# Project B6:

Ordered states in strongly interacting Rydberg gases (2009-2017)

## Summary

In this project, we investigate strongly interacting Rydberg gases (SIRyG) within a theoretical and experimental collaboration. The Rydberg states are coherently excited from an ultra cold atomic gas; the theoretical description of the system dynamics reduces to an effective spin model with strong interactions between spins in the spin state corresponding to the Rydberg excitation. During the time evolution complex many-body states are formed from the atomic gas. On a characteristic time scale present experiments show that the system saturates into a steady light-matter state. This steady state can be viewed in terms of a phase diagram featuring a second order quantum phase transition. Universal behaviour is expected near the critical point, which is experimentally accessible. To understand the scaling behaviour from few-body to many-body systems we plan to determine experimentally the critical exponents and characteristic properties of the manybody state, while the phase diagram and the critical theory is studied within a mean-field theory and a numerical analysis. Time dependent coherent control of the light matter state is envisioned to tailor dynamic cooperative quantum states. By adiabatic and nonadiabatic evolution either energy can be pumped into the system or the evolution can be kept in the effective ground state of the SIRyG. Of special focus is the possible appearance of ordered crystalline states accessible within such an adiabatic evolution. In this regime we plan to determine the density density correlation function. Experimentally this will be done by four wave mixing and/or atom interferometric methods. An alternative method will be electromagnetically induced transparency (EIT) probing of a SIRyG by Rydberg EIT or Rydberg influenced Raman EIT. To probe and influence the effects of decoherence we plan to perform rotating echo experiments.

The Rydberg excitations will exhibit a residual interaction with the atomic background. This allows us to change the view and study Rydberg excited states acting back on the atomic gas; we expect that this influence is most pronounced for a Bose-Einstein condensate (BEC) with high densities, and we are searching for phenomena on the coherent phase of the BEC from the excited Rydberg states. This response of the background to the Rydberg states is present even after times much larger than the characteristic time scales of Rydberg excitation due to the slow motion of the atomic gas. On the other hand, for continuous driving the system with the laser for Rydberg excitation, the time averaged response of the BEC will mimic an effective interaction between the atoms. These phenomena can also be viewed as dressing each atom with an admixture of the strongly interacting Rydberg state. We will experimentally and theoretically explore the prospect of this method for inducing strong interactions in cold atomic gases and study its application towards the creation of strongly correlated many-body states.

Finally, different Rydberg levels can be coupled by microwave fields or an additional Rydberg excitation laser. This opens a route towards the design and control of strong interactions between the Rydberg states; similar phenomena have recently been theoretically analyzed for polar molecules. Of special interest are controlled threebody interactions, which may allow for the creation of novel and exotic phases.

## Project leaders

Prof. Dr. Hans Peter Büchler, Institut für Theoretische Physik III, Universität Stuttgart

Prof. Dr. Tilman Pfau, 5. Physikalisches Institut, Universität Stuttgart

## Refs & Publications

S. Weber, C. Tresp, H. Menke, A. Urvoy, O. Firstenberg, H. P. Büchler, and S. Hofferberth*"Calculation of Rydberg interaction potentials"*

*J. Phys. B: At. Mol. Opt. Phys.*

**50**, 133001 (2017)*;*doi: 10.1088/1361-6455/aa743a

S. Weber, C. Tresp, H. Menke, A. U. Firstenberg, H. P. Büchler and S. Hofferberth

*"TUTORIAL: Calculation of Rydberg interaction potentials"*

*J. Phys. B: At. Mol. Opt. Phys.*

**50**133001 (2017)*;*doi: 10.1088/1361-6455/aa743a

P. Bienias and H. P. Büchler

*"Quantum theory of Kerr nonlinearity with Rydberg slow light polaritons"*

*New J. Phys.*

**18**, 123026 (2016)*;*doi: 10.1088/1367-2630/aa50c3

K. Jachymski, P. Bienias, and H. P. Büchler

*"Three-body interaction of Rydberg slow light polaritons"*

*Phys. Rev. Lett.*

**117**, 053601 (2016)*;*doi: 10.1103/PhysRevLett.117.053601

H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth

*"Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Förster Resonances"*

*arXiv:1511.09445 [quant-ph]*

M. F. Maghrebi, M. J. Gullans, P. Bienias, S. Choi, I. Martin, O. Firstenberg, M. D. Lukin, H. P. Büchler, and A. V. Gorshkov

*"Coulomb bound states of strongly interacting photons"*

*Phys. Rev. Lett.,*; arXiv:1505.03859

**115**, 123601 (2015)*;*doi: 10.1103/PhysRevLett.115.123601

N. Lang and H. P. Büchler

*"Topological states in a microscopic model of interacting fermions"*

*Phys. Rev. B,*; arxiv:1504.04233

**92**, 041118(R) (2015)*;*doi: 10.1103/PhysRevB.92.041118

N. Lang and H. P. Büchler

*"Exploring quantum phases by driven dissipation"*

*Phys. Rev. A,*; arxiv:1408.4616

**92**, 012128 (2015)*;*doi: 10.1103/PhysRevA.92.012128

A. Gaj, A. T. Krupp, P. Ilzhöfer, R. Löw, S. Hofferberth, T. Pfau

*"Hybridization of Rydberg electron orbitals by molecule formation"*

*Phys. Rev. Lett.,*; arXiv:1503.04724

**115**, 023001 (2015)A. Sommer, H. P. Büchler, and J. Simon

*"Quantum Crystals and Laughlin Droplets of Cavity Rydberg Polaritons"*

*arXiv:1506.00341 [cond-mat.quant-gas]*

T. Karpiuk, M. Brewczyk, K. Rzążewski, A. Gaj, J. B. Balewski, A. T. Krupp, M. Schlagmüller, R. Löw, S. Hofferberth, and T. Pfau

*"Imaging single Rydberg electrons in a Bose–Einstein condensate"*

*New Journal of Physics*

**17**, 053046 (2015)*;*doi: 10.1088/1367-2630/17/5/053046

D. Peter, N. Y. Yao, N. Lang, S. D. Huber, M. D. Lukin, and H. P. Büchler

*"Topological bands with Chern number C = 2 by dipolar exchange interactions"*

*Phys. Rev. A,*; arxiv:1410.5667 [cond-mat.quant-gas]

**91**, 053617 (2015)*;*doi: 10.1103/PhysRevA.91.053617

C. Tresp, P. Bienias, S. Weber, H. Gorniaczyk, I. Mirgorodskiy, H. P. Büchler, S. Hofferberth

*"Dipolar dephasing of Rydberg D-state polaritons"*

*Phys. Rev. Lett.*;

**115**, 083602 (2015)*arXiv:1505.03723*

*;*doi: 10.1103/PhysRevLett.115.083602

P. Bienias, S. Choi, O. Firstenberg, M. F. Maghrebi, M. Gullans, M. D. Lukin, A.V. Gorshkov, and H. P. Büchler

*"Scattering resonances and bound states for strongly interacting Rydberg polaritons"*

*Phys. Rev. A,*; arXiv:1402.7333 [quant-ph]

**90**, 053804 (2014)*;*doi: 10.1103/PhysRevA.90.053804

A. Gaj, A. T. Krupp, J. B. Balewski, R. Löw, S. Hofferberth, and T. Pfau

*"From molecular spectra to a density shift in dense Rydberg gases"*

*Nature Comm.*; arXiv:1404.5761

**5**, 4546 (2014)T. Karpiuk, M. Brewczyk, K. Rzążewski, A. Gaj, J. B. Balewski, A. T. Krupp, M. Schlagmüller, R. Löw, S. Hofferberth, and T. Pfau

*"Detecting and imaging single Rydberg electrons in a Bose-Einstein condensate"*

*New Journal of Physics,*; arXiv:1402.6875

**17**, 053046 (2015)A.T. Krupp, A. Gaj, J.B. Balewski, P. Ilzhöfer, S. Hofferberth, R. Löw, T. Pfau, M. Kurz, and P. Schmelcher

*"Alignment of D-state Rydberg molecules"*

Phys. Rev. Lett.

**112**, 143008 (2014)

*;*doi: 10.1103/PhysRevLett.112.143008

J.B. Balewski, A.T. Krupp, A. Gaj, S. Hofferberth, R. Löw, and T. Pfau

*"Rydberg dressing: Understanding of collective many-body effects and implications for experiments"*

*New J. Phys.*;

**16**063012 (2014)*arXiv:1312.6346*

J. B. Balewski, A. T. Krupp, A. Gaj, D. Peter, H. P. Büchler, R. Löw, S. Hofferberth, and T. Pfau

*"Coupling a single electron to a Bose–Einstein condensate"*

*Nature*

**502**, 664 (2013)*;*doi: 10.1038/nature12592

J. B. Balewski, A. T. Krupp, A. Gaj, D. Peter, H. P. Büchler, R. Löw, S. Hofferberth, and T. Pfau

*"Coupling a single electron to a Bose-Einstein condensate"*

Nature

**502**, 664 (2013); arXiv:1306.5181

M. M. Müller, A. Kölle, R. Löw, T. Pfau, T. Calarco, and S. Montangero

*"Room temperature Rydberg Single Photon Source"*

Phys. Rev. A

**87**, 053412 (2013); arXiv:1212.2811v1

*;*doi: 10.1103/PhysRevA.87.053412

N. Lang and H. P. Büchler

*"Minimal instances for toric code ground states"*

*Phys. Rev. A,*; arxiv:1206.6994 [quant-ph]

**86**, 022336 (2012)*;*doi: 10.1103/PhysRevA.86.022336

J. Nipper, J. B. Balewski, A. T. Krupp, S. Hofferberth, R. Löw, and T. Pfau

*"Atomic Pair-State Interferometer: Controlling and Measuring an Interaction-Induced Phase Shift in Rydberg-Atom Pairs"*

*Phys. Rev. X*

**2**, 031011 (2012)*;*doi: 10.1103/PhysRevX.2.031011

R. Löw, H. Weimer, J. Nipper, J. B. Balewski, B. Butscher, H. P. Büchler, and T. Pfau

*"An experimental and theoretical guide to strongly interacting Rydberg gases"*

*J. Phys. B: At. Mol. Opt. Phys.*

**45**, 113001 (2012)*;*doi: 10.1088/0953-4075/45/11/113001

J. Nipper, J. B. Balewski, A. T. Krupp, B. Butscher, R. Löw, and T. Pfau

*"Highly Resolved Measurements of Stark-Tuned Förster Resonances between Rydberg Atoms"*

*Phys. Rev. Lett.*

**108**, 113001 (2012)*;*doi: 10.1103/PhysRevLett.108.113001

W. Li, T. Pohl, J. M. Rost, Seth T. Rittenhouse, H. R. Sadeghpour, J. Nipper, B. Butscher, J. B. Balewski, V. Bendkowsky, R. Löw, and T. Pfau

*"A Homonuclear Molecule with a Permanent Electric Dipole Moment"*

*Science*

**334**, 1110 (2011)*;*doi: 10.1126/science.1211255

H. Weimer, M. Müller, H.P. Büchler, and I. Lesanovsky

*"Digital Quantum Simulation with Rydberg Atoms"*

*Quant. Inf. Proc.*;

**10**, 885 (2011)*arXiv:1104.3081v2*

*;*doi: 10.1007/s11128-011-0303-5

B. Butscher, V. Bendkowsky, J. Nipper, J. B. Balewski, L. Kukota, R. Löw, T. Pfau W. Li, T. Pohl, and J. M. Rost

*"Lifetimes of ultralong-range Rydberg molecules in vibrational ground and excited states"*

*J. Phys. B: At. Mol. Opt. Phys.*

**44**, 184004 (2011)*;*doi: 10.1088/0953-4075/44/18/184004

J. Honer, R. Löw, H. Weimer, T. Pfau, and H. P. Büchler

*"Artificial atoms can do more than atoms: Deterministic single photon subtraction from arbitrary light fields"*

*Phys. Rev. Lett.*

**107**, 093601 (2011)*;*doi: 10.1103/PhysRevLett.107.093601

B. Butscher, J. Nipper, J. B. Balewski, L. Kukota, V. Bendkowsky, R. Löw, and T. Pfau

*"Atom-molecule coherence for ultralong range Rydberg dimers"*

*Nature Physics*

**6**, 970–974 (2010)*;*doi: 10.1038/nphys1828

J. Honer, H. Weimer, T. Pfau, and H. P. Büchler

*"Collective many-body interaction in Rydberg dressed atoms"*

*Phys. Rev. Lett.*

**105**, 160404 (2010)*;*doi: 10.1103/PhysRevLett.105.160404

V. Bendkowsky, B. Butscher, J. Nipper, J. Balewski, J. P. Shaffer, R. Löw, T. Pfau, W. Li, J. Stanojevic, T. Pohl, and J. M. Rost

*"Rydberg trimers and excited dimers bound by internal quantum reflection"*

*Phys. Rev. Lett.*

**105**, 163201 (2010)*;*doi: 10.1103/PhysRevLett.105.163201

H. Weimer, M. Müller, I. Lesanovsky, P. Zoller, and H. P. Büchler

*"A Rydberg quantum simulator"*

*Nature Physics*

**6**, 382-388 (2010)*;*doi: 10.1038/nphys1614

R. Löw, H. Weimer, U. Krohn, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau

*"Universal scaling in a strongly interacting Rydberg gas"*

*Phys. Rev. A*

**80**, 033422 (2009)*;*doi: 10.1103/PhysRevA.80.033422

V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau

*"Observation of ultralong-range Rydberg molecules"*

*Nature*

**458**, 1005-1008 (2009)*;*doi: 10.1038/nature07945

H. Weimer, R. Löw, T. Pfau, H. P. Büchler

*"Quantum critical behavior in strongly interacting Rydberg gases"*

*Phys. Rev. Lett.*

**101,**250601 (2008)*;*doi: 10.1103/PhysRevLett.101.250601