A Cold Atom Experiment

A Cold Atom Experiment

Fuqiang Wang 王福强

Huzhou University, Purdue University

Outline Hydro flow or escape?

Motivation for a cold atom experiment Cold atom laboratory

To verify the uncertainty principle* Summary

Heavy ion experiment

7/26/2017 2 / 19 Sichuan University AMPT Workshop

Model: Song et al. arXiv:1011.2783

The Hydrodynamics Paradigm

4

Strong elliptic anisotropy BNL press release 2005

Nearly perfect fluid (sQGP)

7/26/2017 Sichuan University AMPT Workshop

5

Hydro questionable!

Mean free path: Lmfp = 1/rs

Ncoll = Opacity = L/Lmfp = rsL

AMPT

Ncoll ≈ O(1)

He, FW, et al. PLB753(16)506

Is it really hydro? Heavy ion collision: dN/dy 1000, r 1000/pR2t 6 fm-3

rsL 7fm-3*3mb*3fm 5


Relative escape contribution

• Escape contribution still sizeable even at x10 larger x-sections.

8

Ncoll ≈ 5 20 35 50


Strong anisotropy, but no energy loss

9 7/26/2017 Sichuan University AMPT Workshop

Small system collisions

Flow from Coulomb interaction

• Coulomb interactions

• Can change trap size and anisotropy, and ion density

10

• a = 10 nm, b = 80 nm, c = 100 nm

• Number of ions =1000

• Initial thermal velocity 2000m/s

Sichuan University AMPT Workshop 7/26/2017

Flow from Coulomb and Elastic scattering

11

a = 10 nm, b = 24 nm, c = 50 nm


Trap size: ab = 240 nm2, c = 50 nm. Number of particles: 1000

Anisotropy mechanism

12

Expansion, flow Hydro paradigm

No expansion Escape


13

Heavy ion collisions

Perfect liquid Hydrodynamics

Low density/opacity Mundane physics

Need experimental test!


14

K. M

. O’H

ara

et a

l., S

cien

ce 2

98

, 21

79

(2

00

2)

Another system with large anisotropy

Large elliptic anisotropy in cold atom systems

consistent with hydrodynamic flow


Opacity

15

Mean free path: Lmfp = 1/rs , Ncoll = Opacity = L/Lmfp = rsL

AMPT

Low opacity in AMPT

a ≈ 5×10-5 cm sint ≈ 10-8 cm2

r ≈ 5×1013 /cm3

Lmfp ≈ 2×10-6 cm L ≈ 2×10-3 cm L/Lmfp ≈ 1000

Ncoll ≈ O(1)

Indeed hydro!

Hydro??

Very high opacity for the cold atom system

Heavy ion collision: dN/dy 1000, r 1000/pR2t 6 fm-3

rsL 7fm-3*3mb*3fm 5

Cold atom system:


K. M

. O’H

ara

et a

l., S

cien

ce 2

98

, 21

79

(2

00

2)

To emulate QGP with cold atoms K

. M. O

’Har

a et

al.,

Sci

ence

29

8, 2

17

9 (

20

02

)

rsintL: reduce opacity by 103

1000 1

a ≈ 5×10-5 cm sint ≈ 10-8 cm2

r ≈ 5×1013 /cm3

Lmfp ≈ 2×10-6 cm L ≈ 2×10-3 cm L/Lmfp ≈ 1000

Very high opacity for the cold atom system

Opacity: rsL

X10-3

0-1

Low opacity for the cold atom system

Sichuan University AMPT Workshop 16 7/26/2017

A cold atom experiment Setting up a cold atom experiment in Huzhou University

Sichuan University AMPT Workshop 17 7/26/2017

Summary

• Close connections between hot QGP and cold atoms.

• Cold atoms are hydrodynamical; QGP may not be.

Make it less interacting, more dilute, or smaller to mimic QGP.

• QGP is quantum mechanical; cold atoms are “classical.”

Make it smaller, or colder to mimic QGP, and measure the uncertainty principle.

• Use controllability of cold atom system to address QGP questions


Hot QGP vs Cold Atoms

19 Sichuan University AMPT Workshop 7/26/2017

To verify the uncertainty principle*

20

T = 104 K

Classical?

Quantum Mechanical?


Is QGP classical?

21

?

K. M

. O’H

ara

et a

l., S

cien

ce 2

98

, 21

79

(2

00

2)

Li: M6000 MeV T1mK10-16MeV

x20mm, y100mm p(TM)1/210-6MeV

p quan1/r10-8MeV

E quan1/(mr2)10-20MeV Negligible!

Cold atoms are hot,

“classical” w.r.t. trap size.

Ko

lb, H

ein

z, n

ucl

-th

/03

05

08

4;

Lisa

et

al. N

ew J

. Ph

ys. 1

3 (

20

11

) 0

65

00

6

q,g: M0 MeV T200 MeV

x3fm, y4fm p200MeV

p quan1/r200MeV

E quan200 MeV Comparable!

QGP is cold,

quantum mechanical.


QM uncertainty principle

/ 2x p

y

x

x yp p

2 22 2

22 2 2 2cos2

x y

x y

p py xv

y x p p

- -


Infinite square well

22

cos

2

sin

odd

even

nx

aE

nmx

a

p

p

-

22 2 2 2

2

2 2 22 2 2

Take even mode for example:

2 ; ;

4

2 2 > / 24 4

oddx

x odd

a np k x k

k a

k ap x n

p

p

-

- -

2 2 2 2

2 2 22 2 for all .

x y

x y

p p b av n

b ap p

- -

23

a

b

1 fm

Single state anisotropy


Harmonic oscillator

22 2 21 1

; 2 2 2

m x E E nm

-

22 2

2 2

1 1 1

2 2 2 2 2

1

2

x

x

p Em x n

m

p x n

2 2

2 2 2

2 2

2 2

2 for each and all

x y x y

x yx y

x y

x y

p pv

p p

y x

y x

v n

- -

- -


Thermal probability

then it’s independent of potential. It’s isotropic at all temperature because K=(px

2+py2)/2m is isotropic.

Because This is classical physics limit.

x, y at same Fermi energy, so different number of filled energy levels.

At high temperature, classical limit, sum is approximated by integral:


Thermal probability weight


Quantum physics anisotropy

27

D. Molnar, FW, and C.H. Greene, arXiv:1404.4119


Cold atoms Strong elliptic anisotropy

K. M. O’Hara et al., Science 298, 2179 (2002).

Lithium atoms M ~ 6000 MeV Temperature T ~ 1 mK ~ 10-16 MeV Trap size x ~ 20 mm, y ~ 100 mm Typical momentum (TM)1/2 ~ 10-6 MeV Intrinsic momentum quantum ~ 1/r ~ 10-8 MeV, negligible. Typical energy ~ T ~ 10-16 MeV Intrinsic energy quantum 1/(mr2) ~ 10-20 MeV, negligible. Cold Lithium atoms are actually “hotter” than the hot QGP.

~ 10-5

The observed large v2 is indeed due to strong interactions.


Is quantum v2 real in QGP?

30

K. M

. O’H

ara

et a

l., S

cien

ce 2

98

, 21

79

(2

00

2)

Li: M6000 MeV T1mK10-16MeV

x20mm, y100mm p(TM)1/210-6MeV

p quan1/r10-8MeV

E quan1/(mr2)10-20MeV Negligible!

Cold atoms are hot,

classical.

Ko

lb, H

ein

z, n

ucl

-th

/03

05

08

4;

Lisa

et

al. N

ew J

. Ph

ys. 1

3 (

20

11

) 0

65

00

6

q,g: M0 MeV T200 MeV

x3fm,y4fm p200MeV

p quan1/r200MeV

E quan200 MeV Comparable!

QGP is cold,

quantum mechanical.

X10-2

x10-4

• It should be… but need experiment to verify (cold atom experiment)

• Cold atoms are “classical.” Make it Quantum Mechanical.

• Would be neat to verify QM and uncertainty principle


Summary

• Close connections between hot QGP and cold atoms.

• Cold atoms are hydrodynamical; QGP may not be.

Make it less interacting, more dilute, or smaller to mimic QGP.

• QGP is quantum mechanical; cold atoms are “classical.”

Make it smaller, or colder to mimic QGP, and measure the uncertainty principle.

• Use controllability of cold atom system to address QGP questions


A Cold Atom Experiment

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