Exploring Frustrated Quantum Antiferromagnetism with Ultracold Atoms in Shaken Optical Lattices

Transcription

1 Exporing Frustrated Quantum Antiferromagnetism with Utracod Atoms in Shaken Optica Lattices André Eckardt & Maciej Lewenstein ICFO-Institut de Ciències Fotòniques Barceona, Spain Quantum Optics VII Quantum Engineering of Atoms and Photons Zakopane, June 8-, 9

2 First part of the Outook: First part of the tak Periodicay forced Bose-Hubbard system Ĥ(t) = Jˆb U ˆb + ˆn (ˆn ) R F (t) ˆn, utracod Utracod atoms in shaken optica attice V with F (t) = F c cos(ωt) e c + F s sin(ωt) e s x

3 First part of the Outook: First part of the tak Periodicay forced Bose-Hubbard system Ĥ(t) = Jˆb U ˆb + ˆn (ˆn ) R F (t) ˆn, with F (t) = F c cos(ωt) e c + F s sin(ωt) e s utracod Utracod atoms in shaken optica attice V x For ω U, J system just dressed by the forcing: Ĥ eff = J, eff ˆb ˆb + U ˆn (ˆn ), Eff Hopping Jeff/J Parameter K ω / hω Driving ampitude ψ eff (t) = exp( Ĥefft) i ψ eff () (sow time-evoution governed by Ĥ eff ) ψ(t) exp ( i ˆn R ) p(t) ψeff (t) (fast osciation in quasimomentum) [PRL 95, 644 (5), PRL, 453 (8)]

4 First part of the Outook: First part of the tak Periodicay forced Bose-Hubbard system Ĥ(t) = Jˆb U ˆb + ˆn (ˆn ) R F (t) ˆn, with F (t) = F c cos(ωt) e c + F s sin(ωt) e s utracod Utracod atoms in shaken optica attice V x For ω U, J system just dressed by the forcing: Ĥ eff = J, eff ˆb ˆb + U ˆn (ˆn ), Eff Hopping Jeff/J Parameter K ω / hω Driving ampitude ψ eff (t) = exp( Ĥefft) i ψ eff () (sow time-evoution governed by Ĥ eff ) ψ(t) exp ( i ˆn R ) p(t) ψeff (t) (fast osciation in quasimomentum) [PRL 95, 644 (5), PRL, 453 (8)] It works (!) Experiment by O Morsch and co-workers in Arimondo-group in Pisa: Superfuid Mott-insuator Superfuid [Zenesini et a, PRL, 43 (9)]

5 Second part of t Outook: Second part of the tak

6 Second part of t Outook: Second part of the tak Consider non-bipartite attice geometry Change sign of hopping matrix eements via dressing by shaking Frustrated Quantum System

7 Second part of t Outook: Second part of the tak Consider non-bipartite attice geometry Change sign of hopping matrix eements via dressing by shaking Frustrated Quantum System Weak interaction: BEC with discrete order parameter ψ = n exp(iϕ ) Loca phases ϕ pay roe of cassica rotors

8 Second part of t Outook: Second part of the tak Consider non-bipartite attice geometry Change sign of hopping matrix eements via dressing by shaking Frustrated Quantum System Weak interaction: BEC with discrete order parameter ψ = n exp(iϕ ) Loca phases ϕ pay roe of cassica rotors Hard core bosons: Quantum spin-/ XY-mode Ĥ XY = J xy (ˆσ x ˆσx + ˆσ y ˆσy ) (two occupation numbers resembe and )

9 Second part of t Outook: Second part of the tak Consider non-bipartite attice geometry Change sign of hopping matrix eements via dressing by shaking Frustrated Quantum System Weak interaction: BEC with discrete order parameter ψ = n exp(iϕ ) Loca phases ϕ pay roe of cassica rotors Hard core bosons: Quantum spin-/ XY-mode Ĥ XY = J xy (ˆσ x ˆσx + ˆσ y ˆσy ) (two occupation numbers resembe and ) Quantum antiferromagnetism with bosonic motiona degress of freedom Achievabe in existing experimenta setups with great freedom for manipuation

10 Second part of t Outook: Second part of the tak Consider non-bipartite attice geometry Change sign of hopping matrix eements via dressing by shaking Frustrated Quantum System Weak interaction: BEC with discrete order parameter ψ = n exp(iϕ ) Loca phases ϕ pay roe of cassica rotors Hard core bosons: Quantum spin-/ XY-mode Ĥ XY = J xy (ˆσ x ˆσx + ˆσ y ˆσy ) (two occupation numbers resembe and ) Quantum antiferromagnetism with bosonic motiona degress of freedom Achievabe in existing experimenta setups with great freedom for manipuation Why is this interesting? frustrated quantum magnets hard to simuate vacua for exotic excitations (confinement, anyonic statistics, ) robust nonoca topoogica order (ideas: quantum memories, quantum computation) exotic quantum phase transitions not described by Landau theory supposed to pay a roe in cuperate suerpconductivity

11 Part: First Part: Dressing utracod atoms in optica attices by time-periodic forcing

12 Atoms in shaken Bosonic Atoms in shaken attice Periodicay shaken optica attice potentia V (r) = V cos(k Lr+ϕ cos ωt) V x Co-moving frame: Homogeneous osciating force Ṽ (r) = V cos(k Lr)+K ω cos(ωt) k Lr π V a

13 Atoms in shaken Bosonic Atoms in shaken attice Periodicay shaken optica attice potentia V (r) = V cos(k Lr+ϕ cos ωt) V x Co-moving frame: Homogeneous osciating force Ṽ (r) = V cos(k Lr)+K ω cos(ωt) k Lr π V a Driven Bose-Hubbard Mode in D (D or 3D straightforward): Ĥ BH (t) = J (ˆb ˆb + + ˆb +ˆb ) + U ˆn (ˆn ) + K ω cos(ωt) dimensioness parameters: fiing n, interaction strength U/J, driving frequency ω/j, driving ampitude K ω / ω ˆn

14 Atoms in shaken Bosonic Atoms in shaken attice Periodicay shaken optica attice potentia V (r) = V cos(k Lr+ϕ cos ωt) V x Co-moving frame: Homogeneous osciating force Ṽ (r) = V cos(k Lr)+K ω cos(ωt) k Lr π V a Driven Bose-Hubbard Mode in D (D or 3D straightforward): Ĥ BH (t) = J (ˆb ˆb + + ˆb +ˆb ) + U ˆn (ˆn ) + K ω cos(ωt) dimensioness parameters: fiing n, interaction strength U/J, driving frequency ω/j, driving ampitude K ω / ω ˆn Consider regime of strong, off-resonant forcing: U, J ω K ω Description beyond inear response theory needed

15 Foquet theoreti Quantum Foquet theoretica approach Hamitonian Ĥ(t + T ) = Ĥ(t) (with T = π ω ) gives rise to soutions ψ(t) = c α u α (t) e iε αt/, with uα (t + T ) = u α (t) α Foquet states u α (t) and Quasienergies ε α take over the roe of stationary states and energies [Shirey, PR 38, B979 (965); Sambe, PRA 7, 6 (973)] They

16 Foquet theoreti Quantum Foquet theoretica approach Hamitonian Ĥ(t + T ) = Ĥ(t) (with T = π ω ) gives rise to soutions ψ(t) = c α u α (t) e iε αt/, with uα (t + T ) = u α (t) α Foquet states u α (t) and Quasienergies ε α take over the roe of stationary states and energies [Shirey, PR 38, B979 (965); Sambe, PRA 7, 6 (973)] They are unique ony mod ω : ε αm ε α +m ω with u αm (t) u α (t) e imωt ( photon index m =, ±, ±, )

17 Foquet theoreti Quantum Foquet theoretica approach Hamitonian Ĥ(t + T ) = Ĥ(t) (with T = π ω ) gives rise to soutions ψ(t) = c α u α (t) e iε αt/, with uα (t + T ) = u α (t) α Foquet states u α (t) and Quasienergies ε α take over the roe of stationary states and energies [Shirey, PR 38, B979 (965); Sambe, PRA 7, 6 (973)] They are unique ony mod ω : ε αm ε α +m ω with u αm (t) u α (t) e imωt ( photon index m =, ±, ±, ) sove hermitian eigenvaue probem [Ĥ(t) i t ] u αm = ε αm u αm }{{} Quasienergy operator in extended space = state space T -periodic functions

18 Foquet theoreti Quantum Foquet theoretica approach Hamitonian Ĥ(t + T ) = Ĥ(t) (with T = π ω ) gives rise to soutions ψ(t) = c α u α (t) e iε αt/, with uα (t + T ) = u α (t) α Foquet states u α (t) and Quasienergies ε α take over the roe of stationary states and energies [Shirey, PR 38, B979 (965); Sambe, PRA 7, 6 (973)] They are unique ony mod ω : ε αm ε α +m ω with u αm (t) u α (t) e imωt ( photon index m =, ±, ±, ) sove hermitian eigenvaue probem [Ĥ(t) i t ] u αm = ε αm u αm }{{} Quasienergy operator in extended space = state space T -periodic functions obey an adiabatic principe [Breuer & Hothaus, Phys Lett A 4, 57 (989)]

19 Matter Waves Dressed Matter Waves m Foquet-Fock basis states: [ {n }, m {n } exp i K ω ω sin(ωt) ] n exp(imωt) m m+ m Ĥ interaction + m ω m m m m J m m (K ω / ω) Ĥ tunneing Anaogy between driven matter wave and dressed atom [Cohen-Tannoudji et a, Atom Photon Ineteractions] [Eckardt & Hothaus, J Phys 99, 7 (8)] Quasienergy Matrix ˆQ

20 Matter Waves Dressed Matter Waves m Foquet-Fock basis states: [ {n }, m {n } exp i K ω ω sin(ωt) ] n exp(imωt) m m+ m Ĥ interaction + m ω m m m m J m m (K ω / ω) Ĥ tunneing Anaogy between driven matter wave and dressed atom [Cohen-Tannoudji et a, Atom Photon Ineteractions] [Eckardt & Hothaus, J Phys 99, 7 (8)] Quasienergy Matrix ˆQ Undriven imit Off-resonant imit ω U, nj resembes undriven imit

21 Matter Waves Dressed Matter Waves m Foquet-Fock basis states: [ {n }, m {n } exp i K ω ω sin(ωt) ] n exp(imωt) m m+ m Ĥ interaction + m ω m m m m J m m (K ω / ω) Ĥ tunneing Anaogy between driven matter wave and dressed atom [Cohen-Tannoudji et a, Atom Photon Ineteractions] [Eckardt & Hothaus, J Phys 99, 7 (8)] Quasienergy Matrix ˆQ Undriven imit ( Kω = J ω ) J Off-resonant imit ω U, nj resembes undriven imit (ˆb ˆb + + ˆb +ˆb ) + U }{{} J eff (effective tunneing matrix eement) ˆn (ˆn ) Ĥ eff Eff Hopping Jeff/J Parameter K ω / hω Driving ampitude Singe partices: [Dunap & Kenkre PRB 34, 365 (986)], [Grossmann et a PRL 67, 56 (99)] Here many partices, possiby with strong interaction U nj: [Eckardt et a, PRL 95, 644 (5)]

22 Matter Waves Dressed Matter Waves m Foquet-Fock basis states: [ {n }, m {n } exp i K ω ω sin(ωt) ] n exp(imωt) m m+ m Ĥ interaction + m ω m m m m J m m (K ω / ω) Ĥ tunneing Anaogy between driven matter wave and dressed atom [Cohen-Tannoudji et a, Atom Photon Ineteractions] [Eckardt & Hothaus, J Phys 99, 7 (8)] Quasienergy Matrix ˆQ Undriven imit ( Kω = J ω ) J Off-resonant imit ω U, nj resembes undriven imit (ˆb ˆb + + ˆb +ˆb ) + U }{{} J eff (effective tunneing matrix eement) ˆn (ˆn ) Ĥ eff Eff Hopping Jeff/J Parameter K ω / hω Driving ampitude Singe partices: [Dunap & Kenkre PRB 34, 365 (986)], [Grossmann et a PRL 67, 56 (99)] Here many partices, possiby with strong interaction U nj: [Eckardt et a, PRL 95, 644 (5)] Experiments with singe or weaky interacting partices: Heideberg: singe-partice tunneing in driven doube we [Kierig et a, PRL, 945 (8)] Pisa: Coherent expansion of a BEC in a shaken attice [Lignier et a, PRL 99, 43 (7)]

23 Matter Waves Dressed Matter Waves m Foquet-Fock basis states: [ {n }, m {n } exp i K ω ω sin(ωt) ] n exp(imωt) m m+ m Ĥ interaction + m ω m m m m J m m (K ω / ω) Ĥ tunneing Anaogy between driven matter wave and dressed atom [Cohen-Tannoudji et a, Atom Photon Ineteractions] [Eckardt & Hothaus, J Phys 99, 7 (8)] Quasienergy Matrix ˆQ Undriven imit ( Kω = J ω ) J Off-resonant imit ω U, nj resembes undriven imit (ˆb ˆb + + ˆb +ˆb ) + U }{{} J eff (effective tunneing matrix eement) ˆn (ˆn ) Ĥ eff Eff Hopping Jeff/J Parameter K ω / hω Driving ampitude Singe partices: [Dunap & Kenkre PRB 34, 365 (986)], [Grossmann et a PRL 67, 56 (99)] Here many partices, possiby with strong interaction U nj: [Eckardt et a, PRL 95, 644 (5)] Experiments with singe or weaky interacting partices: Heideberg: singe-partice tunneing in driven doube we [Kierig et a, PRL, 945 (8)] Pisa: Coherent expansion of a BEC in a shaken attice [Lignier et a, PRL 99, 43 (7)] Use drive to coherenty contro many-body phenomena!

24 the Mott-transitio Inducing the Mott-transition by shaking Off-resonanty shaken attice system described by effective time-independet Bose-Hubbard Hamitonian ( Kω Ĥ eff = JJ ω J eff }{{} ) (ˆb ˆb + +ˆb +ˆb )+ U ˆn (ˆn ) Eff Hopping Jeff/J Parameter K ω / hω Driving ampitude Bosonic Mott-transition (for integer fiing n): [Fisher et a, PRB 4, 546 (989)] J eff /U > (J/U) c : gapess Superfuid with (quasi)ong-range order J eff /U < (J/U) c : gaped Mott-insuator with the partices ocaized Induce the Mott-transition by smoothy switching on a time-periodic attice acceeration! [Eckardt et a, PRL 95, 644 (5)] Pisa experiment: [Zenesini et a, PRL, 43 (9)] Superfuid Mott-insuator Superfuid

25 Beyond effective tunneing Beyond effective tunneing + m resonance first order in tunneing m ε / hω m [PRL, 453 (8)] Quasienergy Matrix Q U/ hω For ~ω U, J ony sma resonances spoiing H eff -description (b) ε/j Systematica treatment by stationary degenerate perturbation theory in the extended Hibert space resonance second order in tunneing Resonances can be quenched by chossing the correct ampitude of the forcing Measurabe by avoided eve crossing spectroscopy No true adiabatic imit in arge systems Effective adiabatic motion /3 / U/Jω U/h /3 Quasienergy spectrum for 5 partices on 5 sites with ~ω/j = and Kω /~ω =

26 Part: Second Part: Exporing frustrated antiferromagnetism with dressed matter waves

27 attice with pos Trianguar attice with positive hopping Bosonic atoms in trianguar attice, dressed by a circuar attice acceeration Ĥ eff = J, eff ˆb ˆb + U ˆn (ˆn ) with J, eff >,

28 attice with pos Trianguar attice with positive hopping Bosonic atoms in trianguar attice, dressed by a circuar attice acceeration Ĥ eff = J, eff ˆb ˆb + U ˆn (ˆn ) with J, eff >, Limit of weak repusive interaction: Bose-Einstein condensate, discrete order parameter ψ = n exp(iϕ ) ψ exp(ψ ˆb ψ /) vac = n = exp( n/)n n / exp(in ϕ ) n n! Loca phases ϕ pay roe of cassica rotors, having ong-range Née order ϕ = Q R

29 attice with pos Trianguar attice with positive hopping Bosonic atoms in trianguar attice, dressed by a circuar attice acceeration Ĥ eff = J, eff ˆb ˆb + U ˆn (ˆn ) with J, eff >, Limit of weak repusive interaction: Bose-Einstein condensate, discrete order parameter ψ = n exp(iϕ ) ψ exp(ψ ˆb ψ /) vac = n = exp( n/)n n / exp(in ϕ ) n n! Loca phases ϕ pay roe of cassica rotors, having ong-range Née order ϕ = Q R Limit of strong repusive interaction: Ony two occupation numbers favored, n = [n] and n = [n] +, spin-/ description Ĥ XY = J xy (ˆσ x ˆσx + ˆσy ˆσy ) with J xy = [n] + Strong phase fuctuations: ˆb exp(iˆϕ ) ˆn with [ˆn, ˆϕ ] i ˆϕ ˆn = J eff

30 attice with pos Trianguar attice with positive hopping Bosonic atoms in trianguar attice, dressed by a circuar attice acceeration Ĥ eff = J, eff ˆb ˆb + U ˆn (ˆn ) with J, eff >, Limit of weak repusive interaction: Bose-Einstein condensate, discrete order parameter ψ = n exp(iϕ ) ψ exp(ψ ˆb ψ /) vac = n = exp( n/)n n / exp(in ϕ ) n n! Loca phases ϕ pay roe of cassica rotors, having ong-range Née order ϕ = Q R Limit of strong repusive interaction: Ony two occupation numbers favored, n = [n] and n = [n] +, spin-/ description Ĥ XY = J xy (ˆσ x ˆσx + ˆσy ˆσy ) with J xy = [n] + Strong phase fuctuations: ˆb exp(iˆϕ ) ˆn with [ˆn, ˆϕ ] i ˆϕ ˆn = ( ) cos(ϑ /) [n] + sin(ϑ /)exp(iϕ ) [n] + dressed with quantum fuctuations ψ?? Does spira/née order persist? What ese might happen? J eff

31 Quantum Magn Frustrated Quantum Magnets: Scenarios Cassica Née order Vaence Bond Soids Resonating Vaence Bond Spin Liquids [PW Anderson, Mat Res Bu 8, 53 (973)] (I) Topoogica Spin Liquids (II) Critica Spin Liquids Pictures taken from [Aet et a 6] Review Artices: [Lhuiier, cond-mat/5464]; [Moessner & Ramirez, Physics Today 59/, 4 (6)]; [Aet, Waczak & MPA Fisher, Physica A 369, (6)]; [Sachdev, Nature Phys 4, 73 (8)];

32 attice with pos Trianguar attice with positive hopping XY-mode on trianguar attice: Ĥ eff =, J eff, ˆb ˆb + U ˆn (ˆn ) U/(nJ) Ĥ XY = J xy (ˆσ x ˆσx +ˆσy ˆσy ) Ĥ XY beieved to have cassica spira Née order [Capriotti et a PRL 8, 3899 (999)]

33 attice with pos Trianguar attice with positive hopping XY-mode on trianguar attice: Ĥ eff =, J eff, ˆb ˆb + U ˆn (ˆn ) U/(nJ) Ĥ XY = J xy (ˆσ x ˆσx +ˆσy ˆσy ) Ĥ XY beieved to have cassica spira Née order [Capriotti et a PRL 8, 3899 (999)] Consider anisotropic mode: Ĥ XY = J xy (ˆσ x ˆσx + ˆσ y ˆσy ) with J xy = J, J and J J

34 attice with pos Trianguar attice with positive hopping XY-mode on trianguar attice: Ĥ eff =, J eff, ˆb ˆb + U ˆn (ˆn ) U/(nJ) Ĥ XY = J xy (ˆσ x ˆσx +ˆσy ˆσy ) Ĥ XY beieved to have cassica spira Née order [Capriotti et a PRL 8, 3899 (999)] Consider anisotropic mode: Ĥ XY = J xy (ˆσ x ˆσx + ˆσ y ˆσy ) with J xy = J, J and J Recenty studied by Schmied et a (PEPS and exact diagonaization): [NJP, 457 (8)] J

35 attice with pos Trianguar attice with positive hopping XY-mode on trianguar attice: Ĥ eff =, J eff, ˆb ˆb + U ˆn (ˆn ) U/(nJ) Ĥ XY = J xy (ˆσ x ˆσx +ˆσy ˆσy ) Ĥ XY beieved to have cassica spira Née order [Capriotti et a PRL 8, 3899 (999)] Consider anisotropic mode: Ĥ XY = J xy (ˆσ x ˆσx + ˆσ y ˆσy ) with J xy = J, J and J Recenty studied by Schmied et a (PEPS and exact diagonaization): [NJP, 457 (8)] J Generaized Bogoiubov approach: 8 U/(nJ) U/(nJ) α J /J condensate fraction = % nearest neighbor phase fuctuations = π/ oca number fuctuations = /

36 Phase diagrams: Phase diagrams: spin / >> XY imit D quasi Nee order U/J ~4 spin iquid (exponentia decay) SL ~6 ~ ~4 spira Nee order SL spira Nee order ( chiraities) cassica rotor imit D quasiong range order isotropic D chains trianguar Schmied et a NJP(8) rombic attice Nee order hypothetic phase diagram rombic attice Nee order J /J rombic imit haf odd integer fiing, antiferromagnetic couping

37 Phase diagrams: Phase diagrams: spin / >> XY imit D quasi Nee order U/J ~4 spin iquid (exponentia decay) SL ~6 ~ ~4 spira Nee order SL spira Nee order ( chiraities) cassica rotor imit D quasiong range order isotropic D chains trianguar Schmied et a NJP(8) rombic attice Nee order hypothetic phase diagram rombic attice Nee order J /J rombic imit haf odd integer fiing, antiferromagnetic couping µ/u SF ferromagnetic MI MI MI MI SL <n>= J/U SL antiferromagnetic Nee <n>=3 <n>=5 <n>= <n>=5 <n>=5 anisotropy J /J = 3 Mott insuator phases: strong couping expansion Spin Liquid phases: hypothetic

38 Summary First Part: Time-periodicay forced many-body attice systems (utracod atoms) show far-reaching anaogies with dressed atoms Dressed matter waves

39 Summary First Part: Time-periodicay forced many-body attice systems (utracod atoms) show far-reaching anaogies with dressed atoms Dressed matter waves Powerfu contro options based on (a)diabatic foowing of many-body Foquet states:

40 Summary First Part: Time-periodicay forced many-body attice systems (utracod atoms) show far-reaching anaogies with dressed atoms Dressed matter waves Powerfu contro options based on (a)diabatic foowing of many-body Foquet states: Exampe: Mott-transition induced by time-periodic attice acceeration Theory: [Eckardt et a, PRL 95, 644 (5)] Experiment: [Zenesini et a, PRL, 43 (9)]

41 Summary First Part: Time-periodicay forced many-body attice systems (utracod atoms) show far-reaching anaogies with dressed atoms Dressed matter waves Powerfu contro options based on (a)diabatic foowing of many-body Foquet states: Exampe: Mott-transition induced by time-periodic attice acceeration Theory: [Eckardt et a, PRL 95, 644 (5)] Experiment: [Zenesini et a, PRL, 43 (9)] not shown: AC-induced deocaization (superfuidity) in Wannier-Stark systems [Eckardt & Hothaus, EPL 8, 554 (7)]

42 Summary First Part: Time-periodicay forced many-body attice systems (utracod atoms) show far-reaching anaogies with dressed atoms Dressed matter waves Powerfu contro options based on (a)diabatic foowing of many-body Foquet states: Exampe: Mott-transition induced by time-periodic attice acceeration Theory: [Eckardt et a, PRL 95, 644 (5)] Experiment: [Zenesini et a, PRL, 43 (9)] not shown: AC-induced deocaization (superfuidity) in Wannier-Stark systems [Eckardt & Hothaus, EPL 8, 554 (7)] Understanding, measuring and quenching resonant excitation in the regime of strong forcing [Eckardt & Hothaus, PRL, 453 (8)]

43 Summary First Part: Time-periodicay forced many-body attice systems (utracod atoms) show far-reaching anaogies with dressed atoms Dressed matter waves Powerfu contro options based on (a)diabatic foowing of many-body Foquet states: Exampe: Mott-transition induced by time-periodic attice acceeration Theory: [Eckardt et a, PRL 95, 644 (5)] Experiment: [Zenesini et a, PRL, 43 (9)] not shown: AC-induced deocaization (superfuidity) in Wannier-Stark systems [Eckardt & Hothaus, EPL 8, 554 (7)] Understanding, measuring and quenching resonant excitation in the regime of strong forcing [Eckardt & Hothaus, PRL, 453 (8)] Second Part: Proposa: Use the dressing to guide the system into many-body states associated to quantum antiferromagnetism

44 Summary First Part: Time-periodicay forced many-body attice systems (utracod atoms) show far-reaching anaogies with dressed atoms Dressed matter waves Powerfu contro options based on (a)diabatic foowing of many-body Foquet states: Exampe: Mott-transition induced by time-periodic attice acceeration Theory: [Eckardt et a, PRL 95, 644 (5)] Experiment: [Zenesini et a, PRL, 43 (9)] not shown: AC-induced deocaization (superfuidity) in Wannier-Stark systems [Eckardt & Hothaus, EPL 8, 554 (7)] Understanding, measuring and quenching resonant excitation in the regime of strong forcing [Eckardt & Hothaus, PRL, 453 (8)] Second Part: Proposa: Use the dressing to guide the system into many-body states associated to quantum antiferromagnetism Possibe in existing experimenta setups

45 Summary First Part: Time-periodicay forced many-body attice systems (utracod atoms) show far-reaching anaogies with dressed atoms Dressed matter waves Powerfu contro options based on (a)diabatic foowing of many-body Foquet states: Exampe: Mott-transition induced by time-periodic attice acceeration Theory: [Eckardt et a, PRL 95, 644 (5)] Experiment: [Zenesini et a, PRL, 43 (9)] not shown: AC-induced deocaization (superfuidity) in Wannier-Stark systems [Eckardt & Hothaus, EPL 8, 554 (7)] Understanding, measuring and quenching resonant excitation in the regime of strong forcing [Eckardt & Hothaus, PRL, 453 (8)] Second Part: Proposa: Use the dressing to guide the system into many-body states associated to quantum antiferromagnetism Possibe in existing experimenta setups First aim: Observe Née order in a trianguar attice

46 Summary First Part: Time-periodicay forced many-body attice systems (utracod atoms) show far-reaching anaogies with dressed atoms Dressed matter waves Powerfu contro options based on (a)diabatic foowing of many-body Foquet states: Exampe: Mott-transition induced by time-periodic attice acceeration Theory: [Eckardt et a, PRL 95, 644 (5)] Experiment: [Zenesini et a, PRL, 43 (9)] not shown: AC-induced deocaization (superfuidity) in Wannier-Stark systems [Eckardt & Hothaus, EPL 8, 554 (7)] Understanding, measuring and quenching resonant excitation in the regime of strong forcing [Eckardt & Hothaus, PRL, 453 (8)] Second Part: Proposa: Use the dressing to guide the system into many-body states associated to quantum antiferromagnetism Possibe in existing experimenta setups First aim: Observe Née order in a trianguar attice Second aim: Expore highy correated spin-iquid phases