MRSEC From cosmology to cold atoms: Sakharov acoustic oscillations in atomic superfluids

Cheng Chin

Funding:

James Franck institute Enrico Fermi institute Department of Physics University of Chicago

MRSEC

From cosmology to cold atoms:

Sakharov acoustic oscillations in atomic superfluids

Physics Department, NTU, 12/10/2013

Chicago in 1898

Cosmic microwave background (CMB) radiation

CMB angular power spectrum

South Pole Telescope Survey (University of Chicago)

Courtesy of Kyle Story (John Carlstrom group)

Sakharov acoustic oscillations (1965)

(Andrei Sakharov) Size = velocity × time

CMB anomalies and physics before Big Bang (?)

arXive: 1303.5062-90

axis of evil, cold spot

cyclic universe (Penrose)

Resolution: 1.0 µm Pixel size: 0.66 µm Bose-Einstein condensate of atomic cesium

Particle #: 20,000~40,000

Synopsis

New experimental tools and observables

• Density, correlations and fluctuations

• Inspiration from cmb radiation anisotropy

• Sakharov acoustic oscillations

Future projects: Black hole and gauge-gravity duality

In situ probing a monolayer of 2D quantum gases

Optical Imaging

Vertical lattice beams

Horizontal

trapping beams

High resolution optical imaging

l

Oscillator length l_z: 200nm Radial size: 50 m

10⁴ cesium atoms all in a single 2D trap

l

Quantum gas experiments in Taiwan: Ming-Shien Chang and Yuju Lin

700 800 900 -50

0 50 -1000 0 1000

energy/h (KHz)

magnetic field (G)

scattering length (nm)

a>0 a<0

mol. state

Feshbach resonance: control atomic interaction

C. Chin, R. Grimm, P. Julienne and E. Tiesinga, Rev. Mod. Phys., 82 1225 (2012)

Feshbach resonances in cold atom collisions

atomic separation r potential

) 1

(

B

B a B

a



 



Scattering length:

Transition matrix

2 /

|

|

|

0

|

G + + 



+



i E E

V V

T

T

f

c f

f

c →

E=B

Low energy scattering

a

=8a ² Cross section:

r

Ultracold atoms and molecules

Quantum Simulation based on

Efimov trimer states

Theory: (1970) Experiment: (2006)

Nuclear physics

Superconductivity

BCS = BEC??

Eagles (1969) Leggett (70) Experiment: (2004)

Condensed matter

Systems being simulated:

condensed matter, nuclear physics, HEP,

cosmology…

g=0.05 g=0.26 g=1.3

Interaction strength

Can we see the same anisotropic oscillations?

Sakharov acoustic oscillations in CMB

WMAP

Dr. Chen-lung Hung (postdoc at CalTech)

Prof. Chao-Lin Kuo (Physics, Stanford and south pole)

Power spectrum of fluctuations S(k)

o thermal gas

• g=0.05

• g=0.26

• g=1.3

Hung et al., New Journal of Physics (2011)

Hu & White, Sci. Am., 290 44 (2004)

Evolution of the universe

Opaque

Transparent

Early universe

Sakharov acoustic oscillations in early universe

Inflation

Sakharov acoustic oscillations in atomic superfluids

Something equivalent to Inflation…

Superfluid

Origin of the oscillations in the cmb angular spectrum

W. Hu, CMB tutorials, http://background.uchicago.edu/

Quantum Quench (from g=0.26 to 0.05)

Evolution of density-density correlations

Static Struct ure Factor S (k)

Wave number k (2/m)

0 ms

Evolution of density-density correlations

Static Struct ure Factor S (k)

Wave number k (2/m)

0 ms

0.5 ms

2.0 ms

Evolution of density-density correlations

Static Struct ure Factor S (k)

Wave number k (2/m)

0 ms

0.5 ms

2.0 ms

3.2 ms

Evolution of density-density correlations

Static Struct ure Factor S (k)

Wave number k (2/m)

0 ms

0.5 ms

2.0 ms

3.2 ms

4.7 ms

Evolution of density-density correlations

Static Struct ure Factor S (k)

Wave number k (2/m)

0 ms

0.5 ms

2.0 ms

3.2 ms

4.7 ms

5.9 ms

Evolution of density-density correlations

Static Struct ure Factor S (k)

Wave number k (2/m)

0 ms 0.5 ms 2.0 ms 3.2 ms 4.7 ms 5.9 ms 7.4 ms

Interaction g

Sakharov acoustic oscillations in space coordinate

τ =

Hung, Gurarie and Chin, Science 341 1213 (2013) WMAP

Sakharov oscillations in time domain

k=0.4/m k=0.6/m k=0.8/m k=1.0/m

k=0.4/m

k=0.6/m

k=0.8/m k=1.0/m Quench down

(g=0.26  0.05) Quench up

(g=0.08  0.14)

*each curve is offset by 0.5 for clarity

Time and length scales of Sakharov oscillations

Quench up (g=0.080.14)

Quench down (g=0.260.05)

: healing length v: sound speed

Bogoliubov phonons

Theoretical model (Bogoliubov approximation)

Quench up (g=0.080.14)

Equilibrum contribution Interference of acoustic waves

Landau and Liftshitz, Statistical Physics Vol. 9 P. 386

Conclusion

Quenched superfluids and Sakharov oscillations

– Inference of acoustic waves

– Correlations in time and spatial scales

– Questions: Damping of Sakharov oscillations?

Related projects

Quantum analog of gravitational physics

– Sonic black hole and Hawking radiation and Unruh effect – Quantum criticality and AdS-CFT correspondance

Discrete scaling symmetry

– Discrete scaling symmetry in Efimov three-body bound states – Universality in far from equilibrium quantum dynamics

Experiments

Prof. Nathan Gemelke (Penn state) Dr. Chen-Lung Hung(Caltech)

Dr. Xibo Zhang (JILA)

Dr. Shih-Kuang Tung Harry L.C. Ha

Dr. Colin V. Parker Jacob Johansen Cs 2D gas

Li-Cs Bose-Fermi mixture

Current group members:

Logan Clark Dr. Eric Hazlett