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Physics and Astronomy Dept. Kevin Strecker, Andrew Truscott, Guthrie Partridge, and Randy Hulet Observation of Fermi Pressure in Trapped Atoms: The Atomic White Dwarf Star
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Quantum Gases Quantum regime n7 3 1 Identical particles! Gas phase n 10 12 cm -3 Low temperature T 100 nK 1 m
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Exchange Symmetry Bosons Symmetry with respect to particle exchange 12 (r 1,r 2 ) + 12 (r 2,r 1 ) S. Bose, 1924 A. Einstein, 1924-5 Multiple state occupation
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Vortices Solitons Atom laser Atom wave guides Nonlinear atom optics Superfluidty Andrews et al., Science 275, 637, (1997) Atoms Occupy Lowest Energy State of Trap 7 Li Bose-Einstein Condensation
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Bose-Einstein Condensation in an Almost Ideal Gas T c = (N/1.2) 1/3
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Exchange Symmetry Fermions Symmetry with respect to particle exchange 12 (r 1,r 2 ) - 12 (r 2,r 1 ) Obey Pauli Exclusion Principle Bosons 12 (r 1,r 2 ) + 12 (r 2,r 1 ) S. Bose, 1924 A. Einstein, 1924-5 Multiple state occupation E. Fermi, Feb. 1926 P.A.M. Dirac, Aug. 1926 EFEF
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E. Fermi, Rendiconti Accademia Nazionale dei Lincei (2/2/26)
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P.A.M. Dirac, Proc. Roy. Soc. (8/26/26)
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and it comes in 2 nuclear spin states!
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Lithium: Non-identical Twins 7 Li 3 e’s, 3 p’s, 4 n’s = 10 spin-½ particles Boson 94% abundance 6 Li 3 e’s, 3 p’s, 3 n’s = 9 spin-½ particles Fermion 6% abundance
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Fermions - The Next Frontier Quantum Degenerate Fermi Gases 40 K: Demarco and Jin, Science 285, 1703 (1999) 6 Li: Truscott et al. (Rice), Science 291, 2570 (2001) 6 Li: Schreck et al. (Paris), Phys. Rev. Lett. 87, 080403 (2001). Current status: T 0.25 T F
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Methods Laser cooling T 100 K Atom trapping n 10 12 cm -3 N 10 9 10 6 Evaporative cooling T 100 K 100 nK -wave spin-flips Optical imaging
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Laser Cooling Momentum is imparted to an atom when it scatters light from a laser Can slow or stop atoms in a beam Trapped and cooled to K temperatures
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Evaporative Cooling Spin flip ‘hot’ atoms at edge of trap Collisions re-thermalize distribution colder denser E f(E) RF Remove tail Re-thermalize
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Sympathetic Cooling of 6 Li Pauli principle forbids s-wave interactions between identical fermions Use both 6 Li and 7 Li 6 Li 7 Li
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Dual Source Apparatus 7 Li/ 6 Li Zeeman Slower Cloverleaf Trap Require vacuum pressure ~ 10 -11 Torr Oven
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Imaging CCD Mirror Compound lens -scope Zoom lens r A=e -
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7 Li (Bosons) T = 240 nk T = 510 nk T = 810 nk 6 Li (Fermions) T/T F = 1.0 T/T F = 0.56 T/T F = 0.25 Truscott et al., Science 291, 2570 (2001) Sympathetic Cooling
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Axial Profiles Truscott et al., Science 291, 2570 (2001)
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Fermi Pressure in Trapped Atoms Truscott et al., Science 291, 2570 (2001)
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Fermi Pressure Fermi pressure is result of Pauli Exclusion Principle Stabilizes white dwarf and neutron stars against gravitational collapse E F ~ n 1/3 (non-relativistic) E grav ~ n 1/3 Balance: Chandrasekar limit for white dwarf stars (1931)
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Possible Experiments Boson/Fermion mixture –Phase separation –Superfluid probe Degenerate Fermi gas –BCS phase transition to a gaseous superfluid 6 Li has an enormous attractive interaction
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BCS Transition in 6 Li? Cooper pairing –Superconductivity –Superfluidity 3 He –Dilute gas? – tunable interactions For s-wave pairing, T c T F exp(-1/k F | a |) For 2 H, a = -4 T c = 1 fK @ 10 19 cm -3 –Leggett (1980) For 6 Li, a = -1100 T c = 30 nK @ 10 12 cm -3 –Stoof (1996) Induced interactions (fermi/fermi or bose/fermi) mod. T c –Heiselberg et al. (2000)
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Cooper Pairing in 6 Li S-wave pairing symmetry forbidden between identical atoms Create incoherent mixture of two states Stoof et al., PRL 76, 10 (1996)
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Detecting Cooper Pairs Light scattering sensitive to –normal component, i.e. –pair correlation fcn. + –but r F ~ (E F / ½m 2 ) ½ ~ 50 m normal component r p ~ 1 / k F ~ 0.2 m pair correlation length Experiment: Zhang, Sackett, and Hulet, PRA 60, 504 (1999) Also, Ruostekoski, PRA 60, R1775 (1999) pairs normal << E F no significant change in density
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Detecting Superfluidity Superfluids in anisotropic traps exhibit a “scissors” mode oscillation when displaced – Guery-Odelin and Stringari (theory) – Marago et al. (expt with BEC)
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