Fichas
Quantum optics Set 2
Fichas del conjunto (15)
- 1Laser cooling (temperature measurement)Temperature of a lot of cold atoms
expansion (from trap or molasses)
image after time Δt
measurement of position spread Δx
T∝(Δx/Δt)^2 - 2Magnetic trapclass: E=-μ_m B cosϑ
quant: E=gμ_B m_F B
for an atom in state mF a trap is formed if E(mF) has a local minimum
gmF>0 local minimum low field seekers
gmF<0 local maximum high field seekers
the trap centre is always where B has local minimum - 3Majorana losses- due to non-adiabatic transitions
- spin flips for small or vanishing B-Fields
- if magnetic field is finite like in a Joffe-Pritchard trap, Majorana a losses are supressed - 4Optical lattices- 1D: the electrical field of a one-dim. standing wave formed by two counter prop. lasers
- to avoid interference:
polarisations orthogonal
frequency detuning
- one can have Bragg scattering on lattices - 5Trap geometries- simplest optical trap: Gaussian beam (red detuned δ<0) potential can be approximated as harmonic
- weak confinement along laser beam axis
- crossed dipole trap: overlap of two laser beams
- Advantage: strong confinement in all directions
- but: small volume - 6Magnetooptical trap(MOT)combination of optical (laserfield) trap and magnetic field
F=0 →F‘=1 transition
F=-β ̃v-kz (damped harmonic oscillator)
0-10 ms overdamped
capture velocity ≈50 m/s - 7Optical trapstrapping due to optical potential
U_opt (r ⃗ )≈(ħδ_0 γ_10^2)/8δ
δ>0 atoms are repelled
δ<0 atoms are attracted
(due to radiative force) - 8MOT: Temperature vs. density regimetemperature limited:
overdamped oscillator
1/2 k_B T=1/2 mv_rms^2=1/2 kz_rms^2
z_rms=√((k_B T)/κ)
density limited
if the atom number is increased atoms start to interact →repulsion
max. ≈10^11 atoms/cm³→ Volume increases with number of atoms - 9Evaporative coolingo fast particles escape
o „rest“ thermalizes through collisions
o Abkühlung
o E/N↓→T↓
- theoretical:
o infinitly slow evaporation
o But: in experiment are losses - 10Evaporation in a magnetic trap- transfer all energetic atoms to a magnetic sublevel, that is not trapped
- RF Knife
- inharmonic trap: density may increase while atom number shrinks
- run away evaporation: nσv (n=NT-3/2→∞T1/2)
- RF induced: manipulate potential such, that fast atoms evaporate - 11Feshbach resonances- tune the scattering length by applying an external field (magnetic)
- 12What is a BEC?quantum mechanical phase transition from thermal gas at T≠0
nλ_dB^3=2.612;
caused by quantum statistics not interactions
|p ⃗=0⟩ has macroscopic occipation
can be described as matter wave
Atomic oven → Zeeman slower → MOT →optical molasses → magnetic trap → evaporative cooling → BEC
n(ε_p )=1/(e^β(ε_p-μ) -1) ;μ≤min(εp) for n≥0 - 13Critical temperature macroscopically occupationbelow Tc the ground state is occupied with N0 atoms in the ground state
T_c=(2πħ^2)/(mk_B (2.612)^(2/3) ) p^(2/3)
N_0=N(1-(T/T_c )^(3/2) - 14BEC in a harmonic trap- Δx ist Breite des harmonischen Potentials
- 15Gross-Pitiaevski-Equationiħ ∂/∂t Φ(r ⃗,t)=(-(ħ^2 ∇^2)/2m+V_ext (r ⃗ )+g|Φ(r ⃗ )|^2
„Mean field“: eff.Potential =trap potential +U meanfield Φ(r ⃗,t)=√(ρ(r ⃗ ) ) e^iΦ(r ⃗,t) valid for ρa³ <<1 (a is scattering length)
Interaction energy of BEC much larger than kinetic
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- El usuario ha eliminado su información de asignaturas Fichas sobre Quantum optics Set 2, creado por Usuario eliminado el 24/09/2017.
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- Usuario eliminado · sep 2017
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- Creado por Tom Schobert · 21 sep 2017
- Copiado por Tom Schobert · 24 sep 2017
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