Cooperative Phenomena - Goethe University Frankfurt · Inhomogeneous quantum phases and dynamics in ultracold gases and hybrid atom-ion systems Collective effects and instabilities

Transregio 49 Frankfurt / Kaiserslautern / Mainz

Cooperative Phenomena

Excitations & Interactions

A10, B5,B8, B12

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Materials Design - Synthesis & Modelling

Frankfurt am Main Kaiserslautern Mainz

Materials Design - Synthesis & ModellingMaterials Design - Synthesis & Modelling

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Materials Design - Synthesis & ModellingMaterials Design - Synthesis & ModellingMaterials Design - Synthesis & Modelling

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Materials Design - Synthesis & Modelling

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Excitations & InteractionsExcitations & InteractionsExcitations & Interactions

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Excitations & InteractionsExcitations & Interactions

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critical phenomena

non-equilibrium dynamics

quantum magnetism

phonon & polaron physics

Mott transition

superconductivity

spin liquids

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Model-based systems


Solid state real materials

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Model-based systems


Solid state real materials

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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


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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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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


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:

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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


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PRL 113, 215301 (2014)

µ/kBT

latti

ce h

eigh

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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


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Dynamical arrest & quantum distillation

§  non-adiabatic evolution during lattice ramp

§  fermions

Phys. Rev. Lett. 110, 075302 (2013).


§  bosons, 1D Phys. Rev. A 110, 013615 (2012).

Negative differential conductivity

§  non-equilibirum initial condition

§  current-voltage characteristics

appearance of NDC

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arXiv:1411.5632 9


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)

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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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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

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critical phenomena


quantum magnetism


Mott transition

Superconductivity

spin liquids

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critical phenomena


quantum magnetism


Mott transition

superconductivity

spin liquids

14


Model-based systems


Solid-state real materials

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Cooperative Phenomena - Goethe University Frankfurt · Inhomogeneous quantum phases and dynamics in ultracold gases and hybrid atom-ion systems Collective effects and instabilities