Degenerate Quantum Gases on a Chip

Dept. Of Physics, University of Toronto

Prof: Joseph Thywissen

Post Docs: Seth Aubin Stefan Myrskog

Ph.D. Students: Marcius Extavour

M.Sc. Students: Lindsay LeBlanc

Undergrads: Barbara CieslakIan Leroux

ResearchTechnologist: Alan Stummer

Outline• Quantum Gases – Bosons (87Rb) + Fermions (40K)

• Laser Cooling• Magnetic Traps• Chip Traps• Evaporative/Sympathetic Cooling• Outlook

science!BEC /DFG

thermalatoms

magnetictraps

evap.cooling

MOT

psd10-13 110-6 105

Bose-Einstein Condensation

Phase transition occurs in a gas of particles, when the deBroglie wavelength becomes comparable to the inter-particle separation.

2

00 UHt

i

612.23 dBnd

Phase-Transition

Evolution governed by the GP equation (NLSE)

T=0

Degenerate Fermi Gas

Unlike bosons, identical fermions are not allowed to occupy the same state.

EF

No phase transition, so quantum behaviour gradually emerges

Data from Randy Hulet

T=0

Laser Cooling Atoms

v

Doppler shifted to lower frequency

Doppler shifted to higher frequencyCloser to resonance

Slightly below resonance

Doppler Cooling (Optical Molasses)

F(N)

V(m/s)

a~104 m/s2

DBTkTemperature Limit TD~140 μK

Magneto-Optical Trapping

m=1

m=0

m=-1

z

E

z

B

~10 G/cm

Spatial trapping accomplished byadding a magnetic gradient

I

Add Anti-Helmholtz coils zzByyB

xxB

B ˆ'ˆ2

'ˆ

2'

The System

Spectroscopy and Laser Stabilization

X 4 (2 for Rb, 2 for K)

Amplification

New Focus Vortex lasersStabilized to ~ 300 kHz

~ 7 mW output

780 nm 767 nm

Rb1

Rb2

K1

K2

Optical Fiber

TOPTICAAmplifier ~900 mW

D

109 atoms30 μK600 μm radius

DCWP

Imaging

lneII 0

Data collection performed in 2 ways

Fluorescence Imaging:

Absorption Imaging

CCDCamera

CCDCamera

Beer’s Law

w/o atoms with atoms

Divided image

MicroPix10 bitFirewire

Magnetic Trapping of Neutral Atoms

For an atom in a state having total angular momentum F

U Bcos (FgFB )Bcos where

B e

2me

.

For an atom in the arbitrary hyperfine state

F,mF

U gF mFBB .

cos mF / F so that

B

U

B

Interaction between external magnetic field and atomic magnetic moment:

Magnetic Trapping of Neutral Atoms

Since

B, B 0 , atoms in states having

are magnetically trappable in magnetic field minima.

gF mF 0

min. B min. U

Q: Given that a central B(r) results in a confining potential U(r), how can such a magnetic field geometry be generated?

U gF mFBB

Anti-Helmholtz Coils

quadrupole (linear) magnetic trap

Optical Pumping

Move atomic population into a single internal magnetic sublevel for improved magnetic trapping efficacy.

U gF mFBB

F = 9/2

mF = 9/2

mF = 7/2

mF = -9/2

…U

r

mF = 9/2

mF = 7/2

mF = 5/2

Microtraps for Neutral Atoms

-traps Coils

B’ 104 - 105 G/cm with I=2A

Need I ~ 105 A for comparable B’

B’’ 100 G/cm2

with I=2A

Need I ~ 105 A for comparable B’’

UHV P ~ 10-9 torr OK

P ~ 10-11 torr

Atom # 104 - 106

(“small” traps)

106 -108 (“large” traps)

+

+

+

-

Infinite Wire and External BiasInfinite current-carrying wire, into page at (x=0,z=0)

B(r) 0 I2r

I

I = 2 A Bbias = 150 G z0 = 27 m

atoms confined in 2D here

3D Confinement

based on Biot-Savart-type calculations with finite wire segments

quadrupole “U trap” harmonic “U trap”

Orsay Chip

• gold conductors (yellow) on SiO2-coated Si wafer• wire widths from 20 to 460 m• wire heights of 7 m

16 mm

28 mm

Magnetically Trapped Atoms

Macro. magnetic trap

g

N ~ 106, T ~ 100 K

microchip trap

atoms

Stack

• physical support of atom chip in UHV chamber (macor clamps)

• electrical connections

• heat-sinking

• atom-dispensers

Evaporative Cooling

Remove most energetic (hottest) atoms

Wait for atoms to rethermalize among

themselves

Wait time is given by the elastic collision rate kelastic = n v

Macro-trap: low initial density, evaporation time ~ 10-30 s.

Micro-trap: high initial density, evaporation time ~ 1-2 s.

1. Evaporate atoms remaining atoms get colder.

Natoms decreases.

2. Atoms are less energetic Atoms stay closer to trap center.

Volume decreases.

3. If n=Natoms/Volume increases then atoms undergo runaway evaporation.

Runaway Evaporation

Phase space density: 3

3

pVolume

hNatoms

Typically, 999 out of 1000 atoms are evaporated for 1 BEC atom.

RF evaporation

RF frequency determines energy at which spin flip occurs.

We use a DDS to generate RF at 10 kHz – 200 MHz.

Chip wire serves as RF B-field source.

In a harmonic trap:

Pulse Timing ControlSequencer

Direct Digitial Synthesizer (DDS)

chip

The problem with Fermions

In traps with very low temperatures, 0 prl

If , then two atoms must scatter as an s-wave:0l

r

eaeerrr

rik

sikzikz

waves

2)( 21

s-wave is symmetric under exchange of particles: rr

as T 0:

Identical Bosons undergo s-wave scattering.

Identical Fermions cannot scatters as s-waves.

identical Fermions do not scatter (i.e. interact).

Sympathetic Cooling

Problem:

Cold identical fermions do not interact (cannot rethermalize)

No evaporative cooling

Solution: add non-identical particles

s-wave scattering permitted

We cool our fermionic 40K atoms sympathetically with an 87Rb BEC.

2 possibilities:

1. Evaporate 40K and 87Rb mixture simultaneously.

2. Evaporate 87Rb only, while 40K cools through thermal contact.

What does an Ultra-Cold Fermi gas look like?

BEC DFG

Hulet group, Rice University: Science 291, 2570 (2001).

Condensed Matter Physics Applications

1. BCS Cooper pairing in an ultra-cold fermi gas.

no clean signature yet.

2. Quantum simulation of the Fermi-Hubbard model.

not solved numerically or analytically.

proposed model for high-Tc

superconductors.

3. Low dimensional system.

1-D Fermi gas: Luttinger-Tomonaga liquid

1-D Bose gas: Tonks gas.

Optical lattice for Fermi-Hubbard model.

Interferometry Applications of Degenerate Fermions

1. Atomic Clocks (temporal interferometer -- exp(it) )

DFG significantly reduces collision shift (clock shift).

2. Spatial interferometers – exp(ikz): k=2mv/h780 nm photon: k=8106 m-1, 87Rb at 1 m/s: k=1.4 109 m-1

BEC

Good: Heisenberg limited momentum spread.

Bad: large density dependent atom-atom interactions.

DFG

Good: Vanishing atom-atom interactions.

Less good: small momentum spread. FmEp 2~

Other Experiments

1. Atomic lifetime increase

2. Fermion Evaporation

After excitation, the states into which the atom can decay/recoil are limited due to Pauli blocking.

Lifetime increases.

Linewidth narrows.

RF cutn n

Outlook

Current Status:

40K and 87Rb laser frequency and amplification set-up.

39K MOT, 87Rb MOT.

87Rb quadrupole magnetic trap.

87Rb transported to chip.

87Rb loaded into chip U-trap.

Next Steps:

load chip Z-trap, RF evaporation, BEC.

40K MOT, DFG.

Group Members

Marcius Extavour Lindsay LeBlanc

Ian LerouxBarbara Cieslak

Joseph Thywissen

Seth Aubin

Stefan Myrskog

Alan Stummer