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Lecture II Non dissipative traps Evaporative cooling Bose-Einstein condensation

Lecture II Non dissipative traps Evaporative cooling Bose-Einstein condensation. Phase space density. Magneto-optical trap. From room temperature to 100 m K. Molasses. 100 m K 10 m K. n l 3 = 10 -7. Intrisically limited because of the dissipative character of the MOT.

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Lecture II Non dissipative traps Evaporative cooling Bose-Einstein condensation

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  1. Lecture IINon dissipative traps Evaporative cooling Bose-Einstein condensation

  2. Phase space density Magneto-optical trap From room temperature to 100 mK Molasses 100 mK 10 mK nl3 = 10-7 Intrisically limited because of the dissipative character of the MOT.

  3. Magnetic trapping (1) No light, no heating due to absorption Relies on magnetic moment interaction The force results from the inhomogenity of the magnetic field For an atom with an nuclear spin in the ground state

  4. Magnetic trapping (2) F=1,m=1 F=1,m=0 z F=1,m=-1 Maxwell's equations: No max of |B| in the vaccum. Local minimum of |B| V=|m||B| Photo: Bell Labs + spin polarisation Non dissipative trap !!! Atoms cannot be magnetically trapped in the lower energy state. Two-body inelastic collisions Three-body inelastic collisions (dimer Rb2). Ultra High Vacuum chamber, backgound gas collisions.

  5. Magnetic trap: classical picture versus the quantum one Classical picture Classically, the angle θ between the magnetic moment and the magnetic field is constant due to the rapid precession ofµaround the magnetic field axis. mB F=2 mB/2 Quantum picture 0 -mB/2 mcan take only quantized values -mB V=|m||B| F=1 mB/2 0 -mB/2 Spin flips Majorana losses

  6. Magnetic trap with coils What kind of gradient do we need ? Magneto-optical trap: 1 mm, T=50mK b' = 10 Gauss/cm mb' r = kB T Atoms are further compressed b' ~ 200 Gauss/cm Two kind of solutions I ~ 1000 A, d ~ cm Gradient scales as I/d2 I ~ 0.1 A, d ~ 100 mm Microchip

  7. Magnetic trap with coils B0-2b'x b'y b'z B One coil: y x z Two coils (antiHelmoltz): y x -4b'x 2b'y 2b'z O z B B2=4b'2 (4x2+y2+z2)

  8. 0 B0cos(wt) B0cos(wt) B Time averaged Orbital Potential (TOP) z Quadupolar configuration x y -4b'x 2b'y 2b'z + B O Rotating field = wtrap< < w < < wLarmor 100 Hz 5kHz 1 MHz

  9. Ioffe pritchard trap depth: 1 mK constant bias field curvature gradient

  10. Microchip traps Ioffe Pritchard traps of various aspect ratios: Y-shaped splitting and recombining regions. interferometry device

  11. Atomic conveyer belt

  12. Magnetic guide with wires

  13. Magnetic guide with 4 tubes y 2D Quadrupolar configuration x b'x -b'y B Add a longitudinal bias field to avoid spin flips

  14. Evaporation F=1,m=1 F=1,m=0 z F=1,m=-1 radio frequency wave Relies on the redistribution of energy through elastic collisions

  15. Surface Evaporation works with silicon surface J. Low Temp. Phys. 133, 229 (2003)

  16. Interactions between cold atoms One-body scattering problem Two-body problem: Scattering state (eigenstate of H with a positive energy) scattering amplitude At low energy, and if W decreases faster than r-3 at infinity: scattering length Two interaction potentials with the same scattering length lead to the same properties at sufficiently low temperature Exceptions: dipole-dipole interactions (magnetic or electric) 1/r interactions induced by laser (Kurizki et al)

  17. Interactions between cold atoms F varies rapidly with all parameters: F/p = number of bound states 75% 25% empirical law scattering length -0.04 -0.02 0.02 0.04 0 W(r) r Characteristic length from 0.1 to 10 nm a = 5 nm for 87Rb

  18. Evaporation: a simple model (1) 1) Infinite depth harmonic confinement 2) Finite depth 3) Infinite depth

  19. Evaporation: a simple model (2) and with N: 109 106 T: 100 mK 100 nK We deduce a power law dependence with The phase space density changes according to The real form of the potential only changes the exponent Typical numbers nl3 x 106

  20. Signature of condensation: time of flight Laser atoms Camera CCD 100 mm * 5 mm 3 106 atoms in an anisotropic magnetic trap 0,5 to 1 mK Time of flight T > Tc T < Tc Boltzmann gas condensate anisotropic expansion isotropic expansion

  21. Bose Einstein condensation 2001 Physcis Nobel Prize E. Cornell, W. Ketterle and C. Wieman "for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates" Review of Modern Physics, 74, 875 (2002); ibid 74, 1131 (2002)

  22. Dipole trap gallery

  23. Single atom in a dipole trap possible application in quantum computing ?

  24. Is it possible to realize a continuous source of degenerate atoms ? 10 elastic collisions per atom First signal of evaporation and gain in phase space density PRL 93, 093003 (2004)

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