Thierry Giamarchi
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198525004
- eISBN:
- 9780191711909
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525004.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter examines the canonical microscopic models used to study interacting fermions. Most of these models are quite general and are not special to one dimension. These models try to implement ...
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This chapter examines the canonical microscopic models used to study interacting fermions. Most of these models are quite general and are not special to one dimension. These models try to implement the essential ingredients for studying a strongly interacting electronic system: the kinetic energy, the interaction, and the lattice in order to be able to study effects such as the Mott transition. Single chain fermionic systems are considered, and transport in fermionic systems and the Mott transition are discussed. In addition, the relaxation of the momentum due to scattering on the lattice is analyzed.Less
This chapter examines the canonical microscopic models used to study interacting fermions. Most of these models are quite general and are not special to one dimension. These models try to implement the essential ingredients for studying a strongly interacting electronic system: the kinetic energy, the interaction, and the lattice in order to be able to study effects such as the Mott transition. Single chain fermionic systems are considered, and transport in fermionic systems and the Mott transition are discussed. In addition, the relaxation of the momentum due to scattering on the lattice is analyzed.
Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger
- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199573127
- eISBN:
- 9780191775048
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573127.003.9006
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter presents various methods specific for fermionic systems and Fermi–Bose mixtures. It starts by discussing a lattice version of the BCS theory and then reviews BCS-BEC crossover theory for ...
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This chapter presents various methods specific for fermionic systems and Fermi–Bose mixtures. It starts by discussing a lattice version of the BCS theory and then reviews BCS-BEC crossover theory for trapped Fermi gases close to the Feshbach resonance. The chapter analyses Fermi Hubbard models in the strongly correlated regime and t-J limit, and introduces the Gutzwiller projection method and the slave boson approach. It discusses in detail, in particular in the context of Fermi-Bose mixtures, effective low energy Hamiltonians and their derivation.Less
This chapter presents various methods specific for fermionic systems and Fermi–Bose mixtures. It starts by discussing a lattice version of the BCS theory and then reviews BCS-BEC crossover theory for trapped Fermi gases close to the Feshbach resonance. The chapter analyses Fermi Hubbard models in the strongly correlated regime and t-J limit, and introduces the Gutzwiller projection method and the slave boson approach. It discusses in detail, in particular in the context of Fermi-Bose mixtures, effective low energy Hamiltonians and their derivation.
Hans-Peter Eckle
- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780199678839
- eISBN:
- 9780191878589
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199678839.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials
This chapter introduces a select number of models of strongly interacting quantum many-particle physics and examines their basic properties. These models represent Bosonic and Fermionic systems as ...
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This chapter introduces a select number of models of strongly interacting quantum many-particle physics and examines their basic properties. These models represent Bosonic and Fermionic systems as well as systems where magnetic moments, i.e. spins, interact. The main selection criterion has been the existence of a variant of the model that is quantum integrable using Bethe ansatz methods. After studying the Bose fluid, the Landau Fermi liquid, and the one-dimensional concept of the Luttinger liquid, it reviews some of the major models of condensed matter theory, including the Hubbard model describing itinerant magnetism, the Heisenberg model describing localized magnetism, and the Kondo model describing the interaction of a magnetic impurity and band electrons. It also presents the Rabi model and some of its descendants in order to describe the interaction of light and quantum matter in quantum optics.Less
This chapter introduces a select number of models of strongly interacting quantum many-particle physics and examines their basic properties. These models represent Bosonic and Fermionic systems as well as systems where magnetic moments, i.e. spins, interact. The main selection criterion has been the existence of a variant of the model that is quantum integrable using Bethe ansatz methods. After studying the Bose fluid, the Landau Fermi liquid, and the one-dimensional concept of the Luttinger liquid, it reviews some of the major models of condensed matter theory, including the Hubbard model describing itinerant magnetism, the Heisenberg model describing localized magnetism, and the Kondo model describing the interaction of a magnetic impurity and band electrons. It also presents the Rabi model and some of its descendants in order to describe the interaction of light and quantum matter in quantum optics.
S. Chiesa, R.T. Scalettar, P.J.H. Denteneer, P. Chakraborty, T. Paiva, and S. Story
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199592593
- eISBN:
- 9780191741050
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199592593.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter reviews Determinant Quantum Monte Carlo studies of the disordered Hubbard Hamiltonian. The effect of the interplay of interactions and a variety of realizations of the randomness, ...
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This chapter reviews Determinant Quantum Monte Carlo studies of the disordered Hubbard Hamiltonian. The effect of the interplay of interactions and a variety of realizations of the randomness, including spatially varying hopping and chemical potentials, on the conductivity, magnetism, Mott gap formation, and s-wave superconductivity is evaluated. Advances in algorithms and in computer hardware have made possible an order of magnitude increase in system sizes over the last several years, and optical lattice emulators of the Hubbard Hamiltonian are providing a new experimental realization of disordered and interacting fermions. This suggests the possibility of new efforts in this field.Less
This chapter reviews Determinant Quantum Monte Carlo studies of the disordered Hubbard Hamiltonian. The effect of the interplay of interactions and a variety of realizations of the randomness, including spatially varying hopping and chemical potentials, on the conductivity, magnetism, Mott gap formation, and s-wave superconductivity is evaluated. Advances in algorithms and in computer hardware have made possible an order of magnitude increase in system sizes over the last several years, and optical lattice emulators of the Hubbard Hamiltonian are providing a new experimental realization of disordered and interacting fermions. This suggests the possibility of new efforts in this field.
Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger
- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199573127
- eISBN:
- 9780191775048
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573127.003.0004
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter presents an operational definition of quantum simulators, and discusses what kind of Hubbard models and spin models can, in principle, be simulated with ultracold atoms.
This chapter presents an operational definition of quantum simulators, and discusses what kind of Hubbard models and spin models can, in principle, be simulated with ultracold atoms.
Giuliani Alessandro
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199652495
- eISBN:
- 9780191741203
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199652495.003.0010
- Subject:
- Physics, Atomic, Laser, and Optical Physics
The fermionic Hubbard model on the two-dimensional hexagonal lattice at half-filling is the simplest model for undoped single layer graphene with screened interactions. It is remarkable that, in the ...
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The fermionic Hubbard model on the two-dimensional hexagonal lattice at half-filling is the simplest model for undoped single layer graphene with screened interactions. It is remarkable that, in the weak coupling regime, the ground state thermodynamic functions and the equilibrium correlations can be fully constructed (in the form of convergent resummed series in the coupling strength) by rigorous renormalization group methods. This chapter presents a self-contained proof of the analyticity of the specific ground state energy and it reviews the relevant multiscale cluster expansion methods, which are of growing importance in the condensed matter community and, in particular, in the study of interaction effects in graphene.Less
The fermionic Hubbard model on the two-dimensional hexagonal lattice at half-filling is the simplest model for undoped single layer graphene with screened interactions. It is remarkable that, in the weak coupling regime, the ground state thermodynamic functions and the equilibrium correlations can be fully constructed (in the form of convergent resummed series in the coupling strength) by rigorous renormalization group methods. This chapter presents a self-contained proof of the analyticity of the specific ground state energy and it reviews the relevant multiscale cluster expansion methods, which are of growing importance in the condensed matter community and, in particular, in the study of interaction effects in graphene.
Enric Canadell, Marie-Liesse Doublet, and Christophe Iung
- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199534937
- eISBN:
- 9780191774935
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534937.003.0012
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter shows that the repulsion between correlated electrons can take different mathematical forms depending on the Hamiltonian and wavefunction chosen to describe the n-interacting particles ...
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This chapter shows that the repulsion between correlated electrons can take different mathematical forms depending on the Hamiltonian and wavefunction chosen to describe the n-interacting particles system. It accounts for the electronic repulsion Uee , firstly in an effective manner, starting from the extended Hückel model (Uee = 0) and going to the Hubbard (Uee ≠ 0) and Heisenberg (Uee → +∞) models; and secondly in a more quantitative manner using the exact electronic Hamiltonian of the many-body problem, i.e., a system of n interacting particles.Less
This chapter shows that the repulsion between correlated electrons can take different mathematical forms depending on the Hamiltonian and wavefunction chosen to describe the n-interacting particles system. It accounts for the electronic repulsion Uee , firstly in an effective manner, starting from the extended Hückel model (Uee = 0) and going to the Hubbard (Uee ≠ 0) and Heisenberg (Uee → +∞) models; and secondly in a more quantitative manner using the exact electronic Hamiltonian of the many-body problem, i.e., a system of n interacting particles.
T. Maurice Rice
- Published in print:
- 2007
- Published Online:
- May 2008
- ISBN:
- 9780199238873
- eISBN:
- 9780191716652
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238873.003.0015
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter describes metal-insulator transitions in disorder-free crystals. It reviews excitonic insulators, electron-hole liquids, and metal-insulator transitions due to band crossing. The ...
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This chapter describes metal-insulator transitions in disorder-free crystals. It reviews excitonic insulators, electron-hole liquids, and metal-insulator transitions due to band crossing. The realization of exciton (Bose-Einstein) condensate in the high-density limit is illustrated by experiments on a quantum Hall bilayer. In the second part of the chapter, the Mott transition from a metal to a Coulomb localized insulator is discussed in terms of the one band Hubbard model.Less
This chapter describes metal-insulator transitions in disorder-free crystals. It reviews excitonic insulators, electron-hole liquids, and metal-insulator transitions due to band crossing. The realization of exciton (Bose-Einstein) condensate in the high-density limit is illustrated by experiments on a quantum Hall bilayer. In the second part of the chapter, the Mott transition from a metal to a Coulomb localized insulator is discussed in terms of the one band Hubbard model.
A.J. Leggett
- Published in print:
- 2006
- Published Online:
- January 2008
- ISBN:
- 9780198526438
- eISBN:
- 9780191711954
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526438.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials
Starting with an account of the chemical composition, crystalline structure, and phase diagram of the high-temperature (cuprate) superconductors, this chapter reviews the principal experimental ...
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Starting with an account of the chemical composition, crystalline structure, and phase diagram of the high-temperature (cuprate) superconductors, this chapter reviews the principal experimental properties of the optimally doped normal phase, the superconducting phase, and the so-called “pseudogap” region of the phase diagram, and some general comments made on the implications of the experimental data. The question is then raised: what do we know for sure about cuprate superconductivity in the absence of a specific microscopic model? And some answers are attempted. Next, various ideas which may be important in understanding these systems are reviewed. Finally, some novel consequences of the type of pairing realized in the cuprates are explored.Less
Starting with an account of the chemical composition, crystalline structure, and phase diagram of the high-temperature (cuprate) superconductors, this chapter reviews the principal experimental properties of the optimally doped normal phase, the superconducting phase, and the so-called “pseudogap” region of the phase diagram, and some general comments made on the implications of the experimental data. The question is then raised: what do we know for sure about cuprate superconductivity in the absence of a specific microscopic model? And some answers are attempted. Next, various ideas which may be important in understanding these systems are reviewed. Finally, some novel consequences of the type of pairing realized in the cuprates are explored.
Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger
- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199573127
- eISBN:
- 9780191775048
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573127.003.0007
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter focuses on ultracold gases of atoms that possess internal spin structure. First, it considers spinor interactions, and then turns to trapped spinor Bose–Einstein condensates. In ...
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This chapter focuses on ultracold gases of atoms that possess internal spin structure. First, it considers spinor interactions, and then turns to trapped spinor Bose–Einstein condensates. In particular, the chapter discusses various possible mean field phases, spin textures, and topological defects. Next, it describes bosonic spinor gases in optical lattices, effective Hamiltonians, and possible quantum phases. Finally, spinor Fermi gases in optical lattices for spins larger than ½ are discussed.Less
This chapter focuses on ultracold gases of atoms that possess internal spin structure. First, it considers spinor interactions, and then turns to trapped spinor Bose–Einstein condensates. In particular, the chapter discusses various possible mean field phases, spin textures, and topological defects. Next, it describes bosonic spinor gases in optical lattices, effective Hamiltonians, and possible quantum phases. Finally, spinor Fermi gases in optical lattices for spins larger than ½ are discussed.
Immanuel Bloch
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199661886
- eISBN:
- 9780191748356
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199661886.003.0002
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter provides an introduction to the field of strong correlation physics with ultracold atoms in optical lattices. After a basic introduction to the single-particle band structure and lattice ...
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This chapter provides an introduction to the field of strong correlation physics with ultracold atoms in optical lattices. After a basic introduction to the single-particle band structure and lattice configurations, the effect of strong interactions on the Hubbard model is discussed. Detection methods are introduced, which allow us to reveal in-trap density and (quasi)-momentum distributions, as well as correlations between particles on the lattice. The fundamental phases of the bosonic and fermionic Hubbard model are discussed. Superexchange spin-spin interactions that form the basis of quantum magnetism are introduced and the current status on observing such magnetic phenomena is highlighted. Finally, novel possibilities for detecting single-site and single-atom resolved quantum gases are outlined.Less
This chapter provides an introduction to the field of strong correlation physics with ultracold atoms in optical lattices. After a basic introduction to the single-particle band structure and lattice configurations, the effect of strong interactions on the Hubbard model is discussed. Detection methods are introduced, which allow us to reveal in-trap density and (quasi)-momentum distributions, as well as correlations between particles on the lattice. The fundamental phases of the bosonic and fermionic Hubbard model are discussed. Superexchange spin-spin interactions that form the basis of quantum magnetism are introduced and the current status on observing such magnetic phenomena is highlighted. Finally, novel possibilities for detecting single-site and single-atom resolved quantum gases are outlined.
Hans-Peter Eckle
- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780199678839
- eISBN:
- 9780191878589
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199678839.003.0016
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials
The Bethe ansatz can be generalized to problems where particles have internal degrees of freedom. The generalized method can be viewed as two Bethe ansätze executed one after the other: nested Bethe ...
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The Bethe ansatz can be generalized to problems where particles have internal degrees of freedom. The generalized method can be viewed as two Bethe ansätze executed one after the other: nested Bethe ansatz. Electronic systems are the most relevant examples for condensed matter physics. Prominent electronic many-particle systems in one dimension solvable by a nested Bethe ansatz are the one-dimensional δ-Fermi gas, the one-dimensional Hubbard model, and the Kondo model. The major difference to the Bethe ansatz for one component systems is a second, spin, eigenvalue problem, which has the same form in all cases and is solvable by a second Bethe ansatz, e.g. an algebraic Bethe ansatz. A quantum dot tuned to Kondo resonance and coupled to an isolated metallic ring presents an application of the coupled sets of Bethe ansatz equations of the nested Bethe ansatz.Less
The Bethe ansatz can be generalized to problems where particles have internal degrees of freedom. The generalized method can be viewed as two Bethe ansätze executed one after the other: nested Bethe ansatz. Electronic systems are the most relevant examples for condensed matter physics. Prominent electronic many-particle systems in one dimension solvable by a nested Bethe ansatz are the one-dimensional δ-Fermi gas, the one-dimensional Hubbard model, and the Kondo model. The major difference to the Bethe ansatz for one component systems is a second, spin, eigenvalue problem, which has the same form in all cases and is solvable by a second Bethe ansatz, e.g. an algebraic Bethe ansatz. A quantum dot tuned to Kondo resonance and coupled to an isolated metallic ring presents an application of the coupled sets of Bethe ansatz equations of the nested Bethe ansatz.
Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger
- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199573127
- eISBN:
- 9780191775048
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573127.003.0008
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter examines ultracold dipolar gases. First, it discusses the general properties of dipole–dipole interaction and explains how ultracold dipolar systems can be realized in experiments. The ...
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This chapter examines ultracold dipolar gases. First, it discusses the general properties of dipole–dipole interaction and explains how ultracold dipolar systems can be realized in experiments. The chapter reviews the properties of ultracold trapped dipolar Bose gases, pointing out the appearance of the roton minimum in the excitation spectrum. It then moves on to dipolar gases in a lattice, and investigates the corresponding extended Hubbard models. Dipolar bosons in a 2D optical lattice are discussed within the Gutzwiller approximation in more detail, with an emphasis on the appearance of multiple metastable states. Next, the chapter considers quantum Monte Carlo studies of dipolar gases, and discusses some further dipolar effects, which can be realized with cold atoms.Less
This chapter examines ultracold dipolar gases. First, it discusses the general properties of dipole–dipole interaction and explains how ultracold dipolar systems can be realized in experiments. The chapter reviews the properties of ultracold trapped dipolar Bose gases, pointing out the appearance of the roton minimum in the excitation spectrum. It then moves on to dipolar gases in a lattice, and investigates the corresponding extended Hubbard models. Dipolar bosons in a 2D optical lattice are discussed within the Gutzwiller approximation in more detail, with an emphasis on the appearance of multiple metastable states. Next, the chapter considers quantum Monte Carlo studies of dipolar gases, and discusses some further dipolar effects, which can be realized with cold atoms.
Massimo Inguscio and Leonardo Fallani
- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780198525844
- eISBN:
- 9780191780059
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525844.003.0007
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter extends the investigation of ultracold atoms in optical lattices to the emerging field of ‘quantum simulation’, in which atoms are used to experimentally realize basic condensed-matter ...
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This chapter extends the investigation of ultracold atoms in optical lattices to the emerging field of ‘quantum simulation’, in which atoms are used to experimentally realize basic condensed-matter models to precisely investigate their properties and their quantum phase transitions in an ultimately clean setting, where decoherence or unwanted interactions with the environment can be avoided. The chapter discusses the superfluid/metal-to-insulator transition exhibited by strongly-interacting atoms realizing Hubbard models, as well as the Anderson localization determining the suppression of transport for atoms moving in a disordered potential. It concludes with an illustration of the most recent developments in the field, discussing novel experimental techniques and important frontiers in this research.Less
This chapter extends the investigation of ultracold atoms in optical lattices to the emerging field of ‘quantum simulation’, in which atoms are used to experimentally realize basic condensed-matter models to precisely investigate their properties and their quantum phase transitions in an ultimately clean setting, where decoherence or unwanted interactions with the environment can be avoided. The chapter discusses the superfluid/metal-to-insulator transition exhibited by strongly-interacting atoms realizing Hubbard models, as well as the Anderson localization determining the suppression of transport for atoms moving in a disordered potential. It concludes with an illustration of the most recent developments in the field, discussing novel experimental techniques and important frontiers in this research.
Efstratios Manousakis
- Published in print:
- 2015
- Published Online:
- December 2015
- ISBN:
- 9780198749349
- eISBN:
- 9780191813474
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198749349.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
The book contains lectures notes for a graduate two-semester course in quantum mechanics. It differs from other quantum mechanics textbooks as various parts of the book are inspired by rather recent ...
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The book contains lectures notes for a graduate two-semester course in quantum mechanics. It differs from other quantum mechanics textbooks as various parts of the book are inspired by rather recent advances in various areas of physics. For example, the book begins by putting the Schrödinger equation on a spatial discrete lattice, inspired by Hamiltonian lattice gauge theories (HLGT). The book also discusses the path integral formulation of quantum mechanics and emphasize the adiabatic time evolution in the case of a time-dependent Hamiltonian. As an example of how to use symmetry in quantum mechanics, the book treats one-dimensional periodic potentials. The book also discusses atoms and molecules using mean-field-like treatment, such as the Hartree–Fock approximation, including a discussion on how to go beyond it. Electron–electron correlations in the hydrogen molecule are taken into account with a first quantized formulation of the two-site Hubbard model, which is solved analytically. The book also uses the canonical Hamiltonian quantization of quantum electrodynamics after finding the normal modes, in an analogy with the treatment of the normal modes of an array of atoms, the photons emerge as the quanta of such normal modes, in the same way as the phonons emerge in the treatment of the normal modes of the coupled array of atoms. This Hamiltonian quantization of the electromagnetic field is used later to treat its interaction with atomic matter, without having to follow the usual semiclassical treatment.Less
The book contains lectures notes for a graduate two-semester course in quantum mechanics. It differs from other quantum mechanics textbooks as various parts of the book are inspired by rather recent advances in various areas of physics. For example, the book begins by putting the Schrödinger equation on a spatial discrete lattice, inspired by Hamiltonian lattice gauge theories (HLGT). The book also discusses the path integral formulation of quantum mechanics and emphasize the adiabatic time evolution in the case of a time-dependent Hamiltonian. As an example of how to use symmetry in quantum mechanics, the book treats one-dimensional periodic potentials. The book also discusses atoms and molecules using mean-field-like treatment, such as the Hartree–Fock approximation, including a discussion on how to go beyond it. Electron–electron correlations in the hydrogen molecule are taken into account with a first quantized formulation of the two-site Hubbard model, which is solved analytically. The book also uses the canonical Hamiltonian quantization of quantum electrodynamics after finding the normal modes, in an analogy with the treatment of the normal modes of an array of atoms, the photons emerge as the quanta of such normal modes, in the same way as the phonons emerge in the treatment of the normal modes of the coupled array of atoms. This Hamiltonian quantization of the electromagnetic field is used later to treat its interaction with atomic matter, without having to follow the usual semiclassical treatment.
Tuck C. Choy
- Published in print:
- 2015
- Published Online:
- January 2016
- ISBN:
- 9780198705093
- eISBN:
- 9780191774171
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198705093.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials
In this chapter the analogies between EMT with CPA, ATA and RPA are established. Analogies are made with the mean field concept in statistical mechanics and its more subtle variations in areas like ...
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In this chapter the analogies between EMT with CPA, ATA and RPA are established. Analogies are made with the mean field concept in statistical mechanics and its more subtle variations in areas like fluids or in the quantum case such as Hartree–Fock and the modern density functional theories (DFT). The theoretical similarities are emphasized through their fundamental variational principle treatment. Use of Feynman diagrams, relation of EMT with the localization of light, DFT and the classical theory of liquids will stretch the reader’s imagination and perspectives of EMT. The relevance to the quantum Hall effect and electrolytes is noted. The Hubbard model concludes the chapter and can be treated approximately using either CPA or DFT approaches. Landau’s Fermi liquid theory is mentioned.Less
In this chapter the analogies between EMT with CPA, ATA and RPA are established. Analogies are made with the mean field concept in statistical mechanics and its more subtle variations in areas like fluids or in the quantum case such as Hartree–Fock and the modern density functional theories (DFT). The theoretical similarities are emphasized through their fundamental variational principle treatment. Use of Feynman diagrams, relation of EMT with the localization of light, DFT and the classical theory of liquids will stretch the reader’s imagination and perspectives of EMT. The relevance to the quantum Hall effect and electrolytes is noted. The Hubbard model concludes the chapter and can be treated approximately using either CPA or DFT approaches. Landau’s Fermi liquid theory is mentioned.
Christophe Salomon, Georgy V. Shlyapnikov, and Leticia F. Cugliandolo (eds)
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199661886
- eISBN:
- 9780191748356
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199661886.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This book gathers the lecture notes of courses given at the 2010 summer school in theoretical physics in Les Houches, France, Session XCIV. This book illustrates how the field of quantum gases has ...
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This book gathers the lecture notes of courses given at the 2010 summer school in theoretical physics in Les Houches, France, Session XCIV. This book illustrates how the field of quantum gases has flourished at the interface between atomic physics and quantum optics, condensed matter physics, nuclear and high-energy physics, non-linear physics, and quantum information. The physics of correlated atoms in optical lattices is covered from both theoretical and experimental perspectives, including the Bose and Fermi Hubbard models, and the description of the Mott transition. Few-body physics with cold atoms has made spectacular progress and exact solutions for 3-body and 4-body problems have been obtained. The remarkable collisional stability of weakly bound molecules is at the core of the studies of molecular BEC regimes in Fermi gases. Entanglement in quantum many-body systems is introduced and is a key issue for quantum information processing. Rapidly rotating quantum gases and optically induced gauge fields establish a remarkable connection with the fractional quantum Hall effect for electrons in semiconductors. Dipolar quantum gases with long range and anisotropic interaction lead to new quantum degenerate regimes in atoms with large magnetic moments, or electrically aligned polar molecules. Experiments with ultracold fermions show how quantum gases serve as ‘quantum simulators’ of complex condensed matter systems through measurements of the equation of state. Similarly, the recent observation of Anderson localization of matter waves in a disordered optical potential makes a fruitful link with the behaviour of electrons in disordered systems.Less
This book gathers the lecture notes of courses given at the 2010 summer school in theoretical physics in Les Houches, France, Session XCIV. This book illustrates how the field of quantum gases has flourished at the interface between atomic physics and quantum optics, condensed matter physics, nuclear and high-energy physics, non-linear physics, and quantum information. The physics of correlated atoms in optical lattices is covered from both theoretical and experimental perspectives, including the Bose and Fermi Hubbard models, and the description of the Mott transition. Few-body physics with cold atoms has made spectacular progress and exact solutions for 3-body and 4-body problems have been obtained. The remarkable collisional stability of weakly bound molecules is at the core of the studies of molecular BEC regimes in Fermi gases. Entanglement in quantum many-body systems is introduced and is a key issue for quantum information processing. Rapidly rotating quantum gases and optically induced gauge fields establish a remarkable connection with the fractional quantum Hall effect for electrons in semiconductors. Dipolar quantum gases with long range and anisotropic interaction lead to new quantum degenerate regimes in atoms with large magnetic moments, or electrically aligned polar molecules. Experiments with ultracold fermions show how quantum gases serve as ‘quantum simulators’ of complex condensed matter systems through measurements of the equation of state. Similarly, the recent observation of Anderson localization of matter waves in a disordered optical potential makes a fruitful link with the behaviour of electrons in disordered systems.
Nathan Gemelke and Cheng Chin
- Published in print:
- 2014
- Published Online:
- March 2015
- ISBN:
- 9780198719267
- eISBN:
- 9780191788529
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198719267.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials
The physics of bosonic atoms in optical lattices is described. Starting from the basic experimental tools available to create such systems, the chapter introduces a simple model (known as the ...
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The physics of bosonic atoms in optical lattices is described. Starting from the basic experimental tools available to create such systems, the chapter introduces a simple model (known as the Bose—Hubbard model) for such a system. A mean-field type picture is developed to determine the basic character of the superfluid and Mott-insulating phases, and the physical conditions under which each should arise. A number of experimental methods are outlined to detect the properties of the gas. The fact that two thermodynamic ground states exist at zero temperature with different types of order implies the existence of a quantum phase transition. The behavior of the gas near this transition is described using an entirely different framework—quantum criticality—formed around the concepts of scaling symmetry and the renormalization group.Less
The physics of bosonic atoms in optical lattices is described. Starting from the basic experimental tools available to create such systems, the chapter introduces a simple model (known as the Bose—Hubbard model) for such a system. A mean-field type picture is developed to determine the basic character of the superfluid and Mott-insulating phases, and the physical conditions under which each should arise. A number of experimental methods are outlined to detect the properties of the gas. The fact that two thermodynamic ground states exist at zero temperature with different types of order implies the existence of a quantum phase transition. The behavior of the gas near this transition is described using an entirely different framework—quantum criticality—formed around the concepts of scaling symmetry and the renormalization group.
Tom Lancaster and Stephen J. Blundell
- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter considers how to build single-particle operators out of creation and annihilation operators, and this already gives enough information to discuss the tight-binding model of solid state ...
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This chapter considers how to build single-particle operators out of creation and annihilation operators, and this already gives enough information to discuss the tight-binding model of solid state physics and the Hubbard model.Less
This chapter considers how to build single-particle operators out of creation and annihilation operators, and this already gives enough information to discuss the tight-binding model of solid state physics and the Hubbard model.
Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger
- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199573127
- eISBN:
- 9780191775048
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573127.003.0003
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter describes basic methods to realise optical potentials and optical lattices, listing in detail what can be controlled in ultracold atomic systems. It revisits the properties of ...
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This chapter describes basic methods to realise optical potentials and optical lattices, listing in detail what can be controlled in ultracold atomic systems. It revisits the properties of non-interacting particles in periodic lattices: band structure, Bloch functions, and Wannier states. The chapter derives the Hubbard model in the tight binding approximation, and discusses Bose–Einstein condensates in optical lattices in a weak interacting limit, and in a strongly correlated regime.Less
This chapter describes basic methods to realise optical potentials and optical lattices, listing in detail what can be controlled in ultracold atomic systems. It revisits the properties of non-interacting particles in periodic lattices: band structure, Bloch functions, and Wannier states. The chapter derives the Hubbard model in the tight binding approximation, and discusses Bose–Einstein condensates in optical lattices in a weak interacting limit, and in a strongly correlated regime.
