Exploring transport in a Tonks Girardeau gas

Carlo Sias

www.quantumoptics.eu

£££: EPSRC, University of Cambridge, Herchel-Smith Fund, ERC

Transport – a very general subject!

Open system:energy is continuously transferred into the system

Upotential difference U continuously accelerates electrons

I

Transport experiments in cold atoms

+2ħk0-2ħk

A simple transport experiment

Scattered atoms with spherical (s-wave) symmetry

Ketterle group 2000

Threedimensions

Onedimension

Weiss group 2006

Other transport experiments: ETH, LENS, NIST, Orsay, Pisa, Stanford,, ...

k -k

Transport in solid state: 1-dimension

Solar cell design

Transistors for transparent and flexible electronics

Spin-charge separation

What is a one-dimensional gas?

What is a one-dimensional gas?

• transverse degrees of freedom are frozen out

Conditions for 1DkBT < hw┴

Bosons: m < hw┴

Fermions: EF =N hwz < hw┴

w

1-dimensional Bose gas

• Exactly solvable many-body problem! (Lieb-Liniger)

• The many-body quantum state is characterized by a single parameter

Tonks-Girardeau gas(“Fermionized Bosons”)

weakly interacting Bose gas

crossover

/

)()(

mcnk

rr

F

FermiBose

m

2

...1

;)()( mcrrNi

iBose

D

D

nmg

12

1

D

D

nmg

12

1

)()()(2 ,

12

22

rErxxgxmi ji

jiDi

Bogoliubov spectrum

Excitations in a weakly interacting Bose gas

«1

Excitations in a Tonks gas

Two branches of excitations: “particle” excitations and “hole” excitations

kkF

q

kkF

q

-kF -kF

→∞

Generating tight confining potentials

Induced electric dipole potential: 21

2V E

ac polarizability of the atom electric field of the laser

Two options:L Aw wL Aw w

„red detuned“ „blue detuned“

Optical lattice

l/2

Energy scale:

mkErec 2

22

AwLw

Hybrid optical/magnetic trap

Other experiments in 1D: ENS, ETH, LENS, Mainz, MIT, NIST, Orsay, Penn State, Rice, Vienna, Innsbruck …

Vertical confinement: purely magnetic

Hybrid optical/magnetic trap

Other experiments in 1D: ENS, ETH, LENS, Mainz, MIT, NIST, Orsay, Penn State, Rice, Vienna, Innsbruck …

Experimental parameters:Atoms: 87Rb (bosons)Wavelength of lattice: 764 nmwx= wy ≤ 2 65 kHz (optical lattice)wz= 2 39 Hz (magnetic trap)N<50 per tube0.5 < < 10

Vertical confinement: purely magnetic

Generation of spin impurities

F=2

F=1

z

-2 -1 0 1 2mF:

ΔE(z)

Generation of spin impurities

quick transfer (RF /2-pulse, 200 ms)

F=2

F=1

)(zBRF mw

z

-2 -1 0 1 2mF:

Generation of spin impurities

F=2

F=1

)(zBRF mw

z

-2 -1 0 1 2mF:

Generation of spin impurities• width of impurity wave packet:

2.5 mm (≈ 3 atoms)

• same transverse confinement:propagation of impurities is purely one-dimensional

• same scattering lengths: a-1,-1 ≈ a-1,0 ≈ a0,0

• accelerated impurity breaks integrability of the 1D Bose gas → interesting dynamics

z

In situ detection of the spin wave packet

F=2

F=1

F=2 imaging only

In situ detection of the spin wave packet

F=2 imaging only

F=2

F=1

Distance z [mm]

Time evolution

• strong interaction-induced dynamics

• significant back action of the impurity onto the majority component

• open quantum system: impurity atoms can transfer continuously energy into trapped component by collisions

g

S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

Center-of-mass motion of the impurities

S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

Distance z [mm]

Center-of-mass motion of the impurities

ballistic

Tonks gas

weakly interacting Bose gas

S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

Distance z [mm]

Center-of-mass motion of the impurities

ballisticpart of the impurities have already left the gas

Tonks gas

weakly interacting Bose gas

S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

Release measurement

tdelay

S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

Release measurement

tdelay

S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

Release measurement

tdelay

S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

Release measurement

tdelay

Simple model

Every collision resets the impurity’s velocity to 0, then gravity accelerates again

Mean time between collision events:

Time delay accumulated: total number of collisions x time delay per collision

))(/(2 1 gznt Dcoll

0

21 )()(

z

RcollD tzzndzt

S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

“Far field” distribution of the impurities

“Far field” distribution of the impurities

“Far field” distribution of the impurities

“Far field” distribution of the impurities

=3 =5 =7

unscatteredscattered

S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

a)

b)

c)

“Far field” distribution of the impurities

=3 =5 =7

unscatteredscattered

• Fermionization?• Enhancement of multiple collision events due to strong interactions?• ?

S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

a)

b)

c)

How to control the impurities in the gas?

• Problem: once created, the impurity dynamics cannot be controlled

How to control the impurities in the gas?

• Problem: once created, the impurity dynamics cannot be controlled

FORGET ABOUT SPIN IMPURITIES,WE NEED A NEW STRATEGY!

Quantum degenerate atoms

• Macroscopic quantum systemat nano Kelvin temperature

• Collective quantum states of 106 particles• Very long coherence times

Ultracold trapped ions

• Single particle detection and manipulation

• Pristine source for quantum information processing & precision spectroscopy

Impurities in a Bose gas: a new approach

A new approach to• Ultracold collisions & quantum chemistry• Quantum information processing and decoherence• Quantum many-body physics with impurities

Hybrid quantum system

related work with trapped ions @ MIT, Innsbruck/Ulm, Uconn, Weizmann,UCLA,..[free ions: Rice, Michigan, Durham, Maryland, ... ]

Atom-ion hybrid trap

Ultracold atom-ion collisionsIon trap (level spacing 5 mK)

Bose-Einstein condensateT 100 nK, trap depth 3 mK

Ultracold atom-ion collisionsIon trap (level spacing 5 mK)

Bose-Einstein condensateT 100 nK, trap depth 3 mK

Measured atom loss cross section:sloss = (2.2±0.2)·10-13 m2

Determine ion temperature from sloss sel(kBT) + (2 kBT/mw2)

T 2 mK (almost Doppler temperature)

C. Zipkes, S. Palzer, CS, Michael Köhl, Nature, 464 388(2010)

Sympathetic cooling of an ion in a BEC

• Rapid cooling

• First demonstration of cooling an object different from other neutral species using ultracold atoms

• Ultimate cooling limits need to be explored with a different technique (eg. Raman spectroscopy)

C. Zipkes, S. Palzer, CS, Michael Köhl, Nature, 464 388(2010)

Atom-ion reaction processes

• Elastic collisionsion changes vibrational quantum state, atom heats up

• Charge-exchange collisionsYb+ + Rb → Yb + Rb+

Yb+ + Rb → (YbRb)+

C. Zipkes, S. Palzer, L. Ratschbacher, CS, Michael Köhl, ArXiv:1005.3846

A single impurity as a local probe

C. Zipkes, S. Palzer, L. Ratschbacher, CS, Michael Köhl, ArXiv:1005.3846

Summary

• Quantum transport in a strongly interacting Bose gas with an accelerated impurity

• High resolution tomography

• Strong dynamics and back action of the impurity

• Far field distribution: effects of fermionization?

• New approach to study impurities: single trapped ion in a BEC

Thanks!

Funding: EPSRC, ERC, Univ. of Cambridge, Herchel-Smith Fund

PI M. Köhl

Ion & BEC: S. Palzer, C. Zipkes, L. Ratschbacher, H. Meyer, M. Steiner. C.S.

Fermi gas: M. Feld, B. Fröhlich, E. Vogt, K. Beck (first Fermi gas in the UK since Nov 2009)

Dynamic structure factor

Scattering rate of an impurity (Fermi’s golden rule):

))()()((),( qkkqSddq fi www S(q,w): dynamic structure factorki , kf : initial and final momentum of the impurityw(q): excitation spectrum of the gas

))()()((),( qkkqSddqE fi wwww

Collision rate and energy dissipation

gasGirardeauTonks

1/1/ln

2

gasBoseginteractinweaklyv

21

1

21

21

2

Fi

Fi

FD

D

D

D

kkkk

kman

amn

For equal masses: impurities move collisionless through a superfluid and a Tonks-Girardeau gases for v<c.

Collision rate (v>c)

gasGirardeauTonksv2

gasBoseginteractinweaklyv

1v2

21

12

4

21

12

D

D

D

D

man

cma

n

E

Energy dissipation (v>c)

constant force 50% of gravity

for heavy impurities: Astrakharchik & Pitaevskii, Davis et al., ...