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 Interaction potential of dipole and field:

FORT Trapping Potential Standing-wave in z-direction, Gaussian radially Oscillation frequencies: 450  K

Fermions vs. Bosons Spin-1/2Integer spin State-occupation limitedGregarious Do not collide* Collide

Fermions vs. Bosons Bosonic ground-state occupation fraction Fermionic occupation probabilities Ensher, et al., PRL 77, 4984 (1996)

Potassium Three isotopes: 39 K (93.26%)  boson 40 K (0.01%)  fermion 41 K (6.73%)  boson

Potassium Energy Levels

FORT Experimental Schematic MOT: 5 × 10 7 atoms T ~ 60  K FORT: 5 × 10 5 atoms T = 80  K Absorption beam

Absorption Image from FORT N =  ×    atoms n = 5 ×    cm -3 T = 50 – 80  K dT/dt = 40  K/s  r = 2  × 1 kHz  a = 2  × 600 kHz U 0 =  K 450  K

Elastic Collisions  =  p /2  n    cm  a t = 169(9)a 0  = 10(3) ms

Inelastic Collisions

Frequency Measurements “Parametric Excitation” Driving an oscillator by modulating the spring constant leads to resonances for frequencies 2  0 /n. 00 Here we modulate the dipole-trap laser by a few percent

Parametric Resonances 2a2a 1.8  a

Parametric Heating... and Cooling 2a2a 1.8  a T ex = 10 ms  = 12 % T ex = 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 40 K atoms Goal 2 – (After #1 did not seem to work) Achieve Bose-Einstein condensation for 41 K

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 87 Rb F´= 3 F´= 2 F´= 1 F´= 0 F = 1 F = MHz 267 MHz 157 MHz 72 MHz 780 nm (4×10 8 MHz)

Rubidium Ground-State Apply a B-field: m F = 2 F = 1 F = MHz m F = -1 “Low-field-seeking states”

BEC Procedure Trap 87 Rb, then 41 K in MOT1 Transfer first Rb, then K into MOT2 Now have 10 7 K atoms at 300  K and 5×10 8 Rb atoms at 100  K Load these into the magnetic trap after preparing in doubly-polarized spin state |F=2,m F =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 Figure by Tilman Esslinger, ETH Zurich Quadrupole field Magnetic trap field

Microwave “Knife” (Link to JILA group Rb BEC)

Rb K Temperature and Number of Atoms

Potassium BEC Transition (Link to JILA group Rb BEC) A BC

Optical Density Cross-section Thermal Mixed Condensate

Absorption Images Rb density remains constant K density increases 100x

Elastic Collisional Measurements Return to parametric heating (of Rb) and watch the subsequent temperature increase of K. Determined from absorption images

Elastic Collisional Measurements Ferrari, et al., submitted to PRL Temperature dependence of elastic collision rate (Is a >0 or is a < 0?) Potassium temperature after parametrically heating rubidium

Double Bose Condensate

Future Directions