Experiments on few fermion systems of ultracold atoms · • Quantum control in a many-body system...

Experiments on few fermion systems

of ultracold atoms

…and the crossover to many-body systems

Workshop

Resonances and Non-Hermitian Quantum

Mechanics in Nuclear and Atomic Physics

Trento, June 2014

Gerhard Zürn

Realize a well-controlled and tunable quantum system using ultracold atoms

A tunable few-body system

Few-fermion systems in nature:

• atoms, nuclei

well defined quantum state

limited tunability of interaction

How can one study few body effects?

interaction

Artificial Quantum system:- quantum dots

- atomic clusters

Wide tunability,

but no „identical“ systems

• Quantum control in a many-body system is becoming possible!

W. Bakr et al., Science 329, 547, 2010 C. Weitenberg et al., Nature 471, 319-324, 2011

Control at the single particle level

We aim for bottom up approach:

Start with few-fermion system and then increase towards a many-body system

Outline

• Preparation and control of few-fermion systems

• Pairing in a few-fermion system with attractive interactions

• From few to many: Building a Fermi sea from single

particles

• (Two fermions in a double well)

High Fidelity Preparation

• 2-component mixture in reservoir T=250nK

• superimpose microtrapscattering thermalisation

• switch off reservoir

p0= 0.9999

+ magnetic field gradient in

axial direction

expected degeneracy: T/TF= 0.1

count

F. Serwane, G. Zürn, T. Lompe, T. Ottenstein, A. Wenz and S. Jochim, Science 332, 336 (2011)

Single atom detection

CCD

1-10 atoms can be distiguished

with high fidelity (> 99% )

1/e-lifetime: 250s

Exposure time 0.5s


fluorescence normalized to atom number

2 atoms 8 atoms


Lifetime in ground state ~ 60s

count the

atoms

High Fidelity Preparation

750 800 850 900

-20

-10

0

10

20

a3

D [

10

3 a

0]

magnetic field [G]

3D

-1

0

1

g1

D [

10

ap

erp ħ

p

erp]

750 800 850 900

-20

-10

0

10

20

a3

D [

10

3 a

0]

magnetic field [G]

1D

M. Olshanii, PRL 81, 938 (1998)

2

31D 2

3

2 1g =

1 /

D

D

a

ma Ca a

radially strongly confined

aspect ratio: II / perp 1:10 1D

Z. Idziaszek and T. Calarco, PRA 74, 022712 (2006)

Interaction in 1D

PRL 110, 135301 (2013) PRL 110, 203202 (2013)

Studying few-body physics

control of the particle number

tunability of the interpart. interactionshaping the trapping potential

-3 -2 -1 0 1 2 3

-2

0

2

E [hll]

-1/g

[allh

ll]-1

imbalanced

balanced

T. Busch et al., Found. Phys. 28, 549 (1998)

Outline




particles


Probing the system

Observe tunneling dynamics:

•Tilt the trap such that the highest-lying states have an experimentally

accessible tunneling time of about 10-1000ms.

From the observed tunneling time scale we can then infer the total

energy of the system

G. Zürn, F. Serwane, T. Lompe, A. Wenz, M. Ries, J. Bohn and S. Jochim, PRL 108, 075303 (2012)

Attractive interactions

• Use this to determine the pairing energy

• Problem: tunneling of the two particles is correlated

G. Zürn, A. Wenz , S. Murmann, A. Bergschneider, T. Lompe, and S. Jochim, PRL 111, 175302 (2013)

0 250 500 750 10000.0

0.5

1.0

1.5

2.0

569 G g

= 0.01 [aref

ħref

]

N

Hold time [ms]0 250 500 750 1000

0.0

0.5

1.0

1.5

2.0

569 G g

= 0.01 [aref

ħref

]

350 G g

= - 0.64

N

Hold time [ms]0 250 500 750 1000

0.0

0.5

1.0

1.5

2.0

569 G g

= 0.01 [aref

ħref

]

350 G g

= - 0.64

1202 G g

= - 1.42

N

Hold time [ms]

Correlated tunneling

• Set up rate equation for tunneling


• extract single particle separation energy

• Fit rate coefficients to the data (consistent with subsequent single particle tunneling)

0 100 200 300 400 500

0.0

0.2

0.4

0.6

0.8

1.0

P2 fit

Pi

Hold time [ms]

0 100 200 300 400 500

0.0

0.2

0.4

0.6

0.8

1.0

P2 fit

P1 fit

g

= - 0.64

Pi

Hold time [ms]

2.0 1.5 1.0 0.5 0.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

g

[aref

ħref

]

g

= 0.01

g

= - 0.44

g

= - 0.64

g

= - 1.42

g

= - 1.76

P1

N

-0.3

-0.2

-0.1

0.0

0 0 -1 -2

E

[ħ

ref ]

1 2 3 4 5 6

-0.3

-0.2

-0.1

0.0

0.1

E21

E11

E20

E00

E10

E22

Ese

p [

ħ

ref ]

Particle number

Odd-even effect with ultracold fermions

• How does the energy of the system evolve for larger systems?


Theory: M. Rontani et. al, arXiv:1404.7762

Theory:

- Study non-perturbative regime

- Pairing in higher dimensions (2D, 3D)

- larger systems, superfluidity

Prospects:

Outline




particles


N=2 N=5…N=1

From few to many-body physics

How many is many?

Observable: Interaction energy vs. particle number and interaction strength

RF-Spectroscopy

EintEHFS

-0.2 0.0 0.2 0.4 0.60.0

0.2

0.4

0.6

Tra

nsfe

rred

fra

ction

free-free

Frequency [kHz]

EHFS + Eint

-0.2 0.0 0.2 0.4 0.60.0

0.2

0.4

0.6

Tra

nsfe

rred

fra

ction

free-free

N=1, g1D

= - 0.27 allħ

ll

Frequency [kHz]

Measure the interaction energy

A. N. Wenz, G. Zürn, S. Murmann, I. Brouzos, T. Lompe and S. Jochim, Science 342, 457 (2013)

A single impurity repulsively interacting

with an increasing number of majority particles

Natural scales of the system

The interaction energy diverges for Nmaj∞. Therefore rescale Eint onto natural

scale of a Fermi gas EF to obtain a dimensionless quantity:

Eint Eint/EF

The interaction strength is rescaled with the Fermi momentum kF (~1/interparticle

spacing) to obtain a dimensionless quantity:

g1D g1D/kF

g1D/kF ~ γ the Lieb-Liniger parameter

N=1

N=2

N=3N=4

N=5


Analytic solution of the two particle problem

T.Busch et al., Found. Phys. 28, 549 (1998)

Analytic solution for an infinite number of majority particles

J. McGuire, J. Math. Phys. 6,432 (1965)

Adapted from homogeneous to trapped case by local density approximation

non interacting strongly repulsive



2 particles

N particles

3 particles

non interacting strongly repulsive

S.E. Gharashi et al.,

PRA 86, 042702 (2012)

Four is Many!


see also:

Astrakharchik,

Conduit, T.-L. Ho,

Lewenstein, Rontani,

Santos, Zinner …

Outline




particles

• Realize a tunable potential

Creating a tunable potential

Acousto-

optic

deflector

Tunneling in a double-well

JPreparation Detection scheme

U = 0

• Single-part. tunneling

• Calibration of J

~1/2𝐽

• Correlated tunneling

• Calibration of U

U ≠ 0

9

JPreparation Detection scheme

Tunneling in a double-well

Measuring Energies in a DW

Conditional

single-particle tunnelingResonant pair tunneling

Measure amplitudes of

single-particle and pair

tunneling as a function of

tilt

Preparation of the ground state

The eigenstates

Spectrum of eigenenergies

for the balanced case:

Number statistics for the balanced case depending on the interaction strength:

Single occupancy

Double occupancy

12

Occupation statistics

Single occupancy

Double occupancy

12

Number statistics for the balanced case depending on the interaction

strength:

Occupation statistics

Summary

• We can prepare and control few-fermion systems

• Observed Crossover from few- to many-body regime

• Next: Fermi-Hubbard physics

How to prepare systems which are

not balanced in spin ?

• Go to 27G, where magnetic moment

of state | 2 vanisches

• Gradient only affects atoms in state | 2

• Further changes between hyperfine

states with RF transfer

Breit-Rabi Formula

Creating imbalanced systems

Feshbach resonances in 6Li

The ground state of the double well

Two non-interacting particles:

One particle:

• basis

• Ground state

• Ground state at U=0

11

Eigenenergies in the Hubbard Model

How to measure energy differences between eigenstates?

Experiments on few fermion systems of ultracold atoms · • Quantum control in a many-body system...

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Transcript of Experiments on few fermion systems of ultracold atoms · • Quantum control in a many-body system...