Quantum Geometry - Revision history

Tom: /* Quantum Geometric Tensor */

2025-01-18T07:26:42Z

‎Quantum Geometric Tensor

Tom: /* Quantum Geometric Tensor */

2025-01-18T07:25:26Z

‎Quantum Geometric Tensor

Tom: /* Quantum Geometric Tensor */

2025-01-18T07:23:45Z

‎Quantum Geometric Tensor

Tom: /* Momentum Space */

2025-01-18T07:13:58Z

‎Momentum Space

Tom: /* References */

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‎References

Tom: /* Wave Functions */

2025-01-18T02:36:09Z

‎Wave Functions

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‎Momentum Spacer

Tom: /* Wave Functions */

2025-01-18T02:32:28Z

‎Wave Functions

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‎Wave Functions

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‎Artificial Intelligence

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 ==Quantum Geometric Tensor==
-Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics. The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state.<ref>Ran Cheng, ''Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction'' https://arxiv.org/abs/1012.1337</ref> The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.<ref>Mingu Kang +17, ''Measurements of the quantum geometric tensor in solids'' Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02678-8</ref>
+Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics. The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state.<ref>Ran Cheng, ''Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction'' 2013-04-05 https://arxiv.org/abs/1012.1337</ref> The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.<ref>Mingu Kang +17, ''Measurements of the quantum geometric tensor in solids'' Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02678-8</ref>
 ==References==
 [[Category: Physics]]

@@ Line 16: / Line 16: @@
 ==Quantum Geometric Tensor==
-Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics.<ref>Ran Cheng, ''Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction'' https://arxiv.org/abs/1012.1337</ref> The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.<ref>Mingu Kang +17, ''Measurements of the quantum geometric tensor in solids'' Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02678-8</ref>
+Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics. The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state.<ref>Ran Cheng, ''Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction'' https://arxiv.org/abs/1012.1337</ref> The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.<ref>Mingu Kang +17, ''Measurements of the quantum geometric tensor in solids'' Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02678-8</ref>
 ==References==
 [[Category: Physics]]

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 ==Quantum Geometric Tensor==
-Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics. The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.<ref>Mingu Kang +17, ''Measurements of the quantum geometric tensor in solids'' Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02678-8</ref>
+Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics.<ref>Ran Cheng, ''Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction'' https://arxiv.org/abs/1012.1337</ref> The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.<ref>Mingu Kang +17, ''Measurements of the quantum geometric tensor in solids'' Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02678-8</ref>
 ==References==
 [[Category: Physics]]

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 [[File:Quantum geometry.jpg|800px]]
-==Quantum Geometric Tensor
+==Quantum Geometric Tensor==
 Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics. The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.<ref>Mingu Kang +17, ''Measurements of the quantum geometric tensor in solids'' Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02678-8</ref>
 ==References==
 [[Category: Physics]]

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 [[File:Quantum geometry.jpg|800px]]
 ==References==
 [[Category: Physics]]

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 ==Wave Functions==
-''MIT physicists and colleagues measured the geometry, or shape, of electrons in solids at the quantum level. Scientists have long known how to measure the energies and velocities of electrons in crystalline materials, but until now, those systems’ quantum geometry could only be inferred theoretically, or sometimes not at all.''<ref>Elizabeth A. Thomson, ''Physicists measure quantum geometry for the first time'' 2025-01-13 https://news.mit.edu/2025/physicists-measure-quantum-geometry-first-time-0113</ref>
+MIT physicists and colleagues measured the geometry, or shape, of electrons in solids at the quantum level. Scientists have long known how to measure the energies and velocities of electrons in crystalline materials, but until now, those systems’ quantum geometry could only be inferred theoretically, or sometimes not at all.<ref>Elizabeth A. Thomson, ''Physicists measure quantum geometry for the first time'' 2025-01-13 https://news.mit.edu/2025/physicists-measure-quantum-geometry-first-time-0113</ref>
 ==Momentum Space==

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 ''MIT physicists and colleagues measured the geometry, or shape, of electrons in solids at the quantum level. Scientists have long known how to measure the energies and velocities of electrons in crystalline materials, but until now, those systems’ quantum geometry could only be inferred theoretically, or sometimes not at all.''<ref>Elizabeth A. Thomson, ''Physicists measure quantum geometry for the first time'' 2025-01-13 https://news.mit.edu/2025/physicists-measure-quantum-geometry-first-time-0113</ref>
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 Prof. .Nat Abdel Nasser Tawfik

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 ==Full Title or Meme==
-==Artificial Intelligence==
+==Wave Functions==
 Prof. .Nat Abdel Nasser Tawfik