Cold atoms. 1: Bose-Einstein Condensation. Emil Lundh. April 13, Department of Physics Umeå University
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1 1: Bose-Einstein Condensation Department of Physics Umeå University April 13, 2011
2 Umeå inhabitants Average age 37.9 years Cultural capital of Europe km ski tracks 180 km bicycle paths Umeå University with students
3 Umeå University Master programmes in: Computational Physics Condensed Matter Physics/Nanotechnology Theoretical Physics Optical Physics/Measurement Physics Quantum Mechanics/Quantum Technique Space Physics
4 Lectures 1: Bose-Einstein Condensation (today) 2: Quantum Hydrodynamics 3: Optical lattices
5 : a hot topic
6 : a hot topic Quantum fluids
7 : a hot topic Quantum fluids Monatomic gases, N =
8 : a hot topic Quantum fluids Monatomic gases, N = Trapped with magnetic fields, manipulated with lasers
9 : a hot topic Quantum fluids Monatomic gases, N = Trapped with magnetic fields, manipulated with lasers Cooled to nk temperatures
10 : a hot topic Quantum fluids Monatomic gases, N = Trapped with magnetic fields, manipulated with lasers Cooled to nk temperatures System size: a few µm
11 : a hot topic Quantum fluids Monatomic gases, N = Trapped with magnetic fields, manipulated with lasers Cooled to nk temperatures System size: a few µm Lifetime: seconds
12 : a hot topic Quantum fluids Monatomic gases, N = Trapped with magnetic fields, manipulated with lasers Cooled to nk temperatures System size: a few µm Lifetime: seconds Detection: Photo of actual density!
13 Why low temperatures?
14 Why low temperatures? Quantum effects become noticeable
15 Why low temperatures? Quantum effects become noticeable when the debroglie wavelength is comparable to distance between particles.
16 Why low temperatures? Quantum effects become noticeable when the debroglie wavelength is comparable to distance between particles. Energy of a matter wave is related to wavelength E 2 mλ 2 Long wavelengths means low energies low temperatures!
17 Why low temperatures? Quantum effects become noticeable when the debroglie wavelength is comparable to distance between particles. Energy of a matter wave is related to wavelength E 2 mλ 2 Long wavelengths means low energies low temperatures!
18 Quantum many-body physics
19 Quantum many-body physics We want to investigate what phenomena can arise due to quantum effects in a many-body system.
20 Quantum many-body physics We want to investigate what phenomena can arise due to quantum effects in a many-body system. 3N-dimensional space: the problem scales exponentially with number of particles. (L 3N )
21 Quantum many-body physics We want to investigate what phenomena can arise due to quantum effects in a many-body system. 3N-dimensional space: the problem scales exponentially with number of particles. (L 3N ) Historically: Solid materials, nuclei, or liquid helium. Now have quantum gases - more versatile
22 (blackboard lecture)
23 Brief history of BEC
24 Brief history of BEC 1937: Superfluidity in 4 He: Kapitza; Allen and Misener
25 Brief history of BEC 1937: Superfluidity in 4 He: Kapitza; Allen and Misener 1938: London explains superfluidity in terms of BEC. (However, 4 He is a liquid!)
26 Brief history of BEC 1937: Superfluidity in 4 He: Kapitza; Allen and Misener 1938: London explains superfluidity in terms of BEC. (However, 4 He is a liquid!) 1948: Bogoliubov s theory
27 Brief history of BEC 1937: Superfluidity in 4 He: Kapitza; Allen and Misener 1938: London explains superfluidity in terms of BEC. (However, 4 He is a liquid!) 1948: Bogoliubov s theory 1960s: Theory of dilute Bose gas laid out
28 Brief history of BEC 1937: Superfluidity in 4 He: Kapitza; Allen and Misener 1938: London explains superfluidity in terms of BEC. (However, 4 He is a liquid!) 1948: Bogoliubov s theory 1960s: Theory of dilute Bose gas laid out 1970s: First idea about laser cooling
29 Brief history of BEC 1937: Superfluidity in 4 He: Kapitza; Allen and Misener 1938: London explains superfluidity in terms of BEC. (However, 4 He 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. 87 Rb (Cornell, Wieman); 23 Na (Ketterle)
30 Brief history of BEC 1937: Superfluidity in 4 He: Kapitza; Allen and Misener 1938: London explains superfluidity in terms of BEC. (However, 4 He 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. 87 Rb (Cornell, Wieman); 23 Na (Ketterle) 2003: BCS transition for cold Fermi atoms (Jin)
31 Brief history of BEC 1937: Superfluidity in 4 He: Kapitza; Allen and Misener 1938: London explains superfluidity in terms of BEC. (However, 4 He 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. 87 Rb (Cornell, Wieman); 23 Na (Ketterle) 2003: BCS transition for cold Fermi atoms (Jin) 2007: BEC in polaritons in semiconductors (Snoke)
32 Gross-Pitaevskii equation i Ψ t = 2 2m 2 Ψ + V (r)ψ + U 0 Ψ 2 Ψ GPE is used to simulate:...
33 Gross-Pitaevskii equation Ground state in various traps... (BEC in a toroidal trap; work in progress)
34 Gross-Pitaevskii equation... vortex lattices in rotated BECs... Theory Experiment
35 Gross-Pitaevskii equation... More vortices (now in 3D)...
36 Gross-Pitaevskii equation... coherence, correlations, interference fringes...
37 Gross-Pitaevskii equation... systems of several condensates... Rayleigh-Taylor instability in an interface between two condensates (More about this in Lecture 3)
38 Gross-Pitaevskii equation...even finite-temperature physics and critical phenomena (with modifications)
39 End of lecture 1 Thank you for your attention
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