quantum fluids - 1: bose-einstein condensationlundh/statphys/lecture1_adapted_statfys2.pdfquantum...
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![Page 1: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/1.jpg)
Quantum Fluids1: Bose-Einstein Condensation
Emil Lundh
Department of PhysicsUme̊a [email protected]
May 20, 2011
![Page 2: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/2.jpg)
Quantum theory
Cold atoms: a hot topic
Quantum fluids
Monatomic gases, N = 104 – 109
Trapped with magnetic fields, manipulated with lasers
Cooled to nKtemperatures
System size: a fewµm
Lifetime: seconds
Detection: Photo ofactual density!
Emil Lundh Quantum Fluids
![Page 3: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/3.jpg)
Quantum theory
Cold atoms: a hot topic
Quantum fluids
Monatomic gases, N = 104 – 109
Trapped with magnetic fields, manipulated with lasers
Cooled to nKtemperatures
System size: a fewµm
Lifetime: seconds
Detection: Photo ofactual density!
Emil Lundh Quantum Fluids
![Page 4: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/4.jpg)
Quantum theory
Cold atoms: a hot topic
Quantum fluids
Monatomic gases, N = 104 – 109
Trapped with magnetic fields, manipulated with lasers
Cooled to nKtemperatures
System size: a fewµm
Lifetime: seconds
Detection: Photo ofactual density!
Emil Lundh Quantum Fluids
![Page 5: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/5.jpg)
Quantum theory
Cold atoms: a hot topic
Quantum fluids
Monatomic gases, N = 104 – 109
Trapped with magnetic fields, manipulated with lasers
Cooled to nKtemperatures
System size: a fewµm
Lifetime: seconds
Detection: Photo ofactual density!
Emil Lundh Quantum Fluids
![Page 6: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/6.jpg)
Quantum theory
Cold atoms: a hot topic
Quantum fluids
Monatomic gases, N = 104 – 109
Trapped with magnetic fields, manipulated with lasers
Cooled to nKtemperatures
System size: a fewµm
Lifetime: seconds
Detection: Photo ofactual density!
Emil Lundh Quantum Fluids
![Page 7: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/7.jpg)
Quantum theory
Cold atoms: a hot topic
Quantum fluids
Monatomic gases, N = 104 – 109
Trapped with magnetic fields, manipulated with lasers
Cooled to nKtemperatures
System size: a fewµm
Lifetime: seconds
Detection: Photo ofactual density!
Emil Lundh Quantum Fluids
![Page 8: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/8.jpg)
Quantum theory
Cold atoms: a hot topic
Quantum fluids
Monatomic gases, N = 104 – 109
Trapped with magnetic fields, manipulated with lasers
Cooled to nKtemperatures
System size: a fewµm
Lifetime: seconds
Detection: Photo ofactual density!
Emil Lundh Quantum Fluids
![Page 9: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/9.jpg)
Quantum theory
Cold atoms: a hot topic
Quantum fluids
Monatomic gases, N = 104 – 109
Trapped with magnetic fields, manipulated with lasers
Cooled to nKtemperatures
System size: a fewµm
Lifetime: seconds
Detection: Photo ofactual density!
Emil Lundh Quantum Fluids
![Page 10: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/10.jpg)
Quantum theory
Why low temperatures?
Quantum effects become noticeablewhen the deBroglie wavelength iscomparable to distance betweenparticles.Energy of a matter wave is related towavelength
E ∼ ~2
mλ2
Long wavelengths means lowenergies – low temperatures!
Emil Lundh Quantum Fluids
![Page 11: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/11.jpg)
Quantum theory
Why low temperatures?
Quantum effects become noticeable
when the deBroglie wavelength iscomparable to distance betweenparticles.Energy of a matter wave is related towavelength
E ∼ ~2
mλ2
Long wavelengths means lowenergies – low temperatures!
Emil Lundh Quantum Fluids
![Page 12: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/12.jpg)
Quantum theory
Why low temperatures?
Quantum effects become noticeablewhen the deBroglie wavelength iscomparable to distance betweenparticles.
Energy of a matter wave is related towavelength
E ∼ ~2
mλ2
Long wavelengths means lowenergies – low temperatures!
Emil Lundh Quantum Fluids
![Page 13: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/13.jpg)
Quantum theory
Why low temperatures?
Quantum effects become noticeablewhen the deBroglie wavelength iscomparable to distance betweenparticles.Energy of a matter wave is related towavelength
E ∼ ~2
mλ2
Long wavelengths means lowenergies – low temperatures!
Emil Lundh Quantum Fluids
![Page 14: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/14.jpg)
Quantum theory
Why low temperatures?
Quantum effects become noticeablewhen the deBroglie wavelength iscomparable to distance betweenparticles.Energy of a matter wave is related towavelength
E ∼ ~2
mλ2
Long wavelengths means lowenergies – low temperatures!
Emil Lundh Quantum Fluids
![Page 15: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/15.jpg)
Quantum theory
Quantum many-body physics
We want to investigate what phenomena can arise due toquantum effects in a many-body system.
3N-dimensional space: the problem scales exponentially withnumber of particles. (L3N)
Historically: Solid materials, nuclei, or liquid helium. Nowhave quantum gases - more versatile
Emil Lundh Quantum Fluids
![Page 16: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/16.jpg)
Quantum theory
Quantum many-body physics
We want to investigate what phenomena can arise due toquantum effects in a many-body system.
3N-dimensional space: the problem scales exponentially withnumber of particles. (L3N)
Historically: Solid materials, nuclei, or liquid helium. Nowhave quantum gases - more versatile
Emil Lundh Quantum Fluids
![Page 17: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/17.jpg)
Quantum theory
Quantum many-body physics
We want to investigate what phenomena can arise due toquantum effects in a many-body system.
3N-dimensional space: the problem scales exponentially withnumber of particles. (L3N)
Historically: Solid materials, nuclei, or liquid helium. Nowhave quantum gases - more versatile
Emil Lundh Quantum Fluids
![Page 18: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/18.jpg)
Quantum theory
Quantum many-body physics
We want to investigate what phenomena can arise due toquantum effects in a many-body system.
3N-dimensional space: the problem scales exponentially withnumber of particles. (L3N)
Historically: Solid materials, nuclei, or liquid helium. Nowhave quantum gases - more versatile
Emil Lundh Quantum Fluids
![Page 19: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/19.jpg)
Quantum theory
—
Textbook derivation of BEC(blackboard lecture)
Emil Lundh Quantum Fluids
![Page 20: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/20.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 21: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/21.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 22: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/22.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 23: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/23.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 24: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/24.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 25: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/25.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 26: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/26.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 27: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/27.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 28: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/28.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 29: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/29.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 30: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/30.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 31: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/31.jpg)
Quantum theory
Brief history of quantum fluids
1911: Superconductivity in Hg: Kamerlingh Onnes
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1930s: Landau theory of superfluid 4He
1948: Bogoliubov’s theory of the dilute Bose gas
1973: Superfluidity in 3He: Fermi superfluid
1970s: First idea about laser cooling
1986: High-Tc superconductivity: Bednorz and Mller
1995: BEC in dilute gases. 87Rb (Cornell, Wieman); 23Na(Ketterle)
2003: BCS transition for cold Fermi atoms (Jin)
2007: BEC in polaritons in semiconductors (Snoke)
Emil Lundh Quantum Fluids
![Page 32: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/32.jpg)
Quantum theory
Theory of quantum fluids
Phenomena close to T = 0
Ground state – mean-field approximation
Lowest excited many-body states: Bogoliubov theory
Minimize free energy or use Boltzmann’s law to deducefinite-T properties
Emil Lundh Quantum Fluids
![Page 33: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/33.jpg)
Quantum theory
Theory of quantum fluids
Phenomena close to T = 0
Ground state – mean-field approximation
Lowest excited many-body states: Bogoliubov theory
Minimize free energy or use Boltzmann’s law to deducefinite-T properties
Emil Lundh Quantum Fluids
![Page 34: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/34.jpg)
Quantum theory
Theory of quantum fluids
Phenomena close to T = 0
Ground state – mean-field approximation
Lowest excited many-body states: Bogoliubov theory
Minimize free energy or use Boltzmann’s law to deducefinite-T properties
Emil Lundh Quantum Fluids
![Page 35: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/35.jpg)
Quantum theory
Theory of quantum fluids
Phenomena close to T = 0
Ground state – mean-field approximation
Lowest excited many-body states: Bogoliubov theory
Minimize free energy or use Boltzmann’s law to deducefinite-T properties
Emil Lundh Quantum Fluids
![Page 36: Quantum Fluids - 1: Bose-Einstein Condensationlundh/statphys/lecture1_adapted_statfys2.pdfQuantum theory Brief history of quantum uids 1911: Superconductivity in Hg: Kamerlingh Onnes](https://reader035.vdocuments.site/reader035/viewer/2022070915/5fb6079da40988622d6b628a/html5/thumbnails/36.jpg)
Quantum theory
Theory of quantum fluids
Phenomena close to T = 0
Ground state – mean-field approximation
Lowest excited many-body states: Bogoliubov theory
Minimize free energy or use Boltzmann’s law to deducefinite-T properties
Emil Lundh Quantum Fluids
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Quantum theory
—
Gross-Pitaevskii equation(blackboard lecture)
Emil Lundh Quantum Fluids
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Quantum theory
Gross-Pitaevskii equation
i~∂Ψ
∂t= − ~2
2m∇2Ψ + V (r)Ψ + U0|Ψ|2Ψ
GPE is used to simulate: ...
Emil Lundh Quantum Fluids
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Quantum theory
Gross-Pitaevskii equation
Ground state in various traps ...
(BEC in a toroidal trap; work in progress)
Emil Lundh Quantum Fluids
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Quantum theory
Gross-Pitaevskii equation
... vortex lattices in rotated BECs ...
Theory Experiment
Emil Lundh Quantum Fluids
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Quantum theory
Gross-Pitaevskii equation
... More vortices (now in 3D) ...
Emil Lundh Quantum Fluids
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Quantum theory
Gross-Pitaevskii equation
... coherence, correlations, interference fringes ...
Emil Lundh Quantum Fluids
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Quantum theory
Gross-Pitaevskii equation
... systems of several condensates ...
Rayleigh-Taylor instability in an interface between two condensates
Emil Lundh Quantum Fluids
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Quantum theory
Gross-Pitaevskii equation
...even finite-temperature physics and critical phenomena(with modifications)
Emil Lundh Quantum Fluids
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Quantum theory
End of lecture
Thank you for your attention
Emil Lundh Quantum Fluids