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)

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 gasmicroscope

Polaron physics(Zwierlein)

QS of BCS-BEC

crossover, imb. Spin

mix.(Ketterle, Zwierlein)

Extended Hubbardlong range int.(Molecules: Doyle, cavity: Kasevich)

Itinerant ferromagnetis

m(Ketterle, Demler)

superlattice

d-wave in plaquettes, noise corr. Detection(Rey, Demler, Lukin)

Fermi Hubbard model, Mott

(Bloch, Ketterle, Demler, Lukin,

Duan)

d-wave superfluidity Quantum magnetism

Bose-Hubbard modelFermionic superfluidity

lattice spin control

(Greiner, Thywissen)

Super-exchange interacti

on(Bloch, Demler,

Lukin, Duan)

MURI quantum simulation – map of achievements

Quantum magnetismwith ultracold atoms

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)

Stoner model of ferromagnetism

Mean-field criterion

U N(0) = 1

U – interaction strengthN(0) – density of states at Fermi level

Signatures of ferromagnetic correlations inparticles losses, molecule formation, cloud radius

Observation of Stoner transition by G.B. Jo et al., Science (2009)

Magnetic domains could not be resolved. Why?

Stoner InstabilityNew feature of cold atoms systems: non-adiabatic crossing of Uc

Screening of U (Kanamori) occurs on times 1/EF

Two timescales in the system: screening and magnetic domain formation

Magnetic domain formation takes place on much longer time scales: critical slowing down

Quench dynamics across Stoner instability

Find collective modes

Unstable modes determinecharacteristic lengthscale of magnetic domains

For U<Uc damped collective modes q =’- i ”For U>Uc unstable collective modes q = + i ”

For MIT experiments domain

sizes of the order of a few F

Quench dynamics in D=3

Dynamics of magnetic domain formation near Stoner transition

Moving across transition at a finite rate

0 uu*

domains coarsen

slowgrowth

domainsfreeze

Growth rate of magnetic domains

Domain size

Domains freeze when

Domain size at “freezing” point

Superexchange interaction in experiments with double wells

Theory: A.M. Rey et al., PRL 2008Experiments: S. Trotzky et al., Science 2008

Quantum magnetism of bosons in optical lattices

Duan, Demler, Lukin, PRL (2003)

• Ferromagnetic

• Antiferromagnetic

For spin independent lattice and interactionswe find ferromagnetic exchange interaction.Ferromagnetic ordering is favored by the bosonenhancement factor

J

J

Use magnetic field gradient to prepare a state

Observe oscillations between and states

Observation of superexchange in a double well potentialTheory: A.M. Rey et al., PRL 2008

Experiments:S. Trotzky et al.Science 2008

Comparison to the Hubbard model

[Picture: Greiner (2002)]

Two-Orbital SU(N) Magnetism withUltracold Alkaline-Earth Atoms

Alkaline-Earth atoms in optical lattice:Ex: 87Sr (I = 9/2)

|g = 1S0

|e = 3P0

698 nm150 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)

Mott state of the fermionic Hubbard model

Signatures of incompressible Mott state of fermions in optical lattice

Suppression of double occupancies R. Joerdens et al., Nature (2008)

Compressibility measurementsU. Schneider, I. Bloch et al., Science (2008)

Fermions in optical lattice. Next challenge: antiferromagnetic state

TN

U

Mott

currentexperiments

Lattice modulation experiments with fermions in optical lattice

Probing the Mott state of fermionsPekker, 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

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 fromprobability of finding nearest neighbors

“High” Temperature

“Low” Temperature

Rate of doublon production

• Sharp absorption edge due to coherent quasiparticles

• Spin wave shake-off peaks

Spins are antiferromagnetically ordered

Decay probability

Doublon decay in a compressible stateHow to get rid of the excess energy U?

Doublon can decay into apair 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

d-wave pairing in the fermionic Hubbard model

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 gasmicroscope

Polaron physics(Zwierlein)

QS of BCS-BEC

crossover, imb. Spin

mix.(Ketterle, Zwierlein)

Extended Hubbardlong range int.(Molecules: Doyle, cavity: Kasevich)

Itinerant ferromagnetis

m(Ketterle, Demler)

superlattice

d-wave in plaquettes, noise corr. Detection(Rey, Demler, Lukin)

Fermi Hubbard model, Mott

(Bloch, Ketterle, Demler, Lukin,

Duan)

d-wave superfluidity

Quantum magnetism

Bose-Hubbard modelFermionic superfluidity

lattice spin control

(Greiner, Thywissen)

Super-exchange interacti

on(Bloch, Demler,

Lukin, Duan)

MURI quantum simulation – map of achievements

A.M. Rey et al., EPL 87, 60001 (2009)

Using plaquettes to reach d-wave pairing

x

y

JJ’

Superlattice was a usefultool for observing magneticsuperexchange.

Can we use it to createand observe d-wavepairing?

Minimal system exhibitingd-wave pairing is a 4-siteplaquette

Ground State properties of a plaquetteGround 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)

For weak coupling there are two possible competing configurations:

VS4 2 , 42 3 3

Which one is lower in energy is determined by the binding energy

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

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

Second order interference from paired states

)'()()',( rrrr nnn

n(r)

n(r’)

n(k)

k

0),( BCSn rr

BCS

BEC

kF

Theory: Altman et al., PRA 70:13603 (2004)

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

How to measure the molecular wavefunction?

How to measure the non-trivial symmetry of (p)?

We want to measure the relative phase between components of the molecule at different wavevectors

Two particle interference

Coincidence count on detectorsmeasures two particle interference

– phase controlled by beam splitters and mirrors

Two particle interferenceImplementation for atoms: Bragg pulse before expansion

Bragg pulse mixes statesk 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

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

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

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 gasmicroscope

Polaron physics(Zwierlein)

QS of BCS-BEC

crossover, imb. Spin

mix.(Ketterle, Zwierlein)

Extended Hubbardlong range int.(Molecules: Doyle, cavity: Kasevich)

Itinerant ferromagnetis

m(Ketterle, Demler)

superlattice

d-wave in plaquettes, noise corr. Detection(Rey, Demler, Lukin)

Fermi Hubbard model, Mott

(Bloch, Ketterle, Demler, Lukin,

Duan)

d-wave superfluidity Quantum magnetism

Bose-Hubbard modelFermionic superfluidity

lattice spin control

(Greiner, Thywissen)

Super-exchange interacti

on(Bloch, Demler,

Lukin, Duan)

MURI quantum simulation – map of achievements

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