1: Bose-Einstein Condensation Emil Lundhlundh/bec/lecture1.pdf · 1960s: Theory of dilute Bose gas...
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Cold atoms 1: Bose-Einstein Condensation Emil Lundh Department of Physics Ume˚ a University [email protected] April 13, 2011
Transcript of 1: Bose-Einstein Condensation Emil Lundhlundh/bec/lecture1.pdf · 1960s: Theory of dilute Bose gas...
Cold atoms1: Bose-Einstein Condensation
Emil Lundh
Department of PhysicsUme̊a [email protected]
April 13, 2011
Quantum theory
Ume̊a
114 000 inhabitantsAverage age 37.9 yearsCultural capital of Europe 2014400 km ski tracks180 km bicycle pathsUme̊a University with 35 435students
Emil Lundh Cold atoms
Quantum theory
Ume̊a University
Master programmes in:
Computational Physics
Condensed MatterPhysics/Nanotechnology
Theoretical Physics
Optical Physics/MeasurementPhysics
Quantum Mechanics/QuantumTechnique
Space Physics
Emil Lundh Cold atoms
Quantum theory
Lectures
1: Bose-Einstein Condensation (today)
2: Quantum Hydrodynamics
3: Optical lattices
Emil Lundh Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
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 Cold atoms
Quantum theory
—
(blackboard lecture)
Emil Lundh Cold atoms
Quantum theory
Brief history of BEC
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1948: Bogoliubov’s theory
1960s: Theory of dilute Bose gas laid out
1970s: First idea about laser cooling
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 Cold atoms
Quantum theory
Brief history of BEC
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1948: Bogoliubov’s theory
1960s: Theory of dilute Bose gas laid out
1970s: First idea about laser cooling
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 Cold atoms
Quantum theory
Brief history of BEC
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1948: Bogoliubov’s theory
1960s: Theory of dilute Bose gas laid out
1970s: First idea about laser cooling
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 Cold atoms
Quantum theory
Brief history of BEC
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1948: Bogoliubov’s theory
1960s: Theory of dilute Bose gas laid out
1970s: First idea about laser cooling
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 Cold atoms
Quantum theory
Brief history of BEC
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1948: Bogoliubov’s theory
1960s: Theory of dilute Bose gas laid out
1970s: First idea about laser cooling
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 Cold atoms
Quantum theory
Brief history of BEC
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1948: Bogoliubov’s theory
1960s: Theory of dilute Bose gas laid out
1970s: First idea about laser cooling
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 Cold atoms
Quantum theory
Brief history of BEC
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1948: Bogoliubov’s theory
1960s: Theory of dilute Bose gas laid out
1970s: First idea about laser cooling
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 Cold atoms
Quantum theory
Brief history of BEC
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1948: Bogoliubov’s theory
1960s: Theory of dilute Bose gas laid out
1970s: First idea about laser cooling
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 Cold atoms
Quantum theory
Brief history of BEC
1937: Superfluidity in 4He: Kapitza; Allen and Misener
1938: London explains superfluidity in terms of BEC.(However, 4He is a liquid!)
1948: Bogoliubov’s theory
1960s: Theory of dilute Bose gas laid out
1970s: First idea about laser cooling
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 Cold atoms
Quantum theory
Gross-Pitaevskii equation
i~∂Ψ
∂t= − ~2
2m∇2Ψ + V (r)Ψ + U0|Ψ|2Ψ
GPE is used to simulate: ...
Emil Lundh Cold atoms
Quantum theory
Gross-Pitaevskii equation
Ground state in various traps ...
(BEC in a toroidal trap; work in progress)
Emil Lundh Cold atoms
Quantum theory
Gross-Pitaevskii equation
... vortex lattices in rotated BECs ...
Theory Experiment
Emil Lundh Cold atoms
Quantum theory
Gross-Pitaevskii equation
... More vortices (now in 3D) ...
Emil Lundh Cold atoms
Quantum theory
Gross-Pitaevskii equation
... coherence, correlations, interference fringes ...
Emil Lundh Cold atoms
Quantum theory
Gross-Pitaevskii equation
... systems of several condensates ...
Rayleigh-Taylor instability in an interface between two condensates(More about this in Lecture 3)
Emil Lundh Cold atoms
Quantum theory
Gross-Pitaevskii equation
...even finite-temperature physics and critical phenomena(with modifications)
Emil Lundh Cold atoms
Quantum theory
End of lecture 1
Thank you for your attention
Emil Lundh Cold atoms
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