Within the physics community such loophole-free experiments are perceived as providing nearly definitive proof that local realism is untenable. While, out of principle, local realism can never be excluded entirely, the 2015 achievements narrow down the remaining possibilities for local realistic explanations of the quantum phenomenon of entanglement in a significant way. These experiments may go down in the history books of science. Future experiments will address particularly the freedom-of-choice loophole using cosmic sources of randomness. Such experiments confirm that unconditionally secure quantum cryptography is possible, since quantum cryptography based on Bell's theorem can provide unconditional security. The fact that the experiments were loophole-free proves that an eavesdropper cannot avoid detection in an experiment that correctly follows the protocol. I finally discuss some recent experiments with single-and entangled-photon states in higher dimensions. Such experiments realized quantum entanglement between two photons, each with quantum numbers beyond 10 000 and also simultaneous entanglement of two photons where each carries more than 100 dimensions. Thus they offer the possibility of quantum communication with more than one bit or qubit per photon. The paper concludes discussing Einstein's contributions and viewpoints of quantum mechanics. Even if some of his positions are not supported by recent experiments, he has to be given credit for the fact that his analysis of fundamental issues gave rise to developments which led to a new information technology. Finally, I reflect on some of the lessons learned by the fact that Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
COLLISION-INDUCED ABSORPTION IN ALKALI-METAL-ATOM-.. . 1609 300'K were calculated in the quantum-... more COLLISION-INDUCED ABSORPTION IN ALKALI-METAL-ATOM-.. . 1609 300'K were calculated in the quantum-mechanical formulation. To compare the two methods of calculation, we have evaluated the classical-path expressio~for NaHe it 300'K at several frequencies. The results are included in Fig. 1. The classical approximation is very accurate at low frequencies, but at high frequencies it overestimates the absorption. At high frequencies the classical turning points 8& and 8& in the initial and final states are considerably different and in the quantum-mechanicaltreatment the region 8; &8 &R& contributes little to the matrix elements of D (R). The dependence of the absorption coefficient on the interaction potential is similar to that of the elastic scattering cross section, but the thermal averaging tends to suppress detailed information of the kind that can be obtained from cross-section measurements.
This is the somewhat extended version of the presentation given at the spring meeting of the Deut... more This is the somewhat extended version of the presentation given at the spring meeting of the Deutsche Physikalische Gesellschaft, held at Regensburg, Germany on March 6-11, 2016. It is the extremely compacted part on the Fractional Quantum Hall Effect (FQHE) of the paper " The Physics of the Integer and Fractional Quantum Hall Effects "
ABSTRACT An acceleration of twin A puts him into a relativistic energy state (RES) of kinetic ene... more ABSTRACT An acceleration of twin A puts him into a relativistic energy state (RES) of kinetic energy with respect to twin B where his clock A runs slower than the clock B of twin B who stays at rest. This description of the clock " paradox " is valid for all relativistic energies and for all types of trajectories including circular orbits. In conservative force fields kinetic energy and potential energy become convertible. This allows the description of the rate A of clock A as a function of the potential energy of twin A with respect to twin B. In the limit of small kinetic or potential energies with respect to m 0 c 2 a linear dependence of the rate A on these energies is obtained. This allows the description of rate A with respect to rate B when twin A is subject of all kinds of linear combinations of kinetic and potential energies with respect to twin B. Eight experimental examples are discussed to develop these new interpretations step by step. Since the derivation of the effect of potential energies on the rate A of twin A is not restricted to gravitational potential energies an experiment in electric fields is suggested. A positive result of this experiment would not only provide convincing proof for all interpretations presented here but would have considerable impact in all domains where electric or other type of potential energies play a role.
This paper replaces all my former work on the Quantum Hall Effects. It has the DOI: 10.13140/RG.2... more This paper replaces all my former work on the Quantum Hall Effects. It has the DOI: 10.13140/RG.2.1.3864.7766
A framework is presented for the understanding of both the Integer(I)- and the Fractional(F)-Quan... more A framework is presented for the understanding of both the Integer(I)- and the Fractional(F)-Quantum Hall Effect (QHE), including the widths of their plateaus. It is based on the condition of neutrality which enforces any change in the population of the 2-Dimensional Electron System (2DES) to also occur in an adjacent positive 2-Dimensional Hole Layer (2DHL). The near perfect exchange between the 2DES and the 2DHL allows the description of the IQHE independent of any potential distribution across the 2DES. When on the contrary the 2DHL is nearly constant for all magnetic fields then also the number of electrons in the 2DES has to be nearly constant for all mag-netic fields. This is the condition for the description of the FQHE as the result of a spatial electron and magnetic flux quantization.
The quantum physics of light is a most fascinating field. Here I present a very personal viewpoin... more The quantum physics of light is a most fascinating field. Here I present a very personal viewpoint, focusing on my own path to quantum entanglement and then on to applications. I have been fascinated by quantum physics ever since I heard about it for the first time in school. The theory struck me immediately for two reasons: (1) its immense mathematical beauty, and (2) the unparalleled precision to which its predictions have been verified again and again. Particularly fascinating for me were the predictions of quantum mechanics for individual particles, individual quantum systems. Surprisingly, the experimental realization of many of these fundamental phenomena has led to novel ideas for applications. Starting from my early experiments with neutrons, I later became interested in quantum entanglement, initially focusing on multi-particle entanglement like GHZ states. This work opened the experimental possibility to do quantum teleportation and quantum hyper-dense coding. The latter became the first entanglement-based quantum experiment breaking a classical limitation. One of the most fascinating phenomena is entanglement swapping, the teleportation of an entangled state. This phenomenon is fundamentally interesting because it can entangle two pairs of particles which do not share any common past. Surprisingly, it also became an important ingredient in a number of applications, including quantum repeaters which will connect future quantum computers with each other. Another application is entanglement-based quantum cryptography where I present some recent long-distance experiments. Entanglement swapping has also been applied in very recent so-called loophole-free tests of Bell's theorem. Within the physics community such loophole-free experiments are perceived as providing nearly definitive proof that local realism is untenable. While, out of principle, local realism can never be excluded entirely, the 2015 achievements narrow down the remaining possibilities for local realistic explanations of the quantum phenomenon of entanglement in a significant way. These experiments may go down in the history books of science. Future experiments will address particularly the freedom-of-choice loophole using cosmic sources of randomness. Such experiments confirm that unconditionally secure quantum cryptography is possible, since quantum cryptography based on Bell's theorem can provide unconditional security. The fact that the experiments were loophole-free proves that an eavesdropper cannot avoid detection in an experiment that correctly follows the protocol. I finally discuss some recent experiments with single-and entangled-photon states in higher dimensions. Such experiments realized quantum entanglement between two photons, each with quantum numbers beyond 10 000 and also simultaneous entanglement of two photons where each carries more than 100 dimensions. Thus they offer the possibility of quantum communication with more than one bit or qubit per photon. The paper concludes discussing Einstein's contributions and viewpoints of quantum mechanics. Even if some of his positions are not supported by recent experiments, he has to be given credit for the fact that his analysis of fundamental issues gave rise to developments which led to a new information technology. Finally, I reflect on some of the lessons learned by the fact that Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
A common description of both the Integer(I)-and the Fractional(F)-Quantum Hall Effect (QHE) is pr... more A common description of both the Integer(I)-and the Fractional(F)-Quantum Hall Effect (QHE) is presented. It allows the description of the transition from the IQHE to the FQHE in very good agreement with
A common description of both the Integer (I)-and the Fractional (F)-Quantum Hall Effect (QHE) is ... more A common description of both the Integer (I)-and the Fractional (F)-Quantum Hall Effect (QHE) is presented. It allows for the first time the reproduction of the observed plateaus and their widths. IQHE-plateaus occur when the number of electrons in i fully occupied, spin-resolved Landau levels of the 2-Dimensional Electron System (2DES) increase linearly with the magnetic field B while their energy stays below the Fermi energy. The slope of this increase is proportional to the integer filling factor ν=i which stays constant during a plateau. This description is not perturbed by any non-linear potential distribution across the 2DES. The plateaus of IQHE-measurements are well reproduced. The FQHE shows up when the rectangular QH-bar is specifically produced for the creation of a dominant fraction PQH0 of electrons in the 2DES which stays constant for all magnetic fields B. All ever observed ν=n/m-FQHE-plateaus are then obtained by distributing n electrons on an integer number m of magnetic Flux Quanta (FQ) which cannot overlap with other FQ. The electrons form 2D-square Landau lattices during every ν=n/m-plateau. The primitive cells of these lattices allow the derivation of an effective m=odd-selection rule. Fermi-Dirac-statistics of distributing n electrons on m FQ yields the probabilities STn/m for the creation of the ν=n/m-FQH-states (FQHS). The widths of the plateaus are proportional to (1-PQH0)•STn/m. The enigmatic ν=5/2-, 7/2-, 9/2-, etc.-FQHS are interpreted as due to interactions between electrons in three or more spin-resolved Landau levels obeying specific spin selections rules. Tilted field experiments can be interpreted in terms of symmetry breaking. These descriptions go well beyond existing models or theories which cannot explain the plateaus and their widths and describe at best a limited number of Hall resistances RH=RK/i of the IQHE or RH=RK•m/n of the FQHE. The referee's report and my answer are reproduced in the appendix.
Under strict neutrality conditions the number N e 0 of electrons in a 2DEG is constant at any per... more Under strict neutrality conditions the number N e 0 of electrons in a 2DEG is constant at any perpendicular magnetic field B. Therefore, the standard explanation of the de Haas-van Alphen-(dHvA)-effect has to be modified. It is shown that the spin-dependent total energy of a 2DEG is at the origin of the dHvA-effect. The spin-polarization can show up at extreme conditions. Only when the effective g-factor g*=2 or 0 the resulting 1/B-periods are the same as earlier deduced from the orbital motion of the electrons. For all other g* the observed magnetizations have more complex 1/B-dependences. 1) Introduction In text books [1, 2] the de Haas-van Alphen-(dHvA)-effect is often introduced with the help of a 2-Dimensional Electron Gas (2DEG). The full three-dimensional solid has then to be considered as composed of a huge number of such 2DEG's (of the order of 10 7) with different values of discrete kz. This is justified by the physics of the dHvA which essentially takes place in a plane perpendicular to the external magnetic field B. In all textbooks [1-4], in Onsager's original paper [5], and in a book of reference [6] the explanation of the dHvA-effect relies dominantly on changing populations of the Landau-ensembles as a function of the magnetic field B. It is assumed that these changing populations are responsible for variations of the total energy TE of the electrons. Variations of the magnetization Me=−(1/V)dTE/dB are then described for the 2DEG(kz=0) and for the sum of all 2DEG(kz). It is, however, obvious that neutrality imposes the total number of electrons N e 0 in the 2DEG to stay constant for all magnetic fields. This situation has already been treated in chapter 2.3.3 of Ref.[6] as a digression from the above description. For N e 0(B)=const this digression will become the only contribution to Me while the above description has to be discarded. Unfortunately, this treatment was restricted to a spin g-factor of gs=2.00. It will be extended here to the general case of gs=|g*| with |g*|>0. The result will be compared to the spin-polarization of the Landau ensembles LE still under the condition of N e 0(B)=const. It turns out that every second spin-resolved LE creates a net spin-polarization of the 2DEG. It corresponds to a net magnetization Ms proportional to |g*|. The comparison between Me and Ms clearly establishes a dominance of Me over Ms. This improved approach considerably simplifies the explanation of the dHvA-effect.
Under strict neutrality conditions the number N e 0 of electrons in a 2DEG is constant at any per... more Under strict neutrality conditions the number N e 0 of electrons in a 2DEG is constant at any perpendicular magnetic field B. Therefore, the standard explanation of the de Haas-van Alphen-(dHvA)-effect has to be modified. It is shown that the spin-dependent total energy of a 2DEG is at the origin of the dHvA-effect. The spin-polarization can show up at extreme conditions. Only when the effective g-factor g*=2 or 0 the resulting 1/B-periods are the same as earlier deduced from the orbital motion of the electrons. For all other g* the observed magnetizations have more complex 1/B-dependences. 1) Introduction In text books [1, 2] the de Haas-van Alphen-(dHvA)-effect is often introduced with the help of a 2-Dimensional Electron Gas (2DEG). The full three-dimensional solid has then to be considered as composed of a huge number of such 2DEG's (of the order of 10 7) with different values of discrete kz. This is justified by the physics of the dHvA which essentially takes place in a plane perpendicular to the external magnetic field B. In all textbooks [1-4], in Onsager's original paper [5], and in a book of reference [6] the explanation of the dHvA-effect relies dominantly on changing populations of the Landau-ensembles as a function of the magnetic field B. It is assumed that these changing populations are responsible for variations of the total energy TE of the electrons. Variations of the magnetization Me=−(1/V)dTE/dB are then described for the 2DEG(kz=0) and for the sum of all 2DEG(kz). It is, however, obvious that neutrality imposes the total number of electrons N e 0 in the 2DEG to stay constant for all magnetic fields. This situation has already been treated in chapter 2.3.3 of Ref.[6] as a digression from the above description. For N e 0(B)=const this digression will become the only contribution to Me while the above description has to be discarded. Unfortunately, this treatment was restricted to a spin g-factor of gs=2.00. It will be extended here to the general case of gs=|g*| with |g*|>0. The result will be compared to the spin-polarization of the Landau ensembles LE still under the condition of N e 0(B)=const. It turns out that every second spin-resolved LE creates a net spin-polarization of the 2DEG. It corresponds to a net magnetization Ms proportional to |g*|. The comparison between Me and Ms clearly establishes a dominance of Me over Ms. This improved approach considerably simplifies the explanation of the dHvA-effect.
The Boris-algorithm is adapted to the realistic gyrating motion of charged particles in strong ma... more The Boris-algorithm is adapted to the realistic gyrating motion of charged particles in strong magnetic fields. This includes the procedures for the change of time-steps from Δt to Δt' as well as those for the correct description of collisions with other charged particles. With these procedures examples of simulations of electrons in Electron-Cyclotron-Resonance-Ion-Sources are shown and discussed.
This is the somewhat extended version of the presentation given at the spring meeting of the Deut... more This is the somewhat extended version of the presentation given at the spring meeting of the Deutsche Physikalische Gesellschaft, held at Regensburg, Germany on March 6-11, 2016. It is the extremely compacted part on the Fractional Quantum Hall Effect (FQHE) of the paper " The Physics of the Integer and Fractional Quantum Hall Effects "
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