Nambu Symposium @OCU, Dec. 13, 2018

What can we do witha quantum degenerate mixture ?
v = 41, J = 1(3)1S+

Shin Inouye
Osaka City University

875nm
641nm
v = 91, J = 0
X1S+

Ion counts [arb.units]v = 0, J=0
X1S+
3.0
2.0
1.0
0.0
-50

5
Time [µs]1015Nambu Symposium @OCU, Dec. 13, 2018

Outline
How to cool atoms
Properties of BEC
Tuning interactions (Feshbach resonance)
Cold molecules
Conclusion and Outlook

Everybody loves to cool liquids ...

but, we are interested in cooling gases!

Significance of cold atom research“Ideal system” to study Condensed Matter Physics!
Produced in 1995

Anderson et al., Science, 269 198 (1995)

Awarded in 2001
Cornell, Ketterle, Wiemanphys.org
March 3,2017

What is ultracold quantum gas?

BosonsFurther lower
temperature

Fermions
EFBEC

Fermi sea of atoms

phase transition at TC

gradually emerges for T<TF

Problem with gases: Typical Tc is quite low
2! n $hTc =#&2π mkB " 2.612 %

2/3

0.000 000 1K = 100nK
Tc < 1mm

absolute zero ”Osaka"

300K "Tokyo"

Laser cooling?

?

Technological breakthroughs

laser cooling  evaporative cooling
300 K to 1 mK

1 mK to 100 nK(MOT)(Magnetic trap)-> lowest man-made temperature
A. E. Leanhardt, T. A. Pasquini, M. Saba, A. Schirotzek, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle:
Adiabatic and Evaporative Cooling of Bose-Einstein condensates below 500 Picokelvin.
Science 301, 1513-1515 (2003).

Evaporative coolingBose-Eintein condensation
Time-of-flightRelease atoms from the trap,
wait for tens of milli-seconds,
and take shadow picture.
Suddenly momentum
distribution becomesnarrower.
↓Bose-Einstein
Condensation!
Anderson et al., Science, 269 198 (1995)

Nambu Symposium @OCU, Dec. 13, 2018

Outline
How to cool atoms
Properties of BEC
Tuning interactions (Feshbach resonance)
Cold molecules
Conclusion and Outlook

Typical parameters•Density: ~ 1014 cm-3
•Temperature: < 100 nK•Number of atoms: < 107•Size: 20X20X200 µm•Life time> 10 s
•Atomic speciesRb, Na, Li, …
Properties of a BEC•gaseous superfluid•macroscopic wavefunction(Quantum depletion:alkali BEC < 1%, liq. He >90%)

What we are looking at?

Kinetic
energyConfiningpotentialInteraction
between atoms

It is useful to introduce y(r)c-numberquantum fluctuationOrder parameter and Spontaneous Symmetry Breaking
y(r) satisfies Penrose-Onsager relation:

vanishes as |r-r'|→∞Hamiltonian is unchanged under global gauge transformation:

Nambu-Goldstone mode: phonon

wphonon(~k)

particle (~k2)

kDirect confirmation of macroscopic wavefunction?
Interference!

Classical
mechanics

Quantummechanics

|y1(r,t=0)|2|y2(r,t=0)|2|y1( r, t = T ) + y2( r, t = T ) |2
M. R. Andrews et al., Science 275, 637 (1997)

Measurement of
1st-order spatial coherence
Extract matterwave from two separated
points and make them interfere.
I. Bloch, T. W. Hänsch & T. Esslinger
Nature 403, 166–170 (2000)

Vortex !

Rotate a BEC with a laser beam

K. W. Madison, F. Chevy, W. Wohlleben*, and J. Dalibard
Phys. Rev. Lett. 84, 806–809 (2000)
Vortex Formation in a Stirred Bose-Einstein CondensateVortex lattice !

Abrikosov lattice
J.R. Abo-Shaeer, C. Raman, J.M. Vogels, and W. Ketterle:
Observation of Vortex Lattices in Bose-Einstein Condensates.
Science 292, 476-479 (2001).

sweeping a laser beam to generate vortex!

(wavefronts of matterwaves realeased from two BECs)

BEC with a vortex

Interferometric detection of vortex pair

"Observation of vortex phase singularities in Bose-Einstein condensates."
S. Inouye et al., PRL, 87, 080402 (2001).

Nambu Symposium @OCU, Dec. 13, 2018

Outline
How to cool atoms
Properties of BEC
Tuning interactions (Feshbach resonance)
Cold molecules
Conclusion and Outlook

Kinetic
energyConfiningpotential

Interaction
between atoms

Can we tune the scattering length?

Tuning the interaction(Feshbach resonance)
Herman Feshbachcolliding atoms

Use nuclear spin

Interference!

“U” is modified by factor of 20"Observation of Feshbach resonances in a Bose-Einstein condensate."
S. Inouye et al., Nature 392, 151 (1998).

“U” is modified by seven orders of magnitude"Extreme Tunability of Interactions in a 7Li Bose-Einstein Condensate“
S. E. Pollack, D. Dries, M. Junker, Y. P. Chen, T. A. Corcovilos, and R. G. Hulet,Physical Review Letters 102, 090402 (2009).

¶y (r ) æ ! 2 2
4p ! 2 a2öi!
= çç Ñ + Vtrap (r ) +y (r ) ÷÷y (r )
¶tm
è 2m
ø
"Extreme Tunability of Interactions in a 7Li Bose-Einstein Condensate“
S. E. Pollack, D. Dries, M. Junker, Y. P. Chen, T. A. Corcovilos, and R. G. Hulet,
Physical Review Letters 102, 090402 (2009).

Nambu Symposium @OCU, Dec. 13, 2018

Outline
How to cool atoms
Properties of BEC
Tuning interactions (Feshbach resonance)
Cold molecules
Conclusion and Outlook

What can we do with two BECs?

41K87Rb

Make molecules!?

Cold ions(trapped ions)

Cold atoms

Blatt & Wineland, Nature
453 1008 (2008)

Anderson et al., Science,269 198 (1995)

 Frequency standards
 Quantum Information

 Bose Condensation
 Strongly correlated gas
 Frequency standards

Cold molecules?

“New Frontier”

“Indirect” method (2005~)
degenerate mixture

Feshbach molecule(d:small)ground state(d: large)

Feshbachresonance

T~100nK

T~100nK(Still QuantumDegenerate)

Most difficult?

No heating: 100nK out of 6000K will kill the sample!

STIRAPslowly

100nK

6000 K*Stimulated Raman Adiabatic Passage
 Find the right excited state Stabilize two laser frequencies in ~10-10 level (i.e. ~kHz level )Achieving rovibrational ground state
641nm pulse
875nm pulse

v = 41, J = 1(3)1S+

Intensity [arb.units]

0.16

875nm
641nm

v = 0, J=0X1S+

Ion counts [arb.units]v = 91, J = 0X1S+

0.12
0.08
0.04
0.00
-505Time [µs]

1015

3.0
2.0
1.00.0-505Time [µs]1015K. Aikawa et al.,PRL 105, 203001(2010)

There is a good news and bad news...
--- Good news is we produced ultracold
groundstate polar molecules!
--- Bad news is the density is really really low!

Ultracold polar molecules
near degeneracy (by JILA)

Ultracold KRb molecules imaged by direct absorption
D.S. Jin and J. Ye, Physics Today, May 2011

Directional chemistry(JILA)
same internal states AND
dipoles aligned by an external fieldm=+1/2

1/2

Electric field(~kV/cm)
K.-K. Ni et al., Nature 464, 1324 (2010)

Measure time variation offundamental constants!
General relativity + L-CDM model issuccessful in explaining following phenomena:• accelerating expansion of universe• Cosmic Microwave Background• Large scale structure
However, origin of dark energy(and dark matter) is not understood.

Possible extensions to the L-CDM
Quintessence→Fluctuation of fundamental constants??
e2a=
4pe 0 !c1me
1µ=
»m p 1836

g P , etc.

We focused on electron-to-proton mass ratio µ45

The limit of time variation of me/Mp(≡µ)

Radio-astronomical observations
Alcohol in the early universe(J. Bagdonaite et al, Science 339, 46 (2013))

Dµ / µ = (0.0 ± 1.0) ´10 -7 (in 7109 years)

The limit of time variation of me/Mp(≡µ)
Laboratory observations
molecular spectroscopy of SF6
A. Shelkovnikov et al, PRL 100, 150801 (2008)µ! / µ = (3.8 ± 5.6) ´10 -14 / year

SYRTE

rovibrationaltransition in SF6+ frequency comb
Optical Fiberlink (~43km)
Cs FountainWhy molecule?

Frequencies are directly related
to the inertial mass of nucleus.

δE 1 δm=E 2 m
Large mSmall mUltracold molecule is ideal for precision spectroscopy!
Average of 5000 sweeps(6 hours)

FWHM50Hz

634 963 783.4580.093 Hz
634 963 781.5640.094 Hz

Zeeman shiftcompensation

S/N ~ 500 (c.f. Number of molecules used ~ 106)Calibration of the magnetic field
F = 1 mF = 0

2.4s

2.4s

2.4s

2.4s

mF = 0mF = 0mF = 1

Magnetic Field (mG)

F=0mF = 1Time (hour)mF = 0mF = 1Time

Good News: we broke the world record set by SF6!

Factor offive improvement

1 ∂µ= ( 0.30 ±1.00 Stat ± 0.16 Sys ) ×10 −14 / yearµ ∂t
1 ∂µ= (3.8 ± 5.6 ) ×10 −14 / yearµ ∂t

A. Shelkovnikov et al.,PRL 100, 150801(2008)

J. Kobayashi, A. Ogino, and SI

Francesca Ferlaino and Rudolf Grimm,
Physics 3, 9 (2010).

What can we do with two BECs?

41K

87Rb

Phase separation!?

Phase separation after quenching the interaction

1D

2D

36μm x 208μm(1pix.=2.6μm)

Digital Mirror Device
Holographically generated
ring beam

Conclusion
Cold atom is a versatile ground both forcondensed matter physics

v = 41, J = 1(3)1S+

precision measurement

875nm... please stay tuned

641nm
v = 91, J = 0
X1S+

Ion counts [arb.units]v = 0, J=0X1S+
3.0
2.0
1.0
0.0
-505Time [µs]1015