Measurement of p-wave interaction energy in an ultracold spin-polarized Fermi gas of 6Li

Takashi MukaiyamaInstitute for Laser Science (ILS)

University of Electro-Communications

第３回中性子星核物質研究会 ２０１４年９月２５日熱川ハイツ

Experimental determination of Equation of State (EOS)

S. Nascimbene, et al.Nature 463, 1057 (2010).

M. Horikoshi, et al.Science 327, 442 (2010).

M. Ku, et al.Science 335, 563 (2012).

Our goal:EOS for fermions with p-wave interactions

Scattering of identical particles

Bosons : s-wave (l=0), d-wave (l=2), …Fermions : p-wave (l=1), f-wave (l=3), …

Higher partial wave contribution decreases with temperature.

B. DeMarco et al.Phys. Rev. Lett. 82, 4208 (1999).

s-wave collision cross section between distinguishable fermions

p-wave collision cross section between identical fermions

Threshold energy for 6Li is on theorder of mK.(Typical temperature range ~ 1K)

p-wave Feshbach resonance

・ narrow Feshbach resonance

・ quasi-bound state

Atoms need to tunnel through the barrier

molecular state has finite lifetime even at higher energy than the dissociation limit

E

R

s-wave

centrifugalbarrier

p-wave

・ doublet structure

spin-spin interaction

When the scattering length is tuned to nearly zero,

Atoms would not collide with each other

Trapping laser

Trapping laser

At the unitarity limit,

Trapping laser

トラップレーザー

V. Gurarie et al. PRL 94, 230403 (2005)

Point node

Expected p-wave superfluid phase diagram :

Energy 1/a > 01/a < 0

nE

1nE

“Super” Efimov effect

exp exp 3 4nE A n

doubly-exponential scaling

p-wave resonance in identical fermions (2D)

Y. Nishida et al., Phys. Rev. Lett. 110, 235301 (2013)

Optical dipole trap

Evaporative cooling in an optical dipole trap

Evaporative cooling in an optical dipole trap

Num

ber

EnergyN

umbe

r

Energy

Num

ber

Energy

Size ~ 10-100mAspect ratio ~ 5:4:1Number of atoms ~105-106

Temperature ~ 1K

B = 650 ~ 800 G

molecular BEC

B = 0 ~ 500, 800 ~ Gdegenerate Fermi gas

6Li in quantum degenerate regime6Li in quantum degenerate regime

B

I

I

Interaction and loss are the opposite sides of the same coin…

s-wave case

two-component fermions withs-wave interaction-> stable against 3-body loss

p-wave case

3-body loss is crucial

180x103

160

140

120

100Num

ber o

f ato

ms

1.00.80.60.40.2holdtime [sec]

10-26

10-25

10-24

10-23

10-22

K3 [c

m6 /s

ec]

-200 -100 0 100 200

magnetic field [mG]

33n nK= -&

decay plot

6Li

40K

✓ observation of p-wave Feshbach resonances[4-6]

✓ p-wave Feshbach resonance [1]

✓ “loss” and “recovery” of atoms near the p-wave Feshbach resonance[4]

✓ p-wave molecule creation [3]✓ splitting between ml = 0 and |ml| = 1 resonances[2]

[2] C. Ticknor et. al. PRA 69, 042712 (2004)[1] C. A. Regal et. al. PRL 90, 053201 (2003)

[3] J. P. Gaebler et. al. PRL 98, 200403 (2007)

Work done so far with p-wave Feshbach resonances

✓ determination of the magnetic moment of p-wave molecular state[6]✓ p-wave molecule creation [7,8]

[5] C. H. Schunck et al. PRA 71, 045601 (2005)[4] J. Zhang et al. PRA 70, 030702(R) (2004)

[6] J. Fuchs et al. PRA 77, 053616 (2008) [7] Y. Inada et al. PRL 101, 100401 (2008)[8] R. A. W. Maier et al. PRA 81, 064701 (2010)

-800

-600

-400

-200

0

200

Ener

gy [M

Hz]

300250200150100500Magnetic Field [Gauss]

| F mF ms mI > |1> = |1/2, 1/2, -1/2, 1 > |2> = |1/2, -1/2, -1/2, 0 > |3> = |3/2, -3/2, -1/2, -1 > |4> = |3/2, -1/2, 1/2, -1 > |5> = |3/2, 1/2, 1/2, 0 > |6> = |3/2, 3/2, 1/2, 1 >

The way to probe interaction – RF spectroscopy

|

|

|

RF field

|

|

|

RF field

without interaction

with the presenceof interaction

Energy shift due to p-wave interaction

Apply magnetic field gradientTurn off the trap

| |

| |

Stern-Gerlach measurement

-600

-550

-500

-450

-400

Ener

gy [M

Hz]

161.0160.0159.0158.0Magnetic Field [Gauss]

68.55

68.50

68.45

68.40RF fre

quency

[MH

z]160.5160.0159.5159.0158.5158.0

Magnetic field [Gauss]

Subtract obvious energy shift from data

1.5x10-3

1.0

0.5

0.0RF fre

quency

[MH

z]

160.5160.0159.5159.0158.5158.0

Magnetic field [Gauss]

68.55

68.50

68.45

68.40RF fre

quency

[MH

z]

160.5160.0159.5159.0158.5158.0

Magnetic field [Gauss]

Region where atomic loss is prominent

100

80

60

40

20

Num

ber o

f ato

ms

in |2

>

68.52068.51668.512RF frequency [MHz]

• 12 mG drift corresponds to 1 kHz (half div) shift of the resonance• Slight asymmetry observed

Typical RF spectrum

B fluctuation ~ 300 mG

B fluctuation ~ 4 mG@160G

control voltage

error signalMOSFET60 A

5.0 V

+

-

Hall probe

Coil

ConstantCurrent

current stabilization

Without stabilization

With stabilization

3m

red：near the wallblue：on the machine table

Optical tables

-5

0

5

B [

mG

]

-40 -20 0 20 40

Time [msec]

Magnetic field fluctuation

3B 2 2int

3 22 32

nk T b bn TT

2 2b B 2

2 0bound 0states

dd2 1d

E k lT k

l

kb e l ekk

e2

3

1 1cot p kV

k kk

p-wave scattering phase shift

“Statistical Mechanics” Kerson Huang

T. –L. Ho and E. J. Muller, Phys. Rev. Lett.92, 160404 (2004)

B

20 3

23Tr 2 2H N k T Vze b O z

High-temperature expansion of a grand partition function

Interaction energy

B 1k Tz e B2h mk T

V and ke have to be determined from a separate experiment.

-4000

-2000

0

2000

4000

scat

terin

g le

ngth

[a,u

]

120010008006004002000

Magnetic Field [Gauss]

( ) 3bg

res

1 BV B aB B

踐 D ・・ ・= +・ ・・ ・・ -顏

… unknown parameters-4000

-2000

0

2000

4000

scat

terin

g vo

lum

e[a.

u.]

120010008006004002000

Magnetic Field [Gauss]

??

( ) 1bgres

Ba B aB B

踐 D ・・ ・= +・ ・・ ・・ -顏

bg 0

res

1582

262.3 [G]832.18 [G]

a a

BB

=

D = -

=

G. Zurn et al.Phys. Rev. Lett. 110, 135301 (2013)

s-wave, 6Li, |1>-|2>

p-wave, 6Li, |1>-|1>

( )( ) 2

11 2s

s

f ka B r k ik

=- + -

( )( )

2

2 3e1 2p

kf kV B k k ik

=- + -

Scattering parameters

(1) modulate trap laser intensity at 3.4 kHz to add energy in one direction(2) cross-dimensional thermalization due to elastic collisions

Images taken after ballistic expansion

(1) (2)

1.07

1.06

1.05

1.04

1.03

1.02

1.01

aspe

ct ra

tio

30x10-3252015105

Hold time [s]

Elastic collision cross-section can be derived from the timescale ofthe thermalization.

T. Nakasuji, J. Yoshida, and T. Mukaiyama,Physical Review A 88, 012710 (2013).

0.01

0.1

1

10

100

1000Th

erm

aliz

atio

n ra

te [

Hz]

0.40.20.0-0.2B-Bres [Gauss]

1.5K 2.0K 3.0K 3.8K

( )

( )

2

12 3

e

, 1l

k

kf k Bk ik

V B

= =

- + - ( )

1

res

1bg

1 1V B B B

BV -

-踐 ・・ ・= +・ ・・ ・・ -・

D

・

[ ]6 3bg 0

1e 0

2.8 10 Gauss

0.058

V B a

k a-

ｴ D = ｴ

= -

( ) ( ) ( ) ( )5/ 22 2

B B2 4 2 1 expln k T l f E E E k T dEpmp

-ｴ + -・

0.12

0.08

0.04

0.00

Mag

netic f

ield

[G

]

-2000 -1000 0 1000 2000

RF frequency

12mK

5K

0.12

0.08

0.04

0.00

Mag

netic f

ield

[G

]

-2000 -1000 0 1000 2000

RF frequency

12mK

5K

Calculation result

3 0.03n

Order of energy shift ~ 1 kHzMagnetic field range ~ 40 mG

T=5K

1.5x10-3

1.0

0.5

0.0RF fre

quency

[MH

z]160.5160.0159.5159.0158.5158.0

Magnetic field [Gauss]

Order of energy shift ~ 1 kHzMagnetic field range ~ 1 G

Summary

RF spectroscopy to probe p-wave interaction in a spin-polarized Fermi gas

• Systematic study on temperature dependence• Reduction of magnetic field fluctuation• Further integration to improve S/N ratio

are needed to claim the first measurement of p-wave interaction energy.

研究室メンバー研究室メンバー

土師 慎祐 特任助教齋藤 了一 M2

藤永 宗和 M2

吉田 純 M2

松田 優衣 M1

張 志琪 M1

興野 一樹 B4

服部 敬太 B4

向山 敬 PI