bec polarons quasicrystals - harvard university
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Modulation spectroscopyModulation spectroscopyBEC polaronsQuasicrystals
Everything is work in progress
$$ NSF, MURI ATOMTRONICS, MURI QuISM, DARPA OLE
Harvard-MIT
Lattice modulation experiments as aLattice modulation experiments as a probe of collective mode dispersion
Based on recent discussion with Immanuel BlochRecent results by Michael Knap (Harvard)Earlier results by David Pekker (Harvard,Caltech)
Modulation experiments in optical latticeObservation of the Anderson Higgs modeObservation of the Anderson-Higgs mode
M. Endres et al., Nature 487:454 (2012)
Lattice modulation probe of collective mode dispersion
Modulation performed at zero wavevector.How can this probe finite momentum modes?How can this probe finite momentum modes?
Faraday waves M F d Phil hi l T ti f th R l S i tM. Faraday, Philosophical Transactions of the Royal Society (London), vol. 121, pages 299–318 (1831)
Faraday waves in BEC
From wavefunction
we expect the appearance of and
Density acquires ripples
We expect ripples peaked at the resonance wavevector
Modulation spectroscopyInteresting applications
Particle-hole excitations in the Mott state, excitations in the critical region
Probe of spin waves in a ferromagnetic state
Quantum simulations with ultracold atoms
Atoms in optical lattice
Antiferromagnetic and superconducting Tc
Atoms in optical lattice
Antiferromagnetism and pairing at sub-micro Kelvin p g
of the order of 100 K temperatures
Same microscopic model
Positive U Hubbard modelPositive U Hubbard modelPossible phase diagram. Scalapino, Phys. Rep. 250:329 (1995)
Antiferromagnetic insulator
D-wave superconductorp
--
Signature of d-wave pairing of fermions: dispersion of quasiparticlesdispersion of quasiparticles
- Superconducting gap
++-
Normal state dispersion of quasiparticles
Quasiparticle energies
Low energy quasiparticles correspond to four Dirac nodesto four Dirac nodes
Observed in:
• Photoemission• Raman spectroscopy• T-dependence of thermodynamic and transport properties c and transport properties, cV, , L
• STM• and many other probes
Probing polaronsin bosonic systemsin bosonic systems
Dima Abanin (Harvard Perimeter),Adiya Shashi (Rice/Harvard)Eugene DemlerEugene Demler+ recent discussion with Immanuel Bloch
Polarons in ultracold atoms: fermionic environment
2D Kohl et al., Nature (2012)3D Zwierlein et al., PRL (2009)3D Zwierlein et al., PRL (2009)
Dynamics of BEC polarons. Spectral functionRF t f i t t
Interacting
RF spectroscopy of spin states
g
NoninteractingNoninteracting
Transitions of localized impurity atoms
Change of the impuritywavefunction excitesBogoliubov phononsg pin BEC
Dynamics of BEC polarons. Langs-Firsov transformation approachg pp
Conserved total momentum of the system p is now explicitly separated
Interaction between impurity and phonons was traded forinteractions between phonons
Dynamics of BEC polarons. RF absorption for finite impurity massp p y
Signatures of self-trapping transition?
Quantum quasicrystalsof spin orbit coupled bosons
Sarang Gopalakrishnan (Harvard)
I M ti (L Al /A )Ivar Martin (Los Alamos/Argonne)
Eugene Demler (Harvard)
What are quasicrystals
Associated with fivefold (or sevenfold) symmetry: pentagons
Translational order without periodicity( iti f til d t i th ti tili b t th tili i i di )
in 2D, dodecahahedra/icosahedra in 3D
(position of tile determines the entire tiling, but the tiling is aperiodic)
Sharply defined Bragg peaks that are inconsistent with space group(spatial periodicity)(spatial periodicity)
Conjectured in models with multiple incommensurate length scales(e g Mermin Troian PRL 1985)(e.g. Mermin, Troian, PRL 1985)
Origin is still a subject of debate (equilibrium or metastable states)
Phase diagram of Bose-Fermi mixturewith spin orbit coupling for bosons
2kF
p p g
k0q0
One species of fermions Two species of fermions
Idea: Bose-Fermi mixtures
Use Fermi momentum to engineerUse Fermi momentum to engineermomentum dependent interactions
Make 2kf to provide 5-foldcovering of the spin orbit circlecovering of the spin-orbit circle
Quasicrystals in systems with competing lengthscales Mermin, Troian, PRL 1985
Order parameter y has preferred wave vector q
Order parameters fi have preferred wave vectors kiMany possible phases depending on q, ki
Competition of Bravais lattices and quasicrystals
k k
Competition of Bravais lattices and quasicrystals
k1
q
k k
q q
k1
k2q q
k
q2
Mean-field theory with renormalized interactionsyOne species of fermions
2kF
k0q0
Several competing Bravais latticesNo quasicrystals
Mean-field theory with renormalized interactionsyTwo species of fermions
Quasicrystal is the only configuration that can benefit from both
Quantum quasicrystals beyond mean-fieldNew aspects of crystal order intertwined with superfluidity.Example FFLO
Significance of wavefunction signHybrid defects, e.g. half-vortex half-dislocation orhalf vortex half disclinationhalf-vortex half-disclination
Even richer phenomena for quantum quasicrystals