Degenerate Quantum Gases on a Chip Dept. Of Physics, University of Toronto Prof: Joseph Thywissen...
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Transcript of Degenerate Quantum Gases on a Chip Dept. Of Physics, University of Toronto Prof: Joseph Thywissen...
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