Alkali atoms. ⢠Electronic structure: only one valence electron in a orbital s ... Minimum of the potential depends on the spin polarization. ⢠If the minimum is zero: ...
Which atoms ? • Mostly Alkali atoms (Li, Na, K, Rb, Cs), heavy but: -> suitable for efficient laser cooling. -> interactions large enough for evaporative cooling. • Neutral atoms: no direct coupling of the charge to the electromagnetic field. • Neutral -> no electrostatic repulsion. • Coupling via magnetic and electric dipoles to the gradient of either electric or magnetic field.
Lectures on cold atoms
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Alkali atoms • Electronic structure: only one valence electron in a orbital s -> no orbital moment L=0, only spin S=1/2 -> J=1/2 • Hyperfine coupling to the nuclear spin I -> lifting of the ground state degeneracy. Good quantum number F=I+J.
Lectures on cold atoms
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Zeeman effect in Alkali atoms • Lifts the degeneracy between hyperfine states: • For an atom with I=3/2, S=J=1/2, at zero field: F=I -J=1 (2x1+1= 3 states) F=I+J=2 (2x2+1= 5 states)
They minimize Zeeman energy at low magnetic field
Lectures on cold atoms
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Magnetic trapping • One can only have a minimum of |B| -> low–field seekers. • Minimum of the potential depends on the spin polarization F=1,m=1 F=1,m=0
z
F=1,m=-1
• If the minimum is zero: atoms can be lost via non-adiabatic transitions to high-field seekers states. Solutions: Time averaged Orbital Potential (TOP trap), Ioffe-Pritchard trap. • Close to the minimum, the field is quadratic with distance: -> harmonic potential trap Often: axial symmetry Lectures on cold atoms
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Interaction between light and matter • Electronic dipole: • Polarizability of the atom:
• Classical oscillator picture:
Lectures on cold atoms
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Two-level model • Interaction Hamiltonian: • Detuning parameter: • Polarizability:
Life-time of the excited state Lectures on cold atoms
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Resulting forces • Dipolar force (virtual transitions): sign is given by
Field intensity
• Radiative force (real transitions):
with absorbing rate
Lectures on cold atoms
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Energy scales and transition in Alkali atoms
Lectures on cold atoms
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Cooling techniques
Lectures on cold atoms
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Doppler cooling • Take two lasers with the same frequency in the lab frame chosen to be red-detuned to the atom resonance but in opposite directions. • If an atom goes towards the laser beam, the laser frequency in the atom frame is increased by a factor 1+v/c but if it goes along in the direction, it feels 1-v/c. • Because the laser is red detuned, the atom absorbs more backward scattering photons than forward scattering ones. • This mechanism enables to reach roughly 100µK
Lectures on cold atoms
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Magneto-Optic Trap (MOT)
frequency
• The variation of the static magnetic field with space makes the absorption rate depends on space. The farther from the center the more it absorbs. • Trap and cools the atoms. • Magnetic field can be turned off to keep only the dipolar potential at the end.
Lectures on cold atoms
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Sysiphus cooling and recoil energy
~0.1µK Or energy of an atom confined in a lattice potential Lectures on cold atoms
energy
polarization
• Uses both dispersive and dissipative effects (large red detuned). Uses the hyperfine substates and the fact that the dipolar potential seen by the atom depends on its spin. • If an atom climbs to a maxima of the dipolar potential and undergoes a cycle of absorption and emission, it falls into a valley because its spin changed during the transitions. It thus always has to climb the energy steep, like Sysiphus. • Recoil energy: kinetic energy after absorption of one photon
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Evaporative cooling: down to nK • Relies on the redistribution of energy through elastic collisions and the flip of the spin of high energy atoms with a rf wave.
F=1,m=1 F=1,m=0
z
F=1,m=-1 radio frequency wave Lectures on cold atoms
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Time of flight imaging • Snapshot after releasing the trap, destructive measure. Laser
atoms
Camera CCD
Density profile n(r): 100 µm * 5 µm T < Tc
BEC
Thermal gas
T > Tc Density profile n(p): after a fixed time t of ballistic expansion r=pxt
isotropic
Lectures on cold atoms
anisotropic Page 15
Optical trapping • Create a maximum in space of the intensity of the Laser beam and keep the laser red-detuned away from the resonance. • Example: gaussian laser beam
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