cooperative phenomena - goethe university frankfurt · inhomogeneous quantum phases and dynamics in...
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Transregio 49 Frankfurt / Kaiserslautern / Mainz
Cooperative Phenomena
Excitations & Interactions
A10, B5,B8, B12
A5, A7, A9,A12, B3
A3, A8, B1,B2, B4, B6,
B9, B11, B13N
A10, B5, B8A7, A9, A12B1, B2,B4, B6, B13N
Materials Design - Synthesis & Modelling
Frankfurt am Main Kaiserslautern Mainz
Materials Design - Synthesis & ModellingMaterials Design - Synthesis & Modelling
B1, B2,B4, B6, B13N
Materials Design - Synthesis & ModellingMaterials Design - Synthesis & ModellingMaterials Design - Synthesis & Modelling
A7, A9, A12
Materials Design - Synthesis & Modelling
A10, B5, B8
Excitations & InteractionsExcitations & InteractionsExcitations & Interactions
A3, A8, B1,B2, B4, B6,
B9, B11, B13N
Excitations & InteractionsExcitations & Interactions
A5, A7, A9,A12, B3
A10, B5,B8, B12
Cooperative Phenomena
A5, A7, A9, A12, B3
A3, A8, B1,B2, B4, B6,
B9, B11, B13N
A10, B5,B8, B12
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Cooperative Phenomena
critical phenomena
non-equilibrium dynamics
quantum magnetism
phonon & polaron physics
Mott transition
superconductivity
spin liquids
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Model-based systems
Cooperative Phenomena
Solid state real materials
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Transregio 49 Frankfurt / Kaiserslautern / Mainz
Model-based systems
Cooperative Phenomena
Solid state real materials
3
Transregio 49 Frankfurt / Kaiserslautern / Mainz
Multi-polaron effects with spinless and spinful impurities in a bosonic quantum gas
Advanced numerical methods for correlated quantum gases
Interacting magnons and critical behaviour of bosons
Inhomogeneous quantum phases and dynamics in ultracold gases and hybrid atom-ion systems
Collective effects and instabilities of a magnon gas
Ultracold Bose gases with variable interactions
Designing spin-spin interactions in cold ion crystals
Experiment Theory
Cooperative Phenomena
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A9
A3
A5 A10
A12 A8
B1 B2 B3 B4 B5 B6 B7E B8 B9 B11
B13N B12
B10E
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Bose-Einstein condensation in an ultra-hot gas of pumped magnons
Critical phenomena & dynamics
evaporative supercooling à formation of magnon BEC after pumping is switched off
Nature Commun. 5, 4452 (2014)
Experimental method
Time-, space- and wavevector-resolved BLS spectroscopy
Low temp. magnon gas Hot magnon gas Ultra-hot magnon gas
Pumping power 1 W Pumping power 4 W Pumping power 25 W
PRB 89, 184413 (2014)
magnon-phonon scattering à different thermalization rates and two magnon temperature
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A7 A8
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APL 99, 162501 (2011) APL 103, 142415 (2013) APL 104, 092418 (2014) APL 104, 202408 (2014) APL 105, 232409 (2014)
Dynamics of magnon gases in spatially confined structures
Microsized parametric amplifier
Critical phenomena & dynamics
Spatially confined magnon condensates and coherent magnon transport
Coherent interactions & phase transitions in magnon gases
Theory of magnon-phonon interaction and non-equilibrium dynamics
Next:
A7
A7
A8
à toolbox for magnon BECs in micro-sized samples
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Dimensional phase transition from 1D to 3D
§ study coupled 1D Bose gases à 3D condensation § extract phase diagram & comparison with theory
ultracold bosons in an optical lattice
Transport in mixed dimensions
§ superimpose lattice in longitudinal direction § à coupled 1D Mott insulators
Critical phenomena & dynamics
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B3
A9
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Next:
PRL 113, 215301 (2014)
µ/kBT
latti
ce h
eigh
t
3D condensate
decoupled 1D
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Quench dynamics of strongly correlated bosons in 2d, 3d dynamical arrest
Strongly correlated mass transport
non-equilibrium tunneling transport of atoms in a Mott insulator state
Critical phenomena & dynamics
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A3 A9
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Dynamical arrest & quantum distillation
§ non-adiabatic evolution during lattice ramp
§ fermions
Phys. Rev. Lett. 110, 075302 (2013).
Critical phenomena & dynamics
§ bosons, 1D Phys. Rev. A 110, 013615 (2012).
Negative differential conductivity
§ non-equilibirum initial condition
§ current-voltage characteristics
appearance of NDC
A3 A5
A9
arXiv:1411.5632 9
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Quantum Magnetism
Tunable magnetic order
Phys. Rev. A 86, 043620 (2012)
§ bosonic magnetism on triangular lattice § frustration
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HE, LI, ALTMAN, AND HOFSTETTER PHYSICAL REVIEW A 86, 043620 (2012)
In the following discussion, we assume h = 0, i.e., vanishingspin imbalance (in the case of asymmetric hopping ta = tb, thechemical potentials µa and µb are tuned to achieve this). Onbipartite lattices (e.g., square, cubic) the system supports xy-ferromagnetic order for J⊥ > Jz > 0, which is characterizedby the local correlator ⟨a†b⟩, and z-antiferromagnetic orderfor Jz > J⊥ > 0, characterized by the order parameter!af = |⟨Sz
α⟩ − ⟨Szα⟩| with α (α = −α) being the sublattice
index.We expect new interesting physics to emerge in a system
with a triangular instead of bipartite optical lattice. Forantiferromagnetic exchange coupling Jz, it is impossible tominimize the energy of the spin configuration on each latticebond, i.e., geometric frustration arises and the system maydevelop exotic phases at low temperature. We are particularlyinterested in the extremely asymmetric hopping regime forthe full range of couplings from Mott insulator to superfluid.Since higher-order density fluctuations of the “lighter” speciesare expected to become even larger than the low-order densityfluctuation of the “heavier” ones, their interplay with Ising-type frustration in z allows the system to form novel phases.Also frustration is expected to grow with increasing valuesof the hopping amplitudes since the exchange coupling arisesfrom the itinerancy of atoms. In the following, we shall addressthese two aspects by mapping out the ground-state phasediagram for total filling one per site via BDMFT.
Before going into a detailed discussion of the system’sproperties, let us at this point briefly introduce BDMFT[7–9], which is an extension of dynamical mean-field the-ory (DMFT) [13,14], originally developed to treat stronglycorrelated fermionic systems. It is nonperturbative, captureslocal quantum fluctuations exactly, and becomes exact inthe infinite-dimensional limit. Note that for antiferromagneticexchange Jz the ground state of the system may break thetranslational symmetry of the lattice. We investigate thissystem using real-space BDMFT (R-BDMFT) [15], whichis a generalization of BDMFT to a position-dependent self-energy and captures inhomogeneous quantum phases. WithinBDMFT or R-BDMFT, the physics on each lattice site isdetermined from a local effective action which is obtainedby integrating out all the other degrees of freedom in thelattice model, excluding the lattice site considered. The localeffective action is then represented by an Anderson impuritymodel [7–9]. We use exact diagonalization (ED) [16,17] of theeffective Anderson Hamiltonian with a finite number of bathorbitals to solve the local action (nbath = 4 bath orbitals arechosen in the current work). Details of the R-BDMFT methodhave been published previously [15].
III. RESULTS
Since we are mainly interested in the effects of geometricfrustration, we focus on the parameter regime Va = Vb ≫U , where the leading exchange couplings become Isingantiferromagnetic for highly asymmetric hopping, resultingin Ising-type frustration. In our simulations, the chemicalpotentials µa and µb are tuned to equal particle numberof both species (Na ≡
!i⟨nia⟩ = Nb ≡
!i⟨nib⟩) and a total
filling factor ρ =!
i⟨nia + nib⟩/Nlat = 1 (Nlat is the numberof lattice sites.). The full range of interactions from strong
coupling, deep in the Mott phase, all the way to the superfluidat weak coupling is investigated within BDMFT.
Our main results are summarized in Fig. 1(a), whichshows the ground-state phase diagram for large intraspeciesinteraction strengths (Va,b/U = 48). Two different magneticphases are found in the Mott insulator. When ta and tb areof comparable magnitude, the leading exchange couplingis ferromagnetic in the xy-plane, and the system is in thexy-ferromagnetic phase, characterized by a uniform magne-tization in the xy-plane. On the other hand, for sufficientlylarge asymmetry between the two hopping amplitudes, weobserve two types of SDW phases [insets Figs. 1(a.1) and1(a.2)], which break the translation symmetry of the lattice.All of these spin-ordered phases are found to persist up tothe superfluid transition. For large hopping the ground statebreaks U(1) symmetry and develops superfluid order ⟨a⟩,⟨b⟩.
FIG. 1. (Color online) (a) Ground-state phase diagram at unitfilling ρ = 1, with Va = Vb = 48U , obtained from calculations ona 6 × 6 triangular lattice. We observe four major different phases,which are the homogeneous superfluid (HSF), xy-ferromagnet, SDW,and supersolid (SS). In the SDW region, the area where the SDW hasa 3-sublattice structure is marked in yellow, while the area featuringthe stripe SDW is marked red. The insets (a.1) and (a.2) show thecorresponding z-magnetization distribution ⟨Sz
i ⟩. The small blue areaindicates a coexistence region of HSF and stripe SDW phases. (b)The triangular lattice considered here with sublattice indices A,B,C
marked near the corresponding lattice sites. a1 and a2 are the twolattice vectors. (c) tb dependence of the 3-sublattice SDW orderparameter at fixed 9ta/U = 0.6.
043620-2
ta/U
t b/U
XY ferromag
SS
SS stripe SDW
SDW
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Phonon and Polaron physics
Hybrid quantum simulator § ultracold atoms in a dynamical lattice of trapped ions emulating electronic solids including phonons Phys. Rev. Lett. 111 , 080501 (2013)
A3 A10
ions
atoms
§ planar Paul trap with Yb+ crystal § magnetic trap for Rb BEC § tight confinement à 1D atom-ion system
Paul trap layer
Magnetic trapping layer
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A10 Next:
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Polarons in Solid State Systems Phonon and Polaron physics
Polaron in solid-state physics
A12 Next: Bose-polaron of neutral impurities in a BEC
§ simulate Fröhlich polaron with tunable impurity-BEC interactions § spectroscopy on weak and strongly coupled polarons § lattice-polaron or quasi free-polaron dynamics
BEC density
weak intermediate strong coupling
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§ Bloch oscillations, multiband physics
§ detection of polaron by RF spectroscopy
§ many-polaron phases
§ relaxation dynamics of supersonic impurity in BEC
A3 Hofstetter
studies of polarons in a BEC exist (see for example [26–29]), no experimental observation has yetbeen achieved, although neutral impurities in ultracold bosonic baths have been realized [30–33].We will focus on e↵ects of multiple bands, tilted lattices and interactions between impurities.We treat the BEC within the Bogoliubov approximation, and extend the non-perturbative Lang-Firsov transformation [27] to a system with two (impurity) bands, which yields an e↵ective PolaronHamiltonian including coherent hopping and longer-range interactions
Hpi,j
↵
J↵
a↵
i
a↵
j
i,↵
✏↵
a↵
i
a↵
i
s!sbsbs
i,j,↵
V ↵
i,j
n↵
i
n�
j
(5)
where a and b denote Cs atoms and Bogoliubov phonons, i, j are lattice site indices and ↵ labelsthe Bloch bands. This system can then be described by the Lindblad master equation
d⇢p
dti Hp,⇢p ⇢p (6)
Figure 5: Cs impurity in a Rb BEC. Due toan optical lattice, multiple Bloch bands of theimpurity arise.
where the dissipator models the residual Marko-vian coupling to the phononic bath, capturing dis-sipative impurity dynamics beyond Fermi’s GoldenRule. One focus will be on polaronic Bloch oscillati-ons in an accelerated lattice, which can be monitoredin situ and whose frequency depends on the stronglyenhanced e↵ective mass of the polaron. While single-band polaronic Bloch oscillations have been studiedbefore [27, 29], little is known about the e↵ect of asecond impurity Bloch band, into which single atomscan be excited in a controlled fashion. We will investigate damped Bloch oscillations and Landau-Zener tunneling, and calculate the drift velocity of the polarons and the resulting current-voltagecharacteristics. After controlled preparation of an impurity in the excited band, we will calcula-te the interband relaxation rate and the decoherence time that have already been measured in adi↵erent setup with 6Li in 23Na [34], and the resulting non-equilibrium steady state which resultswhen the interband drive (induced e.g. by microwaves) is continuous. In addition, the RF responseof the dilute impurity system will be calculated, as previously for the single-band case [35], andmeasured in project A12 (Widera), thus allowing for detection of the polaron binding energy andthe quasiparticle residue. By combining an accelerated optical lattice with periodic lattice modula-tion, photon-assisted tunneling resonances will be studied [36], where we expect the polaron massto be visible.We will furthermore investigate the case of multiple bosonic impurities, where clustering of polarons[37] or long-range ordered polaronic phases are expected. These calculations will be based on bosonicGutzwiller and R-DMFT, applied to the e↵ective polaron Hamiltonian (5). The residual dissipativecoupling to the phonon bath in the steady state will first be neglected, and later included viathe recently developed combination of DMFT and the Lindblad equation [39]. For bosons with ahyperfine spin degree of freedom, tunable quantum magnetic order has been shown to arise in theMott insulating state [40]. We will investigate how the coupling to the BEC modifies these magneticphases, i.e. whether it can possibly stabilize and enhance certain types of polaronic magnetic order.Complementary to the above, we will also study static (i.e. spatially frozen) Cs impurities in a RbBEC from a quantum impurity perspective, where two hyperfine states of 133Cs form a two-levelsystem or pseudospin 1 2. Using Wilson’s Numerical Renormalization Group (NRG) [41, 42], wewill study impurity spin dynamics such as dynamical synchronization of driven Rabi-oscillationsfor two Cs impurities interacting with a common bosonic Rb bath, based on our previous work [43],and in cooperation with the planned TEBD simulations in Project A5 (Fleischhauer/Eggert).Polaronic impurity dynamics similar as described above will also be studied in an ongoing colla-boration with project A10 (Gerritsma/Schmidt-Kaler) for the recently proposed hybrid quantum
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Theory of polarons & impurity dynamics in lattices and BECs
Phonon and Polaron physics
Next:
A3 A5
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Cooperative Phenomena
critical phenomena
non-equilibrium dynamics
quantum magnetism
phonon & polaron physics
Mott transition
Superconductivity
spin liquids
14
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Cooperative Phenomena
critical phenomena
non-equilibrium dynamics
quantum magnetism
phonon & polaron physics
Mott transition
superconductivity
spin liquids
14
Transregio 49 Frankfurt / Kaiserslautern / Mainz
Model-based systems
Cooperative Phenomena
Solid-state real materials
15