11

Quantum Phases of Quantum Phases of Dipolar MoleculesDipolar Molecules

Carlos A. R. Sa de Carlos A. R. Sa de MeloMeloGeorgia Institute of TechnologyGeorgia Institute of Technology

Institute of Physics (Belgrade): July 18th, 2011

22

ZAHVALNOSTZAHVALNOSTZELIM DA SE ZAHVALIM ANTUN BALAZ, STO ZELIM DA SE ZAHVALIM ANTUN BALAZ, STO MI JE OMOGUCIO DA ODRZIM PREDAVANJE MI JE OMOGUCIO DA ODRZIM PREDAVANJE NA INSTITUTU ZA FIZIKU U PRELEPOM NA INSTITUTU ZA FIZIKU U PRELEPOM BEOGRADU. IAKO BIH ZELEO DA MOGU DA BEOGRADU. IAKO BIH ZELEO DA MOGU DA ODRZIM PREDAVANJE NA SRPSKOM, MOJE ODRZIM PREDAVANJE NA SRPSKOM, MOJE ZNANJE SRPSKOG JEZIKA JE NA ZALOST ZNANJE SRPSKOG JEZIKA JE NA ZALOST OGRANICENO, ZATO CU SADA MORATI DA OGRANICENO, ZATO CU SADA MORATI DA SE PREBACIM NA ENGLESKI. SE PREBACIM NA ENGLESKI.

33

OutlineOutline

Introduction: Introduction: heteronuclearheteronuclear moleculesmolecules

What are dipolar What are dipolar superfluidssuperfluids??

Quantum phases of dipolar bosons in 2D.Quantum phases of dipolar bosons in 2D.

Conclusions.Conclusions.ConclusionsConclusions..

44

ConclusionsConclusions

The possible quantum phases of dipolar The possible quantum phases of dipolar bosons in 2D include:bosons in 2D include:

SuperfluidSuperfluid, Wigner crystal, and , Wigner crystal, and hexatichexatic and and normal liquid phases.normal liquid phases.

SupersolidSupersolid and and hexatichexatic superfluidsuperfluid..

55

Some of our efforts Some of our efforts on dipolar molecules.on dipolar molecules.

66

Main References for TalkMain References for Talk

+ UNPUBLISHED(in preparation 2011).

77

OutlineOutline

Introduction .Introduction .

What are dipolar What are dipolar superfluidssuperfluids..

Quantum phases of dipolar bosons in 2D.Quantum phases of dipolar bosons in 2D.

Conclusions.Conclusions.

Introduction: Introduction: heteronuclearheteronuclear moleculesmolecules

88

Introduction: Introduction: HeteronuclearHeteronuclear MoleculesMolecules

2

2

2

2

2

2

CsRbNaKLiH

CsCsRbRbNaNaKKLiLiHH

99

Introduction: Dipole Moment of Introduction: Dipole Moment of HeteronuclearHeteronuclear MoleculesMolecules

CsCsRbRbNaNaKKLiLiHHR

2

2

2

ˆˆ

Rotor Quantum Rigid

RLHµ

=

1010

Introduction: Dipole Moment of Introduction: Dipole Moment of HeteronuclearHeteronuclear MoleculesMolecules

),(2

)1(),(2

ˆ:sEigenstate

2

2

2

2

ϕθµ

ϕθµ lmlm Y

RllY

RL h+

=R

2

2

10 2 RE

µh

=∆E0

E1

1111

Introduction: Dipole Moment of Introduction: Dipole Moment of HeteronuclearHeteronuclear MoleculesMolecules

),(2

)1(),(2

ˆ:sEigenstate

2

2

2

2

ϕθµ

ϕθµ lmlm Y

RllY

RL h+

=R

Spherical Harmonics have welldefined parity, thus the expectation

value of the dipole operator in any eigenstate (and in particular

the ground state) is zero.

1212

Introduction: Dipole Moment of Introduction: Dipole Moment of HeteronuclearHeteronuclear MoleculesMolecules

E0

E1R

At low T therelittle admixtureof states with

different parity:need electric field!

2

2

10 2 RET

µh

=∆<<

1313

Dipole Moment of Dipole Moment of HeteronuclearHeteronuclear MoleculesMolecules

Electric dipole moments of molecules at very low T arenot intrinsic, as they would require spontaneous breaking of parity.

R

In contrast, magnetic dipolar moments associated with spin are intrinsic.

1414

Dipole Moment of Dipole Moment of HeteronuclearHeteronuclear MoleculesMolecules

R

E

D

1515

OutlineOutline

Introduction: Introduction: heteronuclearheteronuclear moleculesmolecules

What are dipolar What are dipolar superfluidssuperfluids??

Quantum phases of dipolar bosons in 2D.Quantum phases of dipolar bosons in 2D.

Conclusions.Conclusions.

What are dipolar What are dipolar superfluidssuperfluids??..

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What is a dipolar What is a dipolar superfluidsuperfluid??

A A superfluidsuperfluid with dipolar internal degrees with dipolar internal degrees of freedom.of freedom.

p µ µp

Magnetic DipolesElectric Dipoles

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Candidates for dipolar Candidates for dipolar superfluidssuperfluids

Atoms with large magnetic dipole Atoms with large magnetic dipole moments.moments.

HeteronuclearHeteronuclear molecules with permanent molecules with permanent electric dipole moments.electric dipole moments.

RydbergRydberg atoms with large electric dipole atoms with large electric dipole moments.moments.

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Tuning the ratio of longTuning the ratio of long--range to range to shortshort--range interactionsrange interactions

Distortion of 52Cr cloud via reduction of short range interactions

Th. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, T. Pfau: “Strong dipolar effects in a quantum ferrofluid”, Nature 448; 672 (2007).

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Dipolar Dipolar SuperfluidsSuperfluids in 2Din 2D

2

1st approximation: BKT Physics…

)()(2 212

21

2422

22 rrVrdrdrm

rdH rrrh−+∇= ∫∫ ψθψ

2020

OutlineOutline

Introduction: Introduction: heteronuclearheteronuclear molecules.molecules.

What are dipolar What are dipolar superfluidssuperfluids??

Quantum phases of dipolar bosons in 2D.Quantum phases of dipolar bosons in 2D.

Conclusions.Conclusions.

Quantum phases of dipolar bosons in 2D.Quantum phases of dipolar bosons in 2D.

2121

Dipolar Bosons ContinuumDipolar Bosons Continuum

2

2222

Relevant Parameters Relevant Parameters and Ratios of Energiesand Ratios of Energies

~ Uρ

~ D2ρ3/22rD ~2mD2 ρ1/2/h2

2

rD = ED/K

1<<DrDipolar Superfluid expected forDipolar Wigner Crystal expected for

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Dipolar Dipolar SuperfluidsSuperfluids in 2D: in 2D: rrDD << 1<< 1

rD = ED/K << 1

2

For small dipolar interactions1st approximation: BKT Physics…

)()(2 212

21

2422

22 rrVrdrdrm

rdH rrrh−+∇= ∫∫ ψφψ

2424

First set U = 0 (First set U = 0 (rrUU = 0)= 0)Dipolar Wigner crystal expected for: small masses,large dipole moments andhigh densities. Notice that the dependence on densityis the opposite for the 2D Coulomb-Wigner crystal.

rD ~ ρ1/2

2

rs ~ ρ-1/2 rs >> 1

Ec = C/a rs = 2mCa/h2 Low densities

2525

Transition from Transition from superfluidsuperfluid to to dipolar Wigner crystal (T = 0)dipolar Wigner crystal (T = 0)

s

awα = s/aw

2626

Transition from Transition from SuperfluidSuperfluid to to dipolar Wigner crystaldipolar Wigner crystal

EG

rD = 15

rD = 26rD = 47Super

2727

Phase DiagramPhase Diagram

Hexatic

Wigner CrystalSuperfluid

2828

TwoTwo--stage melting: emergence of stage melting: emergence of the dipolar the dipolar hexatichexatic phasephase

Elastic energy

Lame coefficients 2

Strain tensor

2929

Dislocation mediated meltingDislocation mediated melting

Elementary dislocation

3030

Translational versus Translational versus orientationalorientational(Wigner crystal versus (Wigner crystal versus hexatichexatic))

Hexatic

Wigner Crystal

3131

TwoTwo--stage melting: emergence stage melting: emergence of the normal phaseof the normal phase

Bond angle field

Energy

Critical Temperature

3232

TwoTwo--stage melting: emergence stage melting: emergence of the normal phaseof the normal phase

Hexatic

Wigner CrystalSuperfluid

3333

Bragg Diffraction PatternsBragg Diffraction Patterns

Superfluid Wigner

Hexatic

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Are there any additional phases?Are there any additional phases?

What about a supersolid phase:coexistence of superfluid order and density order, i.e., superfluid density is modulated.

= superfluid regions

s

aSSαss = s/ass

3535

Comparison with Comparison with 44HeHeIn 4He the system is in a solid phase and the superfluid component is due to defects.

In ultra-cold gases there is no solid phase, butinstead the coexistence between superfluidorder and discrete translational order.

s

aSSαss = s/ass

= superfluid regions

3636

Additional phases possible in Additional phases possible in continuum 2D dipolar problem.continuum 2D dipolar problem.

DSS = Dipolar SupersolidDHSF = Dipolar Hexatic Superfluid

DHSFDSS

3737

OutlineOutline

Introduction: Introduction: heteronuclearheteronuclear molecules.molecules.

What is a dipolar What is a dipolar superfluidsuperfluid??

Quantum phases of dipolar bosons in 2D.Quantum phases of dipolar bosons in 2D.

Conclusions.Conclusions.ConclusionsConclusions..

3838

ConclusionsConclusions

The possible quantum phases of dipolar The possible quantum phases of dipolar bosons in 2D include:bosons in 2D include:

SuperfluidSuperfluid, Wigner crystal, and , Wigner crystal, and hexatichexatic and and normal liquid phases.normal liquid phases.

SupersolidSupersolid and and hexatichexatic superfluidsuperfluid..

(HVALA NA PAZNJI)(HVALA NA PAZNJI)

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END OF TALKEND OF TALK