D. Jin

JILA, NIST and the University of Colorado

$ NSF, NIST

An atomic Fermi gas near a

p-wave Feshbach resonance

1. Motivation

2. A p-wave Feshbach resonance

3. Molecule energies and lifetimes

4. Future

Outline

Fermi condensate

Fermionic superfluidityCooper pairing: two correlated fermions act like a boson

Examples

Superconductivity: Cooper pairs of electrons

Superfluid 3He: 3He atom pairs

Superfluidity in nuclear matter:Nucleon pairs

P-wave pairing?Fermi condensates with non-s-wave pairing?

• Examples: • superfluid 3He (p-wave)• high Tc superconductors (d-wave)

• Novel features:• anistropic gap• multiple superfluid phases,• narrow resonance

s-waveL=0

p-waveL=1

m l= -1,0,+1

• This is the first step toward making molecule condensates and fermion pair condensates.

• New possibilities: non-s-wave molecules, heteronuclear molecules, fermionic molecules, ground-state molecules, and polar molecules.

Making molecules

other non-s-wave Feshbach molecule studies:

Grimm (s- to g- wave), Salomon (p-wave)

Molecules can be very efficiently created using a Feshbach resonance.

• magnetic-field sweep across resonance• three-body collisions near a Feshbach resonance• rf association

• magnetic-field modulation

Making molecules

A magnetic-field tunable atomic scattering resonance

Channels are coupled by the hyperfine interaction.

Feshbach resonance

→ ←colliding atoms in channel 1

molecule state in channel 2

P-wave resonance

0

V(R)

R

centrifugal barrier

S

0

V(R)

R

22

)1(

rm

ll

300 K

300 K

0.5 K

Collisions and Fermions

one spin-state

two spin-states

ela

stic

co

llisi

on

cro

ss s

ect

ion

B. DeMarco et al., PRL 82, 4208 (1999)

40K

P-wave resonance

180 200 22010-13

10-12

10-11

10-10

10-9

(cm

2)

B (gauss)

C.A. Regal, C. Ticknor, J.L. Bohn, & D.S. Jin, PRL 90, 053201 (2003)

40K

spin-polarized gas|f=9/2, mf=-7/2>

ela

stic

colli

sion

cro

ss

sect

ion

198 199 2000

2x105

4x105

6x105

8x105

Num

ber

B (Gauss)

Multiplet structure

ml = ±1 ml = 0B0 = 198.3 G B0 = 198.8 G

C. Ticknor, C.A. Regal, D.S. Jin, and J.L. Bohn, PRA 69, 042712 (2004).

ml = ±1ml = 0B

198.8 199.0 199.20

1

20

5

100

10

20

0

20

40

B (G)

EF = 4.4 kHz

EF = 7.7 kHz

EF = 10.4 kHz

Ato

m n

umbe

r (x

104 )

EF = 13.3 kHz

Width of loss feature

ml = 0resonance

Feature of a narrow resonance

B-field modulation

0 20 40 60 80 1000

2x104

4x104

6x104

Ato

m n

umb

er

frequency (kHz)

B below both resonances

dissociation M. Greiner, C.A. Regal, & D.S. Jin, PRL 94, 070403 (2005)association S.T. Thompson, E. Hodby, & C.E. Wieman, PRL 94, 190404 (2005)

Near a Feshbach resonance, a resonant oscillating B-field can create molecules.

0

V(R)

R

centrifugal barrier

Quasi-bound molecules

0

V(R)

R

centrifugal barrier

0 20 40 60 80 1000

2x104

4x104

Nu

mb

er

frequency (kHz)

B above theresonance

-1.0 -0.5 0 0.5 1.0 1.5-300

-200

-100

0

100

200

En

erg

y (k

Hz)

B (Gauss)

P-wave molecule energy

ml = ±1

ml = 0

B

J.P. Gaebler, J.T. Stewart, J.L. Bohn, & D.S. Jin, PRL 98, 200403 (2007)

A way to “see” molecules

0

V(R)

R

Create molecules

Look for energetic atoms created by tunneling

A way to “see” molecules

ml = 0ml = ±1

B

A way to “see” molecules

ml = 0ml = ±1

B

0 0.5 1.0 1.5 2.00

1x104

2x104

Mo

lecu

le N

um

be

r

Hold time (ms)

Molecule lifetime

ml = ±1

B

time

resonance

=1.2 ms

hold time

molecule creation

Quasi-bound molecule lifetime

B

time

resonance

hold time

molecule creation

-200 -100 010-3

10-2

10-1

100

10 100

Energy (kHz)

Life

time

(ms)

Molecule Lifetimes

E32

J.P. Gaebler, J.T. Stewart, J.L. Bohn, & D.S. Jin, PRL 98, 200403 (2007)

ml = 0ml = ±1

Dipolar relaxationSince our atoms are not in the lowest energy spin state, the molecules can undergo “one-body” decay.

2

9,

2

9

2

9,

2

9

2

7,

2

9

2

7,

2

9

2

9,

2

9

2

7,

2

9

This decay process would not exist for atoms in the lowest energy spin state. (6Li has such a p-wave resonance).

bound free

Collisional decayAfter removing atoms (blasting with resonant light)

0 5 10 15 200

5000

10000

15000

N m

olec

ules

time (ms)

= 7 ± 1 msml = 0

-200 -100 010-3

10-2

10-1

100

10 100

Energy (kHz)

Life

time

(ms)

What’s next?

ml = 0ml = ±1 E32

0 2 4 6 80

1x104

2x104

Mol

ecul

e N

umbe

r

Hold time at resonance (ms)0 2 4 6 8

0

1x104

2x104

Mol

ecul

e N

umbe

r

Hold time at resonance (ms)

Molecule CreationB

timeresonance

ml = 0

ml = ±1

Molecule Creation

198.7 198.8 198.9 199.00

5000

10000

15000

N m

olec

ules

B (G)

Molecule Creation

-50 0 50 100 150 2000

4000

8000

12000 Fermi Energy 13.0 kHz 9.8 kHz 6.4 kHz

Nm

olec

ules

B (mG)

Conclusion:

We can create and detect p-wave Feshbach molecules in a Fermi gas of atoms.

Novel aspects include:

• Centrifugal barrier• Quasi-bound state• Narrow resonance

The molecule lifetime is short.

0

V(R)

R

Group MembersJ. Goldwin

M. Olsen

P-wave molecule work: Jayson Stewart, John Gaebler