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Experiments with Trapped Potassium Atoms Robert Brecha University of Dayton Outline Basics of cooling and trapping atoms Fermionic and bosonic atoms - why do we use potassium? Parametric excitation and cooling Sympathetic cooling and BEC Co-workers and Affiliations Giovanni Modugno – LENS Gabriele Ferrari – LENS Giacomo Roati – Università di Trento Nicola Poli – Università di Firenze Massimo Inguscio – LENS and Università di Firenze In the Lab at LENS Motivations for Trapping Atoms Fundamental atomic physics measurements Condensed matter physics with controllable interactions (“soft” condensed matter) Tabletop astrophysics – collapsing stars, black holes, white dwarfs Quantum computing Atomic Cooling Laser photons Physics2000 Demo Cooling Force Random emission directions momentum kicks retarding force Force = (momentum change per absorbed photon) (scattering rate of photons) (Depends on intensity, detuning, relative speed) Force is not position-dependent no permanent trapping Laser Cooling and Trapping Magnetic Field Coils (anti-Helmholtz) Circularly polarized laser beams Far Off-Resonance Trap (FORT) One disadvantage of MOT – presence of magnetic fields; only certain internal states trappable Solution – Use all-optical method Laser electric field induces an atomic dipole E Interaction potential of dipole and field: U dipole 1 1 E Re I 2 2 0c FORT Trapping Potential Standing-wave in z-direction, Gaussian radially U r , z U 0 cos 2 kz exp 2r 2 / w2 Oscillation frequencies: A 2 2U 0 / M t2 R 4U 0 / Mw02 1 2 2 U m x 2 450 mK Fermions vs. Bosons Spin-1/2 Integer spin State-occupation limited Gregarious f 1 e m 1 Do not collide* f 1 e m Collide 1 Fermions vs. Bosons Ensher, et al., PRL 77, 4984 (1996) Fermionic occupation probabilities Bosonic ground-state occupation fraction Potassium Three isotopes: 39K (93.26%) boson 40K (0.01%) fermion 41K (6.73%) boson Potassium Energy Levels FORT Experimental Schematic Absorption beam MOT: 5 × 107 atoms T ~ 60mK FORT: 5 × 105 atoms T = 80 mK Absorption Image from FORT N = 5 × 105 atoms n = 5 × 1011 cm-3 T = 50 – 80 mK dT/dt = 40 mK/s r = 2 × 1 kHz a = 2 × 600 kHz U0 = 300 - 600 mK 450 mK Elastic Collisions t = 10(3) ms s = p/2tnu 41011cm2 at = 169(9)a0 Inelastic Collisions Frequency Measurements “Parametric Excitation” Driving an oscillator by modulating the spring constant leads to resonances for frequencies 20/n. 0 Here we modulate the dipole-trap laser by a few percent Parametric Resonances 1.8a 2 a Parametric Heating ... and Cooling 2 Tex = 10 ms = 12 % a 1.8a Tex = 2 ms = 12 % Trap Anharmonicity Cooling by Parametric Excitation Selective excitation of high-lying levels forced evaporation Occurs on a fast time-scale Independent of internal atomic structure works on external degrees of freedom Somewhat limited in effectiveness The New Experiment Transfer Tube - MOT1 to MOT2 Sympathetic Cooling Use “bath” of Rb to cool a sample of K atoms Goal 1 – Achieve Fermi degeneracy for 40K atoms Goal 2 – (After #1 did not seem to work) Achieve Bose-Einstein condensation for 41K Some Open Questions Do K and Rb atoms collide? (What is the elastic collisional cross-section?) Do K and K atoms collide? Is the scattering length positive (stable BEC) or negative (unstable BEC at best) Some Cold-Collision Physics Scattered particle wavefunction is written as a sum of “partial waves” with l quantum numbers. For l > 0, there is repulsive barrier in the corresponding potential that inhibits collisions at low temperatures. For identical particles, fermions have only l-odd partial waves, bosons have only l-even waves. Identical fermions do not collide at low temperatures. Rubidium Energy Levels 87Rb F´= 3 267 MHz F´= 2 F´= 1 F´= 0 157 MHz 72 MHz F=2 6835 MHz F=1 780 nm (4×108 MHz) Rubidium Ground-State “Low-field-seeking states” Apply a B-field: mF = 2 F=2 6835 MHz mF = -1 F=1 BEC Procedure Trap 87Rb, then 41K in MOT1 Transfer first Rb, then K into MOT2 Now have 107 K atoms at 300mK and 5×108 Rb atoms at 100mK Load these into the magnetic trap after preparing in doubly-polarized spin state |F=2,mF=2> Selective evaporative cooling with microwave knife Check temperature (density) at various stages (a destructive process) QUIC Trap Figure by Tilman Esslinger, ETH Zurich QUIC Trap Transfer Quadrupole field Magnetic trap field Figure by Tilman Esslinger, ETH Zurich Microwave “Knife” (Link to JILA group Rb BEC) Temperature (mK) Temperature and Number of Atoms 100 10 1 Rb 4 Atom Number (10 ) 10000 1000 100 K 10 1 0.1 1 10 Microwave Treshold (MHz) Potassium BEC Transition A B C (Link to JILA group Rb BEC) Optical Density Cross-section Condensate Mixed Thermal Absorption Images 87 Rb 41 K 40mK 1mK 2mK 0mK Rb density remains K density increases constant 100x Elastic Collisional Measurements Return to parametric heating (of Rb) and watch the subsequent temperature increase of K. tequil 3n v s 1 Determined from absorption images Elastic Collisional Measurements Potassium temperature after parametrically heating rubidium Temperature dependence of elastic collision rate (Is a >0 or is a < 0?) Ferrari, et al., submitted to PRL Double Bose Condensate Future Directions