Presentation is loading. Please wait.

Presentation is loading. Please wait.

Quantum Simulation MURI Review Theoretical work by groups lead by Luming Duan (Michigan) Mikhail Lukin (Harvard) Subir Sachdev (Harvard) Peter Zoller (Innsbruck)

Published by Modified over 9 years ago

Similar presentations

Presentation on theme: "Quantum Simulation MURI Review Theoretical work by groups lead by Luming Duan (Michigan) Mikhail Lukin (Harvard) Subir Sachdev (Harvard) Peter Zoller (Innsbruck)"— Presentation transcript:

1 Quantum Simulation MURI Review Theoretical work by groups lead by Luming Duan (Michigan) Mikhail Lukin (Harvard) Subir Sachdev (Harvard) Peter Zoller (Innsbruck) Hans-Peter Buchler (Stuttgart) Eugene Demler (Harvard)

2 new Hamiltonian manipulation cooling Fermionic superfluid in opt. lattice (Ketterle, Bloch, Demler, Lukin, Duan) Spinor gases in optical lattices (Ketterle, Demler) Bose Hubbard QS validation (Bloch) Bose Hubbard precision QS (Ketterle) Single atom single site detection (Greiner) Quantum gas microscope Polaron physics (Zwierlein) QS of BCS- BEC crossover, imb. Spin mix. (Ketterle, Zwierlein) Extended Hubbard long range int. (Molecules: Doyle, cavity: Kasevich) Itinerant ferromagnetism (Ketterle, Demler) superlattice d-wave in plaquettes, noise corr. Detection (Rey, Demler, Lukin) Fermi Hubbard model, Mott (Bloch, Ketterle, Demler, Lukin, Duan) d-wave superfluidityQuantum magnetism Bose-Hubbard modelFermionic superfluidity lattice spin control (Greiner, Thywissen) Super- exchange interaction (Bloch, Demler, Lukin, Duan) MURI quantum simulation – map of achievements

3 Quantum magnetism with ultracold atoms

4 Dynamics of magnetic domain formation near Stoner transition Theory: David Pekker, Rajdeep Sensarma, Mehrtash Babadi, Eugene Demler, arXiv:0909.3483 Experiments: G. B. Jo et al., Science 325:1521 (2009)

5 Stoner model of ferromagnetism Mean-field criterion U N(0) = 1 U – interaction strength N(0) – density of states at Fermi level Signatures of ferromagnetic correlations in particles losses, molecule formation, cloud radius Observation of Stoner transition by G.B. Jo et al., Science (2009) Magnetic domains could not be resolved. Why?

6 Stoner Instability New feature of cold atoms systems: non-adiabatic crossing of U c Screening of U (Kanamori) occurs on times 1/E F Two timescales in the system: screening and magnetic domain formation Magnetic domain formation takes place on much longer time scales: critical slowing down

7 Quench dynamics across Stoner instability Find collective modes Unstable modes determine characteristic lengthscale of magnetic domains For U<U c damped collective modes w q = w ’- i w ” For U>U c unstable collective modes w q = + i w ”

8 For MIT experiments domain sizes of the order of a few l F Quench dynamics in D=3 Dynamics of magnetic domain formation near Stoner transition Moving across transition at a finite rate 0u u*u* domains coarsen slow growth domains freeze Growth rate of magnetic domains Domain size Domains freeze when Domain size at “freezing” point

9 Superexchange interaction in experiments with double wells Theory: A.M. Rey et al., PRL 2008 Experiments: S. Trotzky et al., Science 2008

10 Quantum magnetism of bosons in optical lattices Duan, Demler, Lukin, PRL (2003) Ferromagnetic Antiferromagnetic For spin independent lattice and interactions we find ferromagnetic exchange interaction. Ferromagnetic ordering is favored by the boson enhancement factor

11 J J Use magnetic field gradient to prepare a stateObserve oscillations between and states Observation of superexchange in a double well potential Theory: A.M. Rey et al., PRL 2008 Experiments: S. Trotzky et al. Science 2008

12 Comparison to the Hubbard model

13 [Picture: Greiner (2002)] Two-Orbital SU(N) Magnetism with Ultracold Alkaline-Earth Atoms Alkaline-Earth atoms in optical lattice: Ex: 87 Sr (I = 9/2) |g  = 1 S 0 |e  = 3 P 0 698 nm 150 s ~ 1 mHz orbital degree of freedom ⇒ spin-orbital physics → Kugel-Khomskii model [transition metal oxides with perovskite structure] → SU(N) Kondo lattice model [for N=2, colossal magnetoresistance in manganese oxides and heavy fermion materials] Nuclear spin decoupled from electrons SU(N=2I+1) symmetry → SU(N) spin models ⇒ valence-bond-solid & spin-liquid phases A. Gorshkov, et al., arXiv:0905.2963 (poster)

14 Mott state of the fermionic Hubbard model

15 Signatures of incompressible Mott state of fermions in optical lattice Suppression of double occupancies R. Joerdens et al., Nature (2008) Compressibility measurements U. Schneider, I. Bloch et al., Science (2008)

16 Fermions in optical lattice. Next challenge: antiferromagnetic state TNTN U Mott current experiments

17 Lattice modulation experiments with fermions in optical lattice Probing the Mott state of fermions Pekker, Sensarma, Lukin, Demler (2009) Pekker, Pollet, unpublished Measure number of doubly occupied sites Modulate lattice potential Doublon/hole production rate determined by the spectral functions of excitations Experiments by ETH Zurich group and others

18 Experiment: R. Joerdens et al., Nature 455:204 (2008) Spectral Function for doublons/holes Rate of doublon production All spin configurations are equally likely. Can neglect spin dynamics Temperature dependence comes from probability of finding nearest neighbors “High” Temperature

19 “Low” Temperature Rate of doublon production Sharp absorption edge due to coherent quasiparticles Spin wave shake-off peaks Spins are antiferromagnetically ordered

20 Decay probability Doublon decay in a compressible state How to get rid of the excess energy U? Doublon can decay into a pair of quasiparticles with many particle-hole pairs Perturbation theory to order n=U/6t Consider processes which maximize the number of particle-hole excitations N. Strohmaier, D. Pekker, et al., arXiv:0905.2963

21 d-wave pairing in the fermionic Hubbard model

22 new Hamiltonian manipulation cooling Fermionic superfluid in opt. lattice (Ketterle, Bloch, Demler, Lukin, Duan) Spinor gases in optical lattices (Ketterle, Demler) Bose Hubbard QS validation (Bloch) Bose Hubbard precision QS (Ketterle) Single atom single site detection (Greiner) Quantum gas microscope Polaron physics (Zwierlein) QS of BCS- BEC crossover, imb. Spin mix. (Ketterle, Zwierlein) Extended Hubbard long range int. (Molecules: Doyle, cavity: Kasevich) Itinerant ferromagnetism (Ketterle, Demler) superlattice d-wave in plaquettes, noise corr. Detection (Rey, Demler, Lukin) Fermi Hubbard model, Mott (Bloch, Ketterle, Demler, Lukin, Duan) d-wave superfluidityQuantum magnetism Bose-Hubbard modelFermionic superfluidity lattice spin control (Greiner, Thywissen) Super- exchange interaction (Bloch, Demler, Lukin, Duan) MURI quantum simulation – map of achievements

23 A.M. Rey et al., EPL 87, 60001 (2009) Using plaquettes to reach d-wave pairing x y J J’ Superlattice was a useful tool for observing magnetic superexchange. Can we use it to create and observe d-wave pairing? Minimal system exhibiting d-wave pairing is a 4-site plaquette

24 Ground State properties of a plaquette Unique singlet (S=0) d-wave symmetry Unique singlet (S=0) s-wave symmetry d-wave symmetry d-wave pair creation operator Singlet creation operator 1 3 2 4 4 2 Scalapino,Trugman (1996) Altman, Auerbach (2002) Vojta, Sachdev (2004) Kivelson et al., (2007)

25 For weak coupling there are two possible competing configurations: VS 42, 4233 Which one is lower in energy is determined by the binding energy

26 1. Prepare 4 atoms in a single plaquette: A plaquette is the minimum system that exhibits d- wave symmetry. 3. Weakly connect the 2D array to realize and study a superfluid exhibiting long range d-wave correlations. Melt the plaquettes into a 2D lattice, experimentally explore the regime unaccessible to theory 4. 2. Connect two plaquettes into a superplaquette and study the dynamics of a d-wave pair. Use it to measure the pairing gap. ? Using plaquettes to reach d-wave pairing

27 Phase sensitive probe of d-wave pairing From noise correlations to phase sensitive measurements in systems of ultra-cold atoms T. Kitagawa, A. Aspect, M. Greiner, E. Demler

28 Second order interference from paired states n(r) n(r’) n(k) k BCS BEC k F Theory: Altman et al., PRA 70:13603 (2004)

29 Momentum correlations in paired fermions Experiments: Greiner et al., PRL 94:110401 (2005)

30 How to measure the molecular wavefunction? How to measure the non-trivial symmetry of y (p)? We want to measure the relative phase between components of the molecule at different wavevectors

31 Two particle interference Coincidence count on detectors measures two particle interference c – c phase controlled by beam splitters and mirrors

32 Two particle interference Implementation for atoms: Bragg pulse before expansion Bragg pulse mixes states k and –p = k-G -k and p =-k+G Coincidence count for states k and p depends on two particle interference and measures phase of the molecule wavefunction

33 Description of s-wave Feshbach resonance in an optical lattice p-wave Feshbach resonance in an optical lattice and its phase diagram Research by Luming Duan’s group: poster Low-dimensional effective Hamiltonian and 2D BEC-BCS crossover Anharmonicity induced resonance in a lattice Confinement induced (shift) resonance Anharmonicity induced resonance

34 Other theory projects by the Harvard group Fermionic Mott states with spin imbalance. B. Wunsch (poster) One dimensional systems: nonequilibrium dynamics and noise. T. Kitagawa (poster) Spin liquids.Detection of fractional statistics and interferometry of anions. L. Jiang, A. Gorshkov, Demler, Lukin, Zoller, et al., Nature Physics (2009) Fermions in spin dependent optical lattice. N. Zinner, B. Wunsch (poster). Bosons in optical lattice with disoreder. D. Pekker (poster). Dynamical preparation of AF state using bosons with ferromagnetic interactions. M. Gullans, M. Rudner

35 new Hamiltonian manipulation cooling Fermionic superfluid in opt. lattice (Ketterle, Bloch, Demler, Lukin, Duan) Spinor gases in optical lattices (Ketterle, Demler) Bose Hubbard QS validation (Bloch) Bose Hubbard precision QS (Ketterle) Single atom single site detection (Greiner) Quantum gas microscope Polaron physics (Zwierlein) QS of BCS- BEC crossover, imb. Spin mix. (Ketterle, Zwierlein) Extended Hubbard long range int. (Molecules: Doyle, cavity: Kasevich) Itinerant ferromagnetism (Ketterle, Demler) superlattice d-wave in plaquettes, noise corr. Detection (Rey, Demler, Lukin) Fermi Hubbard model, Mott (Bloch, Ketterle, Demler, Lukin, Duan) d-wave superfluidityQuantum magnetism Bose-Hubbard modelFermionic superfluidity lattice spin control (Greiner, Thywissen) Super- exchange interaction (Bloch, Demler, Lukin, Duan) MURI quantum simulation – map of achievements

36 Summary Quantum magnetism with ultracold atoms Dynamics of magnetic domain formation near Stoner transition Superexchange interaction in experiments with double wells Two-Orbital SU(N) Magnetism with Ultracold Alkaline-Earth Atoms Mott state of the fermionic Hubbard model Signatures of incompressible Mott state of fermions in optical lattice Lattice modulation experiments with fermions in optical lattice Doublon decay in a compressible state Making and probing d-wave pairing in the fermionic Hubbard model Using plaquettes to reach d-wave pairing Phase sensitive probe of d-wave pairing

Download ppt "Quantum Simulation MURI Review Theoretical work by groups lead by Luming Duan (Michigan) Mikhail Lukin (Harvard) Subir Sachdev (Harvard) Peter Zoller (Innsbruck)"

Similar presentations

Creating new states of matter:

Creating new states of matter:
Trapped ultracold atoms: Bosons Bose-Einstein condensation of a dilute bosonic gas Probe of superfluidity: vortices.

Trapped ultracold atoms: Bosons Bose-Einstein condensation of a dilute bosonic gas Probe of superfluidity: vortices.
Dynamics of Spin-1 Bose-Einstein Condensates

Dynamics of Spin-1 Bose-Einstein Condensates
Competing instabilities in ultracold Fermi gases $$ NSF, AFOSR MURI, DARPA ARO Harvard-MIT David Pekker (Harvard), Mehrtash Babadi (Harvard), Lode Pollet.

Competing instabilities in ultracold Fermi gases $$ NSF, AFOSR MURI, DARPA ARO Harvard-MIT David Pekker (Harvard), Mehrtash Babadi (Harvard), Lode Pollet.
Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA,

Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA,
Magnetism in systems of ultracold atoms: New problems of quantum many-body dynamics E. Altman (Weizmann), P. Barmettler (Frieburg), V. Gritsev (Harvard,

Magnetism in systems of ultracold atoms: New problems of quantum many-body dynamics E. Altman (Weizmann), P. Barmettler (Frieburg), V. Gritsev (Harvard,
Nonequilibrium dynamics of ultracold atoms in optical lattices. Lattice modulation experiments and more Ehud Altman Weizmann Institute Peter Barmettler.

Nonequilibrium dynamics of ultracold atoms in optical lattices. Lattice modulation experiments and more Ehud Altman Weizmann Institute Peter Barmettler.
Nonequilibrium dynamics of ultracold fermions Theoretical work: Mehrtash Babadi, David Pekker, Rajdeep Sensarma, Ehud Altman, Eugene Demler $$ NSF, MURI,

Nonequilibrium dynamics of ultracold fermions Theoretical work: Mehrtash Babadi, David Pekker, Rajdeep Sensarma, Ehud Altman, Eugene Demler $$ NSF, MURI,
Lattice modulation experiments with fermions in optical lattice Dynamics of Hubbard model Ehud Altman Weizmann Institute David Pekker Harvard University.

Lattice modulation experiments with fermions in optical lattice Dynamics of Hubbard model Ehud Altman Weizmann Institute David Pekker Harvard University.
Hubbard model(s) Eugene Demler Harvard University Collaboration with

Hubbard model(s) Eugene Demler Harvard University Collaboration with
Nonequilibrium spin dynamics in systems of ultracold atoms Funded by NSF, DARPA, MURI, AFOSR, Harvard-MIT CUA Collaborators: Ehud Altman, Robert Cherng,

Nonequilibrium spin dynamics in systems of ultracold atoms Funded by NSF, DARPA, MURI, AFOSR, Harvard-MIT CUA Collaborators: Ehud Altman, Robert Cherng,
Eugene Demler Harvard University Strongly correlated many-body systems: from electronic materials to ultracold atoms.

Eugene Demler Harvard University Strongly correlated many-body systems: from electronic materials to ultracold atoms.
Modeling strongly correlated electron systems using cold atoms Eugene Demler Physics Department Harvard University.

Modeling strongly correlated electron systems using cold atoms Eugene Demler Physics Department Harvard University.
Conference on quantum fluids and strongly correlated systems Paris 2008.

Conference on quantum fluids and strongly correlated systems Paris 2008.
Multicomponent systems of ultracold atoms Eugene Demler Harvard University Dynamical instability of spiral states In collaboration with Robert Cherng,

Multicomponent systems of ultracold atoms Eugene Demler Harvard University Dynamical instability of spiral states In collaboration with Robert Cherng,
Magnetism in ultracold Fermi gases and New physics with ultracold ions: many-body systems with non-equilibrium noise $$ NSF, AFOSR MURI, DARPA Harvard-MIT.

Magnetism in ultracold Fermi gases and New physics with ultracold ions: many-body systems with non-equilibrium noise $$ NSF, AFOSR MURI, DARPA Harvard-MIT.
Measuring correlation functions in interacting systems of cold atoms Anatoli Polkovnikov Boston University Ehud Altman Weizmann Vladimir Gritsev Harvard.

Measuring correlation functions in interacting systems of cold atoms Anatoli Polkovnikov Boston University Ehud Altman Weizmann Vladimir Gritsev Harvard.
Competing instabilities in ultracold Fermi gases $$ NSF, AFOSR MURI, DARPA ARO Harvard-MIT David Pekker (Harvard) Mehrtash Babadi (Harvard) Lode Pollet.

Competing instabilities in ultracold Fermi gases $$ NSF, AFOSR MURI, DARPA ARO Harvard-MIT David Pekker (Harvard) Mehrtash Babadi (Harvard) Lode Pollet.
Spinor condensates beyond mean-field

Spinor condensates beyond mean-field
Quantum noise studies of ultracold atoms Eugene Demler Harvard University Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA, MURI Collaborators: Ehud Altman,

Quantum noise studies of ultracold atoms Eugene Demler Harvard University Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA, MURI Collaborators: Ehud Altman,

Similar presentations

Ads by Google