Agenda

Wolfgang Ketterle (MIT) Introduction, overview 15Markus Greiner (Harvard) Quantum gas microscopy 25Eugene Demler (Harvard) Exploring exotic states of matter

with interference 20

Quantum dynamics far away from equilibriumUlrich Schneider (Munich) Emergence of coherence at

a quantum phase transition 20Coffee breakJoseph Thywissen (Toronto) Spin dynamics of fermions 10Tarik Yefsah (MIT) Solitary waves in fermionic superfluids 10

Nikolai Prokof'ev (Amherst) New theoretical methods 15Wolfgang Ketterle (MIT) Synthetic magnetic fields in

optical lattices 20

Exploring exotic states of matter with interference

Eugene Demler (Harvard)

Collaborators:S. Gopalakrishnan, M. Knap, M. Lukin, T. Kitagawa (Harvard) D. Abanin (Harvard/Perimeter Inst.),  M. Serbyn (MIT),M. Atala, M. Aidelsburger, J. Barreiro, I. Bloch (MPQ/LMU)A. Kantian, T. Giamarchi (Univ. Geneva)

Antiferromagnetic and superconducting Tc of the order of 100 K

Atoms in optical lattice

Antiferromagnetism and pairing at sub-micro Kelvin temperatures

Same microscopic model

Quantum simulations with ultracold atoms

How to detect many-body phases with ultracold atoms

/2 pulse

Evolution

Ramsey interference 

Used for  atomic clocks, gravitometers, accelerometers, magnetic field measurements

pulse + measurement of Sz gives relative phase accumulated by the two spin components

EvolutionEvolution

Outline

Exploring exotic states of matter with interference

Measuring Berry/Zak phase in optical latticesM. Atala et al., Nature Physics (2013), T. Kitagawa et al., PRL (2013)

Measuring dynamical spin correlation functionsM. Knap, et al., Phys. Rev. Lett. (2013)

Probing many-body localizationM. Serbyn, M. Knap, S. Gopalakrishnan, et al.

Probing band topology with Ramsey/Bloch interference

Theory: D. Abanin, T. Kitagawa, E. Demler

Experiments: M. Atala, M. Aidelsburger, J. Barreiro, I. Bloch (MPQ/LMU) 

M. Atala et al., Nature Physics (2013), T. Kitagawa et al., PRL (2013)

Broken symmetries vs topological order

Order parameters

Berry/Zak phase in 1d

How to measure topological order parameter?

accuracy 10-9

SSH Model with bichromatic lattice

B A B BA

When dz(k)=0, states with t>0 and t<0 are topologically distinct.We can not deform two paths into each other without closing the gap.

Characterizing SSH model using Zak phase Two hyperfine spin states experience the same optical potential

/2a/2a

a

Zak phase is equal to 0

Zak/Berry phase measurements

Exploring dynamical response functions in spin modelsusing many-body Ramsey interference

M. Knap, A. Kantian, T. Giamarchi, I. Bloch, M. Lukin, E. DemlerPhys. Rev. Lett. (2013)

Cold atoms Trapped ions Dipolar interactions

Heisenberg model of XXZ type

super-exchange

e.g. 87Rb mixtures ofand

LR transverse field Ising model

interactions mediated by phonons

e.g. 171Yb

LR XX model

Molecules, e.g. KRb

Atoms w/ large magnetic moments, e.g. Cr

MPQ group JQI group JILA group

Probing spin dynamics in synthetic matter

Many‐body spin Ramsey protocol

Measures the retarded spin correlation function

Systems with interactions and disorder Granular superconductors and Josephson junction networks

– Crane et al. (2007): AC response– Bouadim et al. (2011): numerics– Baturina, Sacepe et. al. (2008): STM– Trivedi et. al. (2012 review)

Central spin problem in q-dotsNV centers in diamond

- Marcus et al. (2004) - Lukin et al. (2006)- Jelezko et a. (2007)- Awschalom et al. (2007)

Polar molecules in optical lattices– Ye et al. (2013)

Rydberg atoms– Ryabtsev et al. (2010)– Bloch et al. (2012)

Gap map in TiN film

Nuclear spin interactions mediated by electron spin

Angular momentum as spin degree of freedom

Strong interactions due to large electric dipole moment

Many-body localization (MBL)

localization in the presence of interactions

system does not act as its own bath (discrete local spectrum)

MBL states vs. Anderson localized states→ interactions create non-local correlations (growth of entanglement)

Bardarson et al., PRL (2012)Vosk, Altman, PRL (2013)Serbyn, et al. PRL (2013)

Temperature

Cond

uctiv

ity

Not activatedconductivity

– Anderson– Basko, Aleiner, Altshuler– Huse, Oganesyan, Pal– Aleiner, Altshuler, Shlyapnikov– …

Spin correlation function as quantum quench

In a localized phase, local quench affectsonly a few excitations. For each eigenstateexpect non‐decaying oscillations

In a delocalized phase (diffusive regime), local quench affects all excitations. Expect decayakin orthogonality catastrophe

After averaging over thermal ensemble(and/or disorder realizization) find decay

Spin correlation function as quantum quench

Ramsey + spin echoM. Knap, S. Gopalakrishnan, M. Serbyn, et al.

“Cartoon” model of the localized phase

Spin echo

M. Knap, S. Gopalakrishnan, M. Serbyn, et al.

Double Electron‐Electron Resonance Ramsey sequence

Double Electron‐Electron Resonance Ramsey sequence

single realizationthermal averaging over 50 eigenstates

For a given time t we can separate fast modesand slow modes

Interaction strength decays as 

“Cartoon” model of MBL phase

MBL as integrable model

Double Electron‐Electron Resonance Ramsey sequence

Summary

Exploring exotic states of matter with interference

Measuring Berry/Zak phase in optical latticesM. Atala et al., Nature Physics (2013), T. Kitagawa et al., PRL (2013)

Measuring dynamical spin correlation functionsM. Knap, et al., Phys. Rev. Lett. (2013)

Probing many-body localizationM. Serbyn, M. Knap, S. Gopalakrishnan, et al.