1. Ultracold Atoms, Mixtures, and Molecules
Subhadeep Gupta
UW Physics 528, 25 Feb 2011

2. Einstein condensate (BEC)
Ultracold Atoms
High sensitivity (large signal to noise, long interrogation times in a well
known atomic system)
Precision measurements (spectroscopy, fund sym, clocks)
Sensing (accelerations, gravity gradients)
Many-body aspects
Quantum Fluids
Condensed Matter Physics
Nuclear Physics
Quantum Engineering (Potentials and Interactions)
Quantum Information Science
Quantum Simulation
Ultracold Molecules (through mixtures)
Formation of a Bose-
Einstein condensate (BEC)
Verifying known Hamiltonians, generating new Hamiltionians, quantum simulations, new entities 2

3. Ultracold Atoms and Molecules at UW
A dual-species experiment (Li-Yb) for
making and studying ultracold polar molecules
and for probing strongly interacting Fermi gases
Development of precision BEC interferometry (Yb)
for fine structure constant a and test of QED

4. Dilute metastable gases n ~ 1014/cm3
Quantum Degeneracy in a gas of atoms
1 atom per quantum state
N atoms
V volume
T temperature
(Dx)3 ~ V
(Dp)3 ~ (m kB T)3/2
(available position space) (available momentum space)
Number of atoms = h3 n
(m kB T)3/2 h3
~ 1
Quantum Phase
Space Density
(n=N/V)
Density n=N/V. Thinner than air. Make equations explicit.
Metastable -> gas for a while -> if within this time you can cool it down to a microK, you’re set…
Air n ~ 1019/cm3, Tc ~ 1mK
Stuff n ~ 1022/cm3, Tc ~ 0.1K
Dilute metastable gases n ~ 1014/cm3
Tc ~ 1mK !! Ultracold !!
Everything (except He) is solid
and ~ non-interacting

5. ABSOLUTE TEMPERATURE (log Kelvin scale)f a c e o f s u n 3 1
Laser cooling
Evaporative cooling r o o m t e m p . l i q u i d
Nitrogen
BCS superconductors, 4He superfluid, CMB
fractional quantum hall effect J o u l e - T h o m p s o n e x p a n s i o n 1 3 H e - 4 H e d i l u t i o n s u p e r f l u i d 3 H e - 3 1 d
p-wave threshold i l u t e B a d i a b a t i c d e m a g n e t i z a t i o n
Introduce s-wave scattering length with p-wave threshold. The scattering length can be manipulated using internal energy tricks. Introduce ease of manipulation with energy scales. Gauss, Bohr magneton, optical trapping. Sufficient trap depth obtained with modest magnetic fields and detuned light. Atomic interactions can be tuned up as well. Mention at this point that the range of control offered by atomic physics techniques – trapping, dimensionality, temperature, spin composition etc. 1 - 6 d
Degenerate Gas i l u t e B E C
Depth of atom traps
atomic interactions 1 - 9
Zero point energy

6. Laser Cooling s- s- s+ s- s+ s+ => COOLING ! P Sz I s-
=> COOLING ! S P s- s+ x s- s+ s+ y I
Right -> different momentum states.
Magneto-Optical Trap (MOT)
“Workhorse” of laser cooling
Atom Source ~ 600 K; UHV environment
(Need a 2 level system)

7. Evaporative Cooling in a Conservative Trap
pre collision
post collision
Optical Dipole Trap
wL << wres
Depth ~ I/D; Heating Rate ~ I/D2
Usually DC magnetic, now optical quite common, AC magnetic, RF and microwave dressing, etc. mK

8. Evaporative Cooling in a Conservative Trap
Optical Dipole Trap
wL << wres
Depth ~ I/D; Heating Rate ~ I/D2
pre collision
post collision mK
V  0

9. Imaging the Atoms (Formation of a Rb BEC, UC Berkeley 2005)
Imaging atoms
Imaging the Atoms
Stolen from post-doc days
Procedure takes about 1 minute. Formation of a dense dark core at sufficiently low (few hundred nK) temp. mention
pulsed experiment. As temperature is lowered etc..
This sort of imaging is destructive - all the work descrived here
(Formation of a Rb BEC, UC Berkeley 2005)

10. Landmark achievements in ultracold atomic physics
Bose-Einstein condensation (JILA, MIT, Rice….)
Macroscopic coherence (Ketterle)
Superfluidity / observation and study of a vortex lattice (Dalibard, Ketterle, Cornell)
Coherent and Superfluid! 2001 Nobel Prize
Superfluid to Mott-insulator quantum phase transition (Hansch)

11. Landmark achievements in ultracold atomic physics
Degenerate Fermi gas
Molecular Bose-Einstein condensate
Mention myself with respect to strongly interacting fermions.
Recently, - other branches of physics: Efimov states, Kosterliz-Thouless transition – note that Efimov and Thouless are both at Washington.
(Jin, Hulet, Thomas, Ketterle, Grimm)
Superfluidity of Fermi pairs

12. Ultracold Polar Molecules
Realization of new quantum gases based on
precise particle manipulation and strong, long-range,
anisotropic, interparticle dipole-dipole interactions
(1/r3 vs 1/r6 “contact” potential)
Quantum Computing and Simulation
Enhanced electric dipole moment sensitivity for
tests of fundamental symmetries
Precision Molecular Spectroscopy for
clocks, time variations of
fundamental constants, others.
Cold and ultracold controlled Chemistry
Refer Krems, Shapiro, Madison, other folks… really don’t need this motivational slide in this milieu, nonetheless for the sake of completeness

13. Polar (diatomic) Molecules from Ultracold Atoms
Need to draw energy levels versus electric field. Simple case of diatomic

14. Polar (diatomic) Molecules from Ultracold Atoms
Unequal sharing of electrons
Polarizable at relatively low field
New degrees of freedom bring with them scientific advantages
New degrees of freedom bring with them technical issues
Shifting Gears picture…
You have to indulge me a bit….
Need to draw energy levels versus electric field.

15. Ultracold Atom Menu
Missing Cadmium.
Very different mass, very different electronic structure  strong dipole moment

16. Selected Molecular Constituents
Various species-selective manipulation methods
Interaction tuning through Feshbach resonances
Yb as an impurity probe of the Li Fermi superfluid.
Large mass difference mixture of interacting fermions
Photo- and magneto-association as starting point for making diatomics
Several Fermi/Bose isotopes available

17. Selected Molecular Constituents
Large difference in electronic structure and mass  Large electric dipole moment and strong, anisotropic interactions
Bosonic or Fermionic Molecules can be formed
Paramagnetic + Diamagnetic Atom  Molecular ground state will also have magnetic moment. Can be magnetically manipulated and trapped.
Paramagnetic ground state, heavy component  candidate for electron EDM search
Quantum computing candidate
Distinctions from bi-alkalis.

18. Dual Species Apparatus
Li Oven
Li Zeeman
Slower
Yb Oven
Yb Zeeman
Main Chamber
Pump
Area
Ultrahigh Vacuum
(UHV < Torr)
Bucket windows for magnetic quadrupole and Feshbach coils. Photo of installed magnetic coils.
AGENDA
Cool and trap Li and Yb
Study interacting mixture
Induce controlled interactions
Form molecules

20. Ytterbium – green, Lithium - red
2-species Magneto-Optic trap
Sequential Loading
Ytterbium – green, Lithium - red
The 2 MOTs are optimized at different parameters of
magnetic field gradient and also exhibit inelastic interactions

21. Optical Dipole Trap
More Li in trap pictures. Showing original position of atoms.
Absorption image of optically trapped lithium atoms
together with uncaptured atoms released from a MOT

22. Evaporative Cooling of Bosonic 174Yb
Temperature evaluated from
size of absorption imaged atoms
after variable time of flight
With forced evaporative cooling, can
cool towards quantum degeneracy
s-wave scattering length = 5.5nm

23. Strong Interactions in Fermionic Lithium
“Feshbach molecule” formation
Feshbach resonance
between |1> and |2>

24. Collisional Properties of the LiYb Mixture
Ytterbium
Lithium
Elastic interactions dominate forming a stable mixture.
From the timescale of the thermalization process, we extract the
interspecies collisional cross-section and s-wave scattering length
magnitude of 13 bohrs. Establishment of a new two-species mixture.

25. Sympathetic Cooling of Lithium by Ytterbium
T/TF = 0.7
With improvements to cooling
procedures (in progress), double
degeneracy should be possible

26. Ultracold Molecules through PhotoAssociation
Scan
Great success in bi-alkali KRb system (JILA)
Trap loss measurement
in the 6Li system
Provides information on excited potential
First step towards ground LiYb molecule

27. Ground state polar molecules
Future Li-Yb Work
UltracoldStable Mixture
Simultaneous degeneracy
Yb as probe of Feshbach molecules
Yb as probe of Fermi superfluid
Induce strong Li-Yb interactions
Scan
2 photon PA +
2 photon Raman
Photoassociation in LiYb system
Ground state polar molecules
through multiple2-photon processes,

28. neutron interferometry
Precision Measurement of Fine Structure Constant a - 2 5 1 – i n p b
atomic physics route a 9 8 æ è ç
ac Josephson effect
neutron interferometry
h/mn
Quantum Hall effect
g-2 of electron + QED
Cross-field comparisons
Precision test of QED
(2000)
Lot of recent results in the field
(2008)

29. BEC is a bright coherent source for atom interferometry
QED-free Atomic Physics Route to 
motivation2
0.008 ppb: hydrogen spectroscopy, (Udem et al.,1997; Schwob et al.,1999)
Penning trap mass spectroscopy
Frequency comb -
Cs (Berkeley)
Rb (Paris)
0.7 ppb: penning trap mass spectr.
(Beier et al., 2002)
BEC is a bright coherent
source for atom interferometry

30. principle2 Contrast Interferometry with a BEC Advantages:
no sensitivity to mirror vibrations, ac stark shift,
rotation, magnetic field gradients
quadratic enhancement with additional momenta
(x N2)
single shot acquisition of interference pattern
The phase of the matter wave grating is encoded in oscillating contrast.
The phase of the contrast signal for various T gives rec.

31. principle2 Contrast Interferometry with a BEC Na BEC 2002
The phase of the matter wave grating is encoded in oscillating contrast.
The phase of the contrast signal for various T gives rec.

32. 7ppm precision achieved, attributed to mean field.
Contrast Interferometry with a BEC
principle2
Na BEC
2002
With Na BEC experiment
7ppm precision achieved,
but inaccuracy at 200ppm,
attributed to mean field.

33. Contrast Interferometry with a BEC
Scale Up
Increase sensitivity by increasing momenta
of 1 and 3 by 20-fold and increasing T
We then expect sub-ppb precision in less than a day of data.
Use of a Yb BEC – no B field sensitivity and multiple isotopes for systematic checks
At this level, have to very carefully account for atomic interactions and the mean
field shift. Theoretical analysis performed in collaboration with Nathan Kutz (AMath).
Gearing up for the experiment - expect the next generation result in 2-3 years.

34. UW Ultracold Atoms Team
Undergrad Students: Jason Grad, Jiawen Pi, Eric Lee-Wong
Grad Students: Anders Hansen, Alex Khramov, Will Dowd, Alan Jamison
Post-doc: Vladyslav Ivanov
$$$ - NSF, Sloan Foundation, UW RRF, NIST

35. One- and Two- Electron Atoms
6Lithium

36. Yb (Crossed)Beam Spectroscopy
Fluor [arb]
Freq [MHz]
Label all the transitions? Note the linewidths.
Fluor [arb]
Freq [MHz]

37. Magneto-Optical Trapping of Li
few x 108 atoms loaded
in a few seconds
Load time (s)
Fluor (arb)
Expansion time (ms)
Size (mm)
Temp ~ 400mK

38. Ultracold Mixtures of Lithium and Ytterbium Atoms
Preliminary Evidence
of Elastic Interactions
Yb lifetime is a bit lower than otherwise.hg

39. Ultracold Atoms
High sensitivity (large signal to noise, long interrogation times in a well
known atomic system)
Precision measurements (spectroscopy, fund sym, clocks)
Sensing (accelerations, gravity gradients)
Many-body aspects
Quantum Fluids
Condensed Matter Physics
Nuclear Physics
Quantum Engineering (Potentials and Interactions)
Quantum Information Science
Quantum Simulation
Ultracold Molecules (through mixtures)
Verifying known Hamiltonians, generating new Hamiltionians, quantum simulations, new entities

40. Macroscopic coherence
Some major achievements in ultracold atomic physics
Bose-Einstein condensation (JILA, MIT, Rice….)
Macroscopic coherence
Refer Chandra about vortex
Superfluidity / observation and study of a vortex lattice
Degenerate Fermi gas

41. Evaporative Cooling of Fermionic Lithium
vacuum limited
lifetime ~ 40 secs

42. Evaporative Cooling of Bosonic 174Yb
Plain evaporation at B=0
N ~ up to 106 (here ~ 3 x 105)
Side view of
released Yb
N ~ 50,000
With forced evaporation, can reach sub-microKelvin
Here, temp X 2 above degeneracy for 50,000 atoms

43. Dual Species Apparatus
Omitting up-down beams for clarity
1 inch

44. Optical Dipole Trap Shallow angle (10 degrees)
Omitting up-down beams for clarity
Shallow angle (10 degrees)
crossed beam dipole trap
1064nm, up to 50 Watts

45. LiYb Molecule: Theory ~ 0.4 Debye Electric dipole moment
Exotic molecule – unknown spectrum. Preliminary ab-initio theory. First help from Roman Krems. Unknown spectrum.
Svetlana Kotochigova,
Temple Univ/ NIST
preliminary results
Peng Zhang, ITAMP Harvard

46. Fermi Degeneracy in 6Li DF TF T (calc) T (meas) Top view of Trapped Li
With evaporation
at 300 G, can
achieve T/TF ~ 0.5 DF
Size gets clamped by
the Fermi Diameter