Quantum Phases of Dipolar Molecules - scl.rs€¦ · 1 Quantum Phases of Dipolar Molecules Carlos...
Transcript of Quantum Phases of Dipolar Molecules - scl.rs€¦ · 1 Quantum Phases of Dipolar Molecules Carlos...
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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
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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.
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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..
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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..
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Some of our efforts Some of our efforts on dipolar molecules.on dipolar molecules.
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Main References for TalkMain References for Talk
+ UNPUBLISHED(in preparation 2011).
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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
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Introduction: Introduction: HeteronuclearHeteronuclear MoleculesMolecules
2
2
2
2
2
2
CsRbNaKLiH
CsCsRbRbNaNaKKLiLiHH
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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.
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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
=∆<<
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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.
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Dipole Moment of Dipole Moment of HeteronuclearHeteronuclear MoleculesMolecules
R
E
D
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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
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2422
22 rrVrdrdrm
rdH rrrh−+∇= ∫∫ ψθψ
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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.
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Dipolar Bosons ContinuumDipolar Bosons Continuum
2
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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
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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
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Transition from Transition from superfluidsuperfluid to to dipolar Wigner crystal (T = 0)dipolar Wigner crystal (T = 0)
s
awα = s/aw
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Transition from Transition from SuperfluidSuperfluid to to dipolar Wigner crystaldipolar Wigner crystal
EG
rD = 15
rD = 26rD = 47Super
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Phase DiagramPhase Diagram
Hexatic
Wigner CrystalSuperfluid
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TwoTwo--stage melting: emergence of stage melting: emergence of the dipolar the dipolar hexatichexatic phasephase
Elastic energy
Lame coefficients 2
Strain tensor
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Dislocation mediated meltingDislocation mediated melting
Elementary dislocation
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Translational versus Translational versus orientationalorientational(Wigner crystal versus (Wigner crystal versus hexatichexatic))
Hexatic
Wigner Crystal
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TwoTwo--stage melting: emergence stage melting: emergence of the normal phaseof the normal phase
Bond angle field
Energy
Critical Temperature
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TwoTwo--stage melting: emergence stage melting: emergence of the normal phaseof the normal phase
Hexatic
Wigner CrystalSuperfluid
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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
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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
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Additional phases possible in Additional phases possible in continuum 2D dipolar problem.continuum 2D dipolar problem.
DSS = Dipolar SupersolidDHSF = Dipolar Hexatic Superfluid
DHSFDSS
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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..
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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