Humboldt Kolleg Controlling quantum matter From ultracold atoms

Humboldt Kolleg: Controlling quantum matter: From ultracold atoms to solids, Vilnius, 7/30/18 Super resolution imaging with ultracold atoms Cheng Chin James Franck institute Enrico Fermi institute Department of Physics University of Chicago National FUNDING: Science Foundation Army Research Office Material Research Science & Engineering center MRSEC

Imaging atomic quantum gas in a 2 D optical lattices Microscope objective Lattice beams Particle number: 6000~15000 Imaging resolution: 1 micron Lattice and bulk meaurement Imaging beam Vertical compress. beams In situ observation of Mott plateau, Nature 2009

Single site microscope gallery Greiner Group, Harvard University Other groups: Munich/MPQ, MIT, Kyoto, Toronto, Princeton, Strathclyde…

$Diffraction limit of optical microscopy 2$

Diffraction limit of optical microscopy 2

Stochastic super-resolution imaging 2~5 nm in position uncertainty Stochastic Optical Reconstruction Microscopy (STORM) 1. 7 nm in position uncertainty Monroe group, “High resolution adaptive imaging of a single atom, ” Nature Photonics (2016). 2014 Chemistry Prize — Eric Betzig, Stefan W. Hell and William E. Moerner

Deterministic super-resolution Multi-photon microscopy Biophotonics Imaging Laboratory, UIUC E(x)2 E(x)3

Nonlinear response of optical pumping ar. Xiv: 1807. 02906 Optical pumping efficiency : branching ratio : linewidth Isat: saturation intensity t: time Similar work based on dark state transfer (JQI): ar. Xiv: 1807. 02871

Converting nonlinearity to high-resolution Exp setup OP lattice Trapping lattice

Experimental setup (Instability < 10 nm) Sample: Cs atoms cooled to the ground state of a 1 D optical lattice.

Non-linear optical response 0. 2 ~ 2. 7 Isat 0. 04 Isat 0. 02 Isat

Imaging ground state wavefunction Theory data ground state FWHM 90% ground state FWHM Super resolution FWHM

Application 1: nanometer dynamics within a lattice site Experiment Numerical calculation

Application 2: Trap parameter inhomogeneity Density Temperature Trap frequency Damping

Bonus: Morie pattern trap=852. 37 nm OP=852. 34 nm trap op/( trap- op) ~ 1 cm

Morie magnification Magnification = 1, 000~1, 000 x We slice the wavefunction Into 20, 000 pieces and distribute them in a single image.

Morie microscopy and validation

Conclusion • Super resolution based on strong optical pumping – Resolution (FWHM) = 32(3) nm – Localization resolution 1 = 400 pm • Super fast imaging at 1 s – No measurement backaction – No cooling is needed • Morie magnification from nanometer to millimeter • Observations – Inhomogeneity of temperature and lattice parameters – Coherent, anharmonic dynamics within a lattice site

Postdocs Group Members Jiazhong Hu Grads Brian De. Salvo Mickey Mc. Donald Krutik Patel Jonathan Trisnadi Lei Feng Geyue Cai Kai-Xuan Yao Zhendong Zhang

Postdocs Group Members Grads Brian De. Salvo Bose-Fermi-Bose interactions Krutik Patel Geyue Cai EF

Postdocs Group Members Quantum simulation of Hawking-Unruh radiation Grads Jiazhong Hu Lei Feng Zhendong Zhang ar. Xiv: 1807. 07504

Morie microscopy

A closer cook… Resolution: 1. 0 µm Pixel: 0. 6 µm Lattice const. : 0. 53 µm Averaged image

Super resolution imaging in optical lattices • Super resolution imaging based on non-linear optical response? (Typically 50 nm in biological microscopy) • Can we do better localization resolution (2 nm) than biologists and ion trappers? • Can we see wavefunctions and what physics can we learn from super imaging?

First idea: Optical pumping lattice

Exp set up and procedure Exp steps 1. Load atoms to a far-detuned optical lattice 2. Cool atoms to ground state 3. Apply a short an intense OP standing wave 4. Measure excitation fractions 5. Tune the OP wave with a piezo. Lattice beam Optical pumping beam Piezo

Increasing nonlinearlity I/Is = 20 I/Is = 2. 5 = … FWHM = 55(2) nm = 0. 1 = 0. 05 Piezo displacement (nm) 1 s OP pulse Super-resolution microscopy of cold atoms in an optical lattice Mickey Mc. Donald, Jonathan Trisnadi, Kai-Xuan Yao, Cheng Chin Ar. Xiv: 1807. 02906

Can we see wavefunction in a lattice site? Combined resolution 90% Ground state FWHM Estimated optical resolution

Observation: Morie pattern Lattice constant mismatch =fop-flattice

Morie pattern: >10, 000 x imaging magnification OP lattice Trapping lattice Morie pattern (~1 mm) Piezo tunning x (nm)

Dynamics of atoms in lattices (preliminary)

Croucher Summer Course “Ultracold Atom Physics”, 6/13/2018 Super resolution imaging of atoms in optical lattices Cheng Chin James Franck institute Enrico Fermi institute Department of Physics University of Chicago National FUNDING: Science Foundation Army Research Office Material Research Science & Engineering center MRSEC

Cold atom research at UChicago Nuclear Physics: Feshbach molecules Efimov physics Cosmology Sakharov oscillations Kibble mechanism Inflation Hawking-Unruh radiation Condensed Matter: Quantum criticality Exotic excitations Mediated interactions Particle Physics Jet formation Matterwave HHG Pattern recognition Thermal Levitation

Our DAMOP 18 presentations Fermi sea mediated interactions Super resolution imaging Poster (Tu) E 01. 00118 Talk (Th) Q 03. 00001 Poster (W) M 01. 00138 Bose fireworks 2. 0 L. Clark thesis award talk (Tu) D 03. 00002 Talk (W) J 04. 00005/6 Poster (Th) T 01: 00071

Sakharov acoustic oscillations 1 degree Simulation with cold atoms, C-L Hung, V Gurarie, CC, Science 2012

Inflation in cosmology symmetry breaking inflation reheating A. Guth 1981 Figure from Alan H Guth, J. Phys. A: Math. Theor. 40 (2007)

Quantum phase transition Energy s<sc s=sc Quantum critical piont or s>sc

Is quantum phase transition coherent? Fast ramp Energy Non- adiabatic Zone Slow ramp or s<sc s=sc Quantum critical piont s>sc

Ferromagnetic domains “More Is Different”, P. W. Anderson, Science 177, 393 (1972)

Can we reverse the water flow?

Synopsis Quantum phase transition Our system: • Interacting quantum gas in shaken optical lattices • Excitations: Domain walls, rotons, inflatons • Universality: Kibbe-Zurek spacetime Coherent inflation dynamics across a quantum critical point

How do we understand quantum phase transition? T. W. B. Kibble, PHYSICSREPORTS 67, 183 (1980) M. Morikawa, Progress of Theoretical Physics 93, 685 (1995)

Our 133 Cs BEC machine

Optical lattice phase modulation laser isolator Standing waves mirror isolator Phase modulator

Our system: Driven Bose gas in gauge field Ground band expanded view strong modulation critical modulation zero modulation �� : modulation frequency : modulation strength

In situ domain structure in a shaken lattice 5 m Few 10 ms after transition 100 ms after transition C. Parker et al. , Nat. Phys (2013) L. Clark et al. , Science (2016) See our papers for the domain reconstruction imaging.

Domain Gallery

How do we understand quantum phase transition? T. W. B. Kibble, PHYSICSREPORTS 67, 183 (1980) M. Morikawa, Progress of Theoretical Physics 93, 685 (1995)

In situ and time-of-flight after quantum phase transition nk momentum population S(k) Structure Factor Lei Feng

Inflation Hamiltonian Bogoliubov Hamiltonian: Inflation Hamiltonian: Solution: nk<<n 0 stimulated emission spontaneous emission

Phase imprint a BEC with momentum k cos kx

$Bogoliubov Theory Growh rate (1/s) Excitation fraction N-k /N 0 Growth of different modes$

Bogoliubov Theory Growh rate (1/s) Excitation fraction N-k /N 0 Growth of different modes Fit function: n=n 0 cosh 2 kt Numerics Theory:

Higher harmonic generation of inflatons Experiment Phase imprinting Simulation

Coherent critical dynamics in momentum space 0 ms 14 ms exp theory Feng, Clark, Gaj and Chin, Nat. Phys. (2018)

Coherent evolution in real space

Coherent quantum critical dynamics Initial state: (x) =e i �� P space Initial state “symmetry breaking” fluctuations x inflation x High harmonic generation Relaxation amplification x x Coherent final state

Conclusion Quantum phase transition in shaken lattices: • Superfluid domains are coherent • Inflation dynamics is coherent • Relaxation is coherent Bose fireworks: • Dynamic instability in 2 D • Is fireworks also coherent matterwaves?

Hybridization of Bloch bands Ground band expanded view strong modulation critical modulation zero modulation �� : modulation frequency : modulation strength

Coherent evolution of density wave factor

Inflation in cosmology A. Guth 1981 Figure from Alan H Guth, J. Phys. A: Math. Theor. 40 (2007)

Simplest inflation model A. Guth 1981 Figure from Alan H Guth, J. Phys. A: Math. Theor. 40 (2007)

Quantum phase transition of bosons in 2 D lattices Sachdev (2007) Critical scaling laws: Zhou and Ho, PRL (2010) Conformal symmetry and Ad. S-CFT duality in 2 D optical lattices: Sachdev, Nature physics (2007)

MCAW 2013 -11 -16 Dynamics instability in 1 d Stochastic model: Exponential decay Exponential growth condensate density Space time Mathematica 71

Inflation in cosmology symmetry breaking inflation new equilibrium A. Guth 1981 Figure from Alan H Guth, J. Phys. A: Math. Theor. 40 (2007)

Characterizing the Jets Bose fireworks

In situ images g=0. 05 g=0. 26 g=1. 3 Interaction strength Cs superfluid: 20, 000~100, 000 atoms Imaging resolution: 1. 0 µm 20~100 atoms/micron 3 Nature 2009, Nature 2011