
Lauritz Klaus, Thomas Bland, Elena Poli, Claudia Politi, Giacomo Lamporesi, Eva Casotti, R. N. Bisset, Manfred J. Mark, Francesca Ferlaino Observation of vortices and vortex stripes in a dipolar condensate,
Nature Phys. (20221031),
http://dx.doi.org/10.1038/s41567022017938 doi:10.1038/s41567022017938 (ID: 720846)

G. Natale, T. Bland, Simon Gschwendtner, Louis Lafforgue, Daniel S. Grün, A. Patscheider, Manfred J. Mark, F. Ferlaino Bloch oscillations and matterwave localization of a dipolar quantum gas in a onedimensional lattice,
Communications Physics 5 227 (20220915),
http://dx.doi.org/10.1038/s42005022010098 doi:10.1038/s42005022010098 (ID: 720840)
Toggle Abstract
Threedimensional quantum gases of strongly dipolar atoms can undergo a crossover from a dilute gas to a dense macrodroplet, stabilized by quantum fluctuations. Adding a onedimensional optical lattice creates a platform where quantum fluctuations are still unexplored, and a rich variety of new phases may be observable. We employ Bloch oscillations as an interferometric tool to assess the role quantum fluctuations play in an array of quasitwodimensional BoseEinstein condensates. Longlived oscillations are observed when the chemical potential is balanced between sites, in a region where a macrodroplet is extended over several lattice sites. Further, we observe a transition to a state that is localized to a single lattice plane−driven purely by interactions−marked by the disappearance of the interference pattern in the momentum distribution. To describe our observations, we develop a discrete onedimensional extended GrossPitaevskii theory, including quantum fluctuations and a variational approach for the onsite wavefunction. This model is in quantitative agreement with the experiment, revealing the existence of single and multisite macrodroplets, and signatures of a twodimensional bright soliton.

M. Norcia, E. Poli, C. Politi, L. Klaus, T. Bland, M. J. Mark, L. Santos, R. N. Bisset, F. Ferlaino Can angular oscillations probe superfluidity in dipolar supersolids?,
Phys. Rev. Lett. 129 40403 (20220722),
http://dx.doi.org/10.1103/PhysRevLett.129.040403 doi:10.1103/PhysRevLett.129.040403 (ID: 720697)
Toggle Abstract
Angular oscillations can provide a useful probe of the superfluid properties of a system. Such<br />
measurements have recently been applied to dipolar supersolids, which exhibit both density modulation and phase coherence, and for which robust probes of superfluidity are particularly interesting.<br />
So far, these investigations have been confined to linear droplet arrays. Here, we explore angular<br />
oscillations in systems with 2D structure, which in principle have greater sensitivity to superfluidity.<br />
Surprisingly, in both experiment and simulation, we find that the frequency of angular oscillations<br />
remains nearly unchanged even when the superfluidity of the system is altered dramatically. This<br />
indicates that angular oscillation measurements do not always provide a robust experimental probe<br />
of superfluidity with typical experimental protocols.

S. JuliaFarre, D. GonzalezCuadra, A. Patscheider, M. J. Mark, F. Ferlaino, M. Lewenstein, L. Barbiero, A. Dauphin Revealing the topological nature of the bond order wave in a strongly correlated quantum system,
Phys. Rev. Research 4 L032005 (20220708),
http://dx.doi.org/10.1103/PhysRevResearch.4.L032005 doi:10.1103/PhysRevResearch.4.L032005 (ID: 720727)

A. Patscheider, L. Chomaz, G. Natale, D. Petter, M. J. Mark, S. Baier, B. Yang, R. R. Wang, J. L. Bohn, F. Ferlaino Determination of the scattering length of erbium atoms,
Phys. Rev. A 105 63307 (20220608),
http://dx.doi.org/10.1103/PhysRevA.105.063307 doi:10.1103/PhysRevA.105.063307 (ID: 720739)
Toggle Abstract
An accurate knowledge of the scattering length is fundamental in ultracold quantum gas experiments and essential for the characterisation of the system as well as for a meaningful comparison to theoretical models. Here, we perform a careful characterisation of the swave scattering length as for the four highestabundance isotopes of erbium, in the magnetic field range from 0 G to 5 G. We report on crossdimensional thermalization measurements and apply the Enskog equations of change to numerically simulate the thermalization process and to analytically extract an expression for the socalled number of collisions per rethermalization (NCPR) to obtain as from our experimental data. We benchmark the applied crossdimensional thermalization technique with the experimentally more demanding lattice modulation spectroscopy and find good agreement for our parameter regime. Our experiments are compatible with a dependence of the NCPR with as, as theoretically expected in the case of strongly dipolar gases. Surprisingly, we experimentally observe a dependency of the NCPR on the density, which might arise due to deviations from an ideal harmonic trapping configuration. Finally, we apply a model for the dependency of the background scattering length with the isotope mass, allowing to estimate the number of bound states of erbium.

C. Politi, A. Trautmann, P. Ilzhöfer, G. Durastante, M. J. Mark, M. Mondugno, F. Ferlaino Interspecies interactions in an ultracold dipolar mixture,
Phys. Rev. A (20220203),
http://dx.doi.org/10.1103/PhysRevA.105.023304 doi:10.1103/PhysRevA.105.023304 (ID: 720698)
Toggle Abstract
We experimentally and theoretically investigate the influence of the dipoledipole interactions (DDIs) on the total interspecies interaction in an erbiumdysprosium mixture. By rotating the dipole orientation we are able to tune the effect of the longrange and anisotropic DDI, and therefore the intrap displacements of the erbium and dysprosium clouds. We present a theoretical description for our binary system based on an extended GrossPitaevskii theory, including the singlespecies beyond meanfield terms, and we predict a lower and an upper bound for the interspecies scattering length
a
12
=
105
[
−
65
,
+
162
]
a
0
. Our work is a step towards the investigation of the experimentally unexplored dipolar miscibilityimmiscibility phase diagram and the realization of quantum droplets and supersolid states with heteronuclear dipolar mixtures.

A. Patscheider, B. Yang, G. Natale, D. Petter, L. Chomaz, M. J. Mark, G. Hovhannesyan, M. Lepers, F. Ferlaino Observation of a narrow innershell orbital transition in atomic erbium at 1299 nm,
Phys. Rev. Research 3 33256 (20210917),
http://dx.doi.org/10.1103/PhysRevResearch.3.033256 doi:10.1103/PhysRevResearch.3.033256 (ID: 720648)
Toggle Abstract
We report on the observation and coherent excitation of atoms on the narrow innershell orbital transition, connecting the erbium ground state [Xe]4f12(3H6)6s2 to the excited state [Xe]4f11(4I15/2)05d(5D3/2)6s2(15/2,3/2)07. This transition corresponds to a wavelength of 1299 nm and is optically closed. We perform highresolution spectroscopy to extract the gJfactor of the 1299nm state and to determine the frequency shift for four bosonic isotopes. We further demonstrate coherent control of the atomic state and extract a lifetime of 178(19) ms which corresponds to a linewidth of 0.9(1) Hz. The experimental findings are in good agreement with our semiempirical model. In addition, we present theoretical calculations of the atomic polarizability, revealing several different magicwavelength conditions. Finally, we make use of the vectorial polarizability and confirm a possible magic wavelength at 532 nm.

A. Trautmann, M. J. Mark, P. Ilzhöfer, H. Edri, A. El Arrach, J. G. Maloberti, C. Greene, F. Robicheaux, F. Ferlaino Spectroscopy of Rydberg States in Erbium using Electromagnetically Induced Transparency,
Phys. Rev. Research 3 33165 (20210819),
http://dx.doi.org/10.1103/PhysRevResearch.3.033165 doi:10.1103/PhysRevResearch.3.033165 (ID: 720647)
Toggle Abstract
We present a study of the Rydberg spectrum in 166Er for series connected to the 4f12(3H6)6s, Jc=13/2 and Jc=11/2 ionic core states using an alloptical detection based on electromagnetically induced transparency in an effusive atomic beam. Identifying approximately 550 individual states, we find good agreement with a multichannel quantum defect theory (MQDT) which allows assignment of most states to ns or nd Rydberg series. We provide an improved accuracy for the lowest two ionization thresholds to EIP,Jc=13/2=49260.750(1)cm1 and EIP,Jc=11/2=49701.184(1)cm1 as well as the corresponding quantum defects for all observed series. We identify Rydberg states in five different isotopes, and states between the two lowest ionization thresholds. Our results open the way for future applications of Rydberg states for quantum simulation using erbium and exploiting its special openshell structure.

M. Norcia, C. Politi, L. Klaus, E. Poli, M. Sohmen, M. J. Mark, R. N. Bisset, L. Santos, F. Ferlaino Twodimensional supersolidity in a dipolar quantum gas,
Nature 596 361 (20210818),
http://dx.doi.org/10.1038/s41586021037257 doi:10.1038/s41586021037257 (ID: 720624)

D. Petter, A. Patscheider, G. Natale, M. J. Mark, M. Baranov, R. van Bijnen, S. M. Roccuzzo, A. Recati, B. Blakie, D. Baillie, L. Chomaz, F. Ferlaino Bragg scattering of an ultracold dipolar gas across the phase transition from BoseEinstein condensate to supersolid in the freeparticle regime,
Phys. Rev. A 104 L011302 (20210722),
http://dx.doi.org/10.1103/PhysRevA.104.L011302 doi:10.1103/PhysRevA.104.L011302 (ID: 720484)
Toggle Abstract
We present an experimental and theoretical study of the highenergy excitation spectra of a dipolar supersolid. Using Bragg spectroscopy, we study the scattering response of the system to a highenergy probe, enabling measurements of the dynamic structure factor. We experimentally observe a continuous reduction of the response when tuning the contact interaction from an ordinary BoseEinstein condensate to a supersolid state. Yet the observed reduction is faster than the one theoretically predicted by the BogoliubovdeGennes theory. Based on an intuitive semianalytic model and realtime simulations, we primarily attribute such a discrepancy to the outofequilibrium phase dynamics, which although not affecting the system global coherence, reduces its response.

M. Sohmen, C. Politi, L. Klaus, L. Chomaz, M. J. Mark, M. Norcia, F. Ferlaino Birth, life, and death of a dipolar supersolid,
Phys. Rev. Lett. 126 233401 (20210607),
http://dx.doi.org/10.1103/PhysRevLett.126.233401 doi:10.1103/PhysRevLett.126.233401 (ID: 720625)
Toggle Abstract
In the short time since the first observation of supersolid states of ultracold dipolar atoms, substantial progress has been made in understanding the zerotemperature phase diagram and lowenergy excitations of these systems. Less is known, however, about their finitetemperature properties, particularly relevant for supersolids formed by cooling through direct evaporation. Here, we explore this realm by characterizing the evaporative formation and subsequent decay of a dipolar supersolid by combining highresolution intrap imaging with timeofflight observables. As our atomic system cools toward quantum degeneracy, it first undergoes a transition from thermal gas to a crystalline state with the appearance of periodic density modulation. This is followed by a transition to a supersolid state with the emergence of longrange phase coherence. Further, we explore the role of temperature in the development of the modulated state.

P. Ilzhöfer, M. Sohmen, G. Durastante, C. Politi, A. Trautmann, G. Morpurgo, T. Giamarchi, L. Chomaz, M. J. Mark, F. Ferlaino Phase coherence in outofequilibrium supersolid states of ultracold dipolar atoms,
Nature Phys. 17 361 (20210104),
http://dx.doi.org/10.1038/s41567020011003 doi:10.1038/s41567020011003 (ID: 720437)

L. R. Picard, M. J. Mark, F. Ferlaino, R. van Bijnen Deep LearningAssisted Classification of SiteResolved Quantum Gas Microscope Images,
Measurement Science and Technology 31 25201 (20191105),
http://dx.doi.org/10.1088/13616501/ab44d8 doi:10.1088/13616501/ab44d8 (ID: 720262)

G. Natale, R. van Bijnen, A. Patscheider, D. Petter, M. J. Mark, L. Chomaz, F. Ferlaino Excitation spectrum of a trapped dipolar supersolid and its experimental evidence,
Phys. Rev. Lett. 123 50402 (20190801),
http://dx.doi.org/10.1103/PhysRevLett.123.050402 doi:10.1103/PhysRevLett.123.050402 (ID: 720313)
Toggle Abstract
We study the spectrum of elementary excitations of a trapped dipolar Bose gas across the superfluidsupersolid phase transition. Our calculations, accounting for the experimentally relevant case of confined systems, show that, when entering the supersolid phase, two distinct excitation branches appear, respectively connected to crystal or superfluid orders. These results confirm infinitesystem predictions, showing that finitesize effects play only a small qualitative role. Experimentally, we probe compressional excitations in an Er quantum gas across the phase diagram. While in the BEC regime the system exhibits an ordinary quadrupole oscillation, in the supersolid regime, we observe a striking twofrequency response of the system, related to the two spontaneously broken symmetries.

D. Petter, G. Natale, R. van Bijnen, A. Patscheider, M. J. Mark, L. Chomaz, F. Ferlaino Probing the roton excitation spectrum of a stable dipolar Bose gas,
Phys. Rev. Lett. 122 183401 (20190508),
http://dx.doi.org/10.1103/PhysRevLett.122.183401 doi:10.1103/PhysRevLett.122.183401 (ID: 720098)
Toggle Abstract
We measure the excitation spectrum of a stable dipolar BoseEinstein condensate over a wide momentumrange via Bragg spectroscopy. We precisely control the relative strength, εdd, of the dipolar to the contact interactions and observe that the spectrum increasingly deviates from the linear phononic behavior for increasing εdd. Reaching the dipolar dominated regime εdd>1, we observe the emergence of a roton minimum in the spectrum and its softening towards instability. We characterize how the excitation energy and the strength of the densitydensity correlations at the roton momentum vary with εdd. Our findings are in excellent agreement with numerical calculations based on meanfield Bogoliubov theory. When including beyondmeanfield corrections, in the form of a LeeHuangYang potential, we observe a quantitative deviation from the experiment, questioning the validity of such a description in the roton regime.

L. Chomaz, D. Petter, P. Ilzhöfer, G. Natale, A. Trautmann, C. Politi, G. Durastante, R. van Bijnen, A. Patscheider, M. Sohmen, M. J. Mark, F. Ferlaino LongLived and Transient Supersolid Behaviors in Dipolar Quantum Gases,
Phys. Rev. X 9 21012 (20190419),
http://dx.doi.org/10.1103/PhysRevX.9.021012 doi:10.1103/PhysRevX.9.021012 (ID: 720203)
Toggle Abstract
By combining theory and experiments, we demonstrate that dipolar quantum gases of both 166Er and 164Dy support a state with supersolid properties, where a spontaneous density modulation and a global phase coherence coexist. This paradoxical state occurs in a well defined parameter range, separating the phases of a regular BoseEinstein condensate and of an insulating droplet array, and is rooted in the roton mode softening, on the one side, and in the stabilization driven by quantum fluctuations, on the other side. Here, we identify the parameter regime for each of the three phases. In the experiment, we rely on a detailed analysis of the interference patterns resulting from the free expansion of the gas, quantifying both its density modulation and its global phase coherence. Reaching the phases via a slow interaction tuning, starting from a stable condensate, we observe that 166Er and 164Dy exhibit a striking difference in the lifetime of the supersolid properties, due to the different atom loss rates in the two systems. Indeed, while in 166Er the supersolid behavior only survives a few tens of milliseconds, we observe coherent density modulations for more than 150ms in 164Dy. Building on this long lifetime, we demonstrate an alternative path to reach the supersolid regime, relying solely on evaporative cooling starting from a thermal gas.

M. J. Mark, F. Meinert, K. Lauber, H. Nägerl MottInsulatorAided Detection of UltraNarrow Feshbach Resonances,
SciPost Phys. 5 55 (20181129),
http://dx.doi.org/10.21468/SciPostPhys.5.5.055 doi:10.21468/SciPostPhys.5.5.055 (ID: 720052)
Toggle Abstract
We report on the detection of extremely narrow Feshbach resonances by employing a Mottinsulating state for cesium atoms in a threedimensional optical lattice. The Mott insulator protects the atomic ensemble from high background threebody losses in a magnetic field region where a broad Efimov resonance otherwise dominates the atom loss in bulk samples. Our technique reveals three ultranarrow and previously unobserved Feshbach resonances in this region with widths below ≈10μG, measured via LandauZenertype molecule formation and confirmed by theoretical predictions. For comparatively broader resonances we find a latticeinduced substructure in the respective atomloss feature due to the interplay of tunneling and strong particle interactions. Our results provide a powerful tool to identify and characterize narrow scattering resonances, particularly in systems with complex Feshbach spectra. The observed ultranarrow Feshbach resonances could be interesting candidates for precision measurements.

T. Langen, M. J. Mark Ultrakalt magnetisiert,
Physik Journal 12/2018 35 (20181122),
URL (ID: 720092)

A. Trautmann, P. Ilzhöfer, G. Durastante, C. Politi, M. Sohmen, M. J. Mark, F. Ferlaino Dipolar Quantum Mixtures of Erbium and Dysprosium Atoms,
Phys. Rev. Lett. 121 213601 (20181121),
http://dx.doi.org/10.1103/PhysRevLett.121.213601 doi:10.1103/PhysRevLett.121.213601 (ID: 720050)
Toggle Abstract
We report on the first realization of heteronuclear dipolar quantum mixtures of highly magnetic erbium and dysprosium atoms. With a versatile experimental setup, we demonstrate binary BoseEinstein condensation in five different ErDy isotope combinations, as well as one ErDy BoseFermi mixture. Finally, we present first studies of the interspecies interaction between the two species for one mixture.

S. Baier, D. Petter, J. H. Becher, A. Patscheider, G. Natale, L. Chomaz, M. J. Mark, F. Ferlaino Realization of a Strongly Interacting Fermi Gas of Dipolar Atoms,
Phys. Rev. Lett. 121 93602 (20180829),
http://dx.doi.org/10.1103/PhysRevLett.121.093602 doi:10.1103/PhysRevLett.121.093602 (ID: 720004)
Toggle Abstract
We realize a twocomponent dipolar Fermi gas with tunable interactions, using erbium atoms. Employing a latticeprotection technique, we selectively prepare deeply degenerate mixtures of the two lowest spin states and perform highresolution Feshbach spectroscopy in an optical dipole trap. We identify a comparatively broad Feshbach resonance and map the interspin scattering length in its vicinity. The Fermi mixture shows a remarkable collisional stability in the strongly interacting regime, providing a first step towards studies of superfluid pairing, crossing from Cooper pairs to bound molecules, in presence of dipoledipole interactions.

V. Veljic, A. R. Lima, L. Chomaz, S. Baier, M. J. Mark, F. Ferlaino, A. Pelster, A. Balaz Ground state of an ultracold Fermi gas of tilted dipoles,
New J. Phys. 20 93016 (20180614),
http://dx.doi.org/10.1088/13672630/aade24 doi:10.1088/13672630/aade24 (ID: 720051)
Toggle Abstract
Manybody dipolar effects in Fermi gases are quite subtle as they energetically compete with the large kinetic energy at and below the Fermi surface (FS). Recently it was experimentally observed that its FS is deformed from a sphere to an ellipsoid due to the presence of the anisotropic and longrange dipoledipole interaction. Moreover, it was suggested that, when the dipoles are rotated by means of an external field, the Fermi surface follows their rotation, thereby keeping the major axis of the momentumspace ellipsoid parallel to the dipoles. Here we generalise a previous HartreeFock meanfield theory to systems confined in an elongated triaxial trap with an arbitrary orientation of the dipoles relative to the trap. With this we study for the first time the effects of the dipoles' arbitrary orientation on the groundstate properties of the system. Furthermore, taking into account the geometry of the system, we show how the ellipsoidal FS deformation can be reconstructed, assuming ballistic expansion, from the experimentally measurable realspace aspect ratio after a free expansion. We compare our theoretical results with new experimental data measured with erbium Fermi gas for various trap parameters and dipole orientations. The observed remarkable agreement demonstrates the ability of our model to capture the full angular dependence of the FS deformation. Moreover, for systems with even higher dipole moment, our theory predicts an additional unexpected effect: the FS does not simply follow rigidly the orientation of the dipoles but softens showing a change in the aspect ratio depending on the dipoles' orientation relative to the trap geometry, as well as on the trap anisotropy itself. Our theory provides the basis for understanding and interpreting phenomena in which the investigated physics depends on the underlying structure of the FS, such as fermionic pairing and superfluidity.

L. Chomaz, R. van Bijnen, D. Petter, G. Faraoni, S. Baier, M. J. Mark, F. Wächtler, L. Santos, F. Ferlaino Observation of roton mode population in a dipolar quantum gas,
Nature Phys. 14 446 (20180305),
http://dx.doi.org/10.1038/s4156701800547 doi:10.1038/s4156701800547 (ID: 719813)
Toggle Abstract
The concept of a roton, a special kind of elementary excitation, forming a minimum of energy at finite momentum, has been essential to understand the properties of superfluid 4He. In quantum liquids, rotons arise from strong interparticle interactions, whose microscopic description remains debated. In the realm of highlycontrollable quantum gases, a roton mode has been predicted to emerge due to dipolar interparticle interactions despite of their weaklyinteracting character. Yet it has remained elusive to observations. Here we report momentumdistribution measurements in dipolar quantum gases of highlymagnetic erbium atoms, revealing the existence of the longsought roton. We observe the appearance of peculiar peaks at welldefined momentum matching the inverse of the tight confinement length as expected for dipolar rotons. Our combined theoretical and experimental work demonstrates unambiguously the roton softening of the excitation spectrum and provides a further step in the quest towards supersolidity.

P. Ilzhöfer, G. Durastante, A. Patscheider, A. Trautmann, M. J. Mark, F. Ferlaino Twospecies fivebeam magnetooptical trap for erbium and dysprosium,
Phys. Rev. A 97 23633 (20180226),
http://dx.doi.org/10.1103/PhysRevA.97.023633 doi:10.1103/PhysRevA.97.023633 (ID: 719919)
Toggle Abstract
We report on the first realization of a twospecies magnetooptical trap (MOT) for erbium and dysprosium. The MOT operates on an intercombination line for the respective species. Owing to the narrowline character of such a cooling transition and the action of gravity, we demonstrate a novel trap geometry employing only five beams in orthogonal configuration. We observe that the mixture is cooled and trapped very efficiently, with up to \num{5e8} Er atoms and \num{e9} Dy atoms at temperatures of about 10μK. Our results offer an ideal starting condition for the creation of a dipolar quantum mixture of highly magnetic atoms.

L. Chomaz, S. Baier, D. Petter, M. J. Mark, F. Wächtler, L. Santos, F. Ferlaino QuantumFluctuationDriven Crossover from a Dilute BoseEinstein Condensate to a Macrodroplet in a Dipolar Quantum Fluid,
Phys. Rev. X 6 41039 (20161122),
http://dx.doi.org/10.1103/PhysRevX.6.041039 doi:10.1103/PhysRevX.6.041039 (ID: 719687)
Toggle Abstract
In a joint experimental and theoretical effort, we report on the formation of a macrodroplet state in an ultracold bosonic gas of erbium atoms with strong dipolar interactions. By precise tuning of the s wave scattering length below the socalled dipolar length, we observe a smooth crossover of the ground state from a dilute BoseEinstein condensate to a dense macrodroplet state of more than 2×10 4 atoms . Based on the study of collective excitations and loss features, we prove that quantum fluctuations stabilize the ultracold gas far beyond the instability threshold imposed by meanfield interactions. Finally, we perform expansion measurements, showing that although selfbound solutions are prevented by losses, the interplay between quantum stabilization and losses results in a minimal timeofflight expansion velocity at a finite scattering length.

F. Meinert, M. J. Mark, K. Lauber, A. J. Daley, H. Nägerl Floquet engineering of correlated tunneling in the BoseHubbard model with ultracold atoms,
Phys. Rev. Lett. 116 205301 (20160417),
http://dx.doi.org/10.1103/PhysRevLett.116.205301 doi:10.1103/PhysRevLett.116.205301 (ID: 719499)
Toggle Abstract
We report on the experimental implementation of tunable occupationdependent tunneling in a BoseHubbard system of ultracold atoms via timeperiodic modulation of the onsite interaction energy. The tunneling rate is inferred from a timeresolved measurement of the lattice site occupation after a quantum quench. We demonstrate coherent control of the tunneling dynamics in the correlated manybody system, including full suppression of tunneling as predicted within the framework of Floquet theory. We find that the tunneling rate explicitly depends on the atom number difference in neighboring lattice sites. Our results may open up ways to realize artificial gauge fields that feature density dependence with ultracold atoms.

S. Baier, M. J. Mark, D. Petter, K. Aikawa, L. Chomaz, Z. Cai, M. Baranov, P. Zoller, F. Ferlaino Extended BoseHubbard Models with Ultracold Magnetic Atoms,
Science 352 205 (20160408),
http://dx.doi.org/10.1126/science.aac9812 doi:10.1126/science.aac9812 (ID: 719290)
Toggle Abstract
The Hubbard model underlies our understanding of strongly correlated materials. While its standard form only comprises interaction between particles at the same lattice site, its extension to encompass longrange interaction, which activates terms acting between different sites, is predicted to profoundly alter the quantum behavior of the system. We realize the extended BoseHubbard model for an ultracold gas of strongly magnetic erbium atoms in a threedimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics, and their influence on the superfluidtoMott insulator quantum phase transition. Moreover, we observe nearestneighbor interaction, which is a genuine consequence of the longrange nature of dipolar interactions. Our results lay the groundwork for future studies of novel exotic manybody quantum phases.
(local copy)

T. A. Maier, H. Kadau, M. Schmitt, M. Wenzel, I. FerrierBarbut, T. Pfau, A. Frisch, S. Baier, K. Aikawa, L. Chomaz, M. J. Mark, F. Ferlaino, C. Makrides, E. Tiesinga, A. Petrov, S. Kotochigova Emergence of chaotic scattering in ultracold Er and Dy,
Phys. Rev. X 5 41029 (20151119),
http://dx.doi.org/10.1103/PhysRevX.5.041029 doi:10.1103/PhysRevX.5.041029 (ID: 719275)
Toggle Abstract
We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field. This scattering is studied in a collaborative experimental and theoretical effort for both dysprosium and erbium. We present extensive measurements of their dense magnetic Feshbach resonance spectra, analyze their statistical properties, and compare to predictions from a randommatrixtheory inspired model. Furthermore, theoretical coupledchannels simulations of the molecular Hamiltonian at zero magnetic field show that shortranged anisotropic interactions are sufficiently strong that weaklybound diatomic levels form overlapping, uncoupled chaotic series that when combined are randomly distributed. The Zeeman interaction shifts and couples these levels, leading to a Feshbach spectrum of zeroenergy bound states with nearestneighbor spacings that changes from randomly to chaotically distributed for increasing magnetic field.

F. Meinert, M. Panfil, M. J. Mark, K. Lauber, J. Caux, H. Nägerl Probing the Excitations of a LiebLiniger Gas from Weak to Strong Coupling,
Phys. Rev. Lett. 115 85301 (20150820),
http://dx.doi.org/10.1103/PhysRevLett.115.085301 doi:10.1103/PhysRevLett.115.085301 (ID: 719264)
Toggle Abstract
We probe the excitation spectrum of an ultracold onedimensional Bose gas of Cesium atoms with repulsive contact interaction that we tune from the weakly to the strongly interacting regime via a magnetic Feshbach resonance. The dynamical structure factor, experimentally obtained using Bragg spectroscopy, is compared to integrabilitybased calculations valid at arbitrary interactions and finite temperatures. Our results unequivocally underly the fact that holelike excitations, which have no counterpart in higher dimensions, actively shape the dynamical response of the gas.

E. Kirilov, M. J. Mark, M. Segl, H. Nägerl Compact, robust, and spectrally pure diodelaser system with a filtered output and a tunable copy for absolute referencing,
Appl. Phys. B Las. Opt. 119/2 09462171 (20150307),
http://dx.doi.org/10.1007/s0034001560495 doi:10.1007/s0034001560495 (ID: 719196)
Toggle Abstract
We report on a design of a compact laser system composed of an extendedcavity diode laser with high passive stability and a prefilter Fabry–Perot cavity. The laser is frequencystabilized relative to the cavity using a serrodyne technique with a correction bandwidth of ≥6 MHz and a dynamic range of ≥700 MHz. The freerunning laser system has a power spectral density (PSD) ≤100 Hz2/Hz centered mainly in the acoustic frequency range. A highly tunable, 0.5–1.3 GHz copy of the spectrally pure output beam is provided, which can be used for further stabilization of the laser system to an ultrastable reference. We demonstrate a simple onechannel lock to such a reference that brings down the PSD to the subHz level. The tuning, frequency stabilization, and sideband imprinting are achieved by a minimum number of key elements comprising a fibered electrooptic modulator, acoustooptic modulator, and a nonlinear transmission line. The system is easy to operate, scalable, and highly applicable to atomic/molecular experiments demanding high spectral purity, longterm stability, and robustness.

E. Haller, M. Rabi, M. J. Mark, J. Danzl, R. Hart, K. Lauber, G. Pupillo, H. C. Nägerl Threebody correlation functions and recombination rates for bosons in three and one dimensions.,
Phys. Rev. Lett. 107 230404 (20111202),
http://dx.doi.org/10.1103/PhysRevLett.107.230404 doi:10.1103/PhysRevLett.107.230404 (ID: 717742)
Toggle Abstract
We investigate local threebody correlations for bosonic particles in three and one dimensions as a function
of the interaction strength. The threebody correlation function g(3) is determined by measuring the threebody
recombination rate in an ultracold gas of Cs atoms. In three dimensions, we measure the dependence of g(3)
on the gas parameter in a BEC, finding good agreement with the theoretical prediction accounting for beyondmean
field effects. In one dimension, we observe a reduction of g(3) by several orders of magnitude upon
increasing interactions from the weakly interacting BEC to the strongly interacting TonksGirardeau regime, in
good agreement with predictions from the LiebLiniger model for all strengths of interaction.

M. J. Mark, E. Haller, K. Lauber, J. Danzl, A. J. Daley, H. Nägerl Precision Measurements on a Tunable Mott Insulator of Ultracold Atoms,
Phys. Rev. Lett. 107 175301 (20111018),
http://dx.doi.org/10.1103/PhysRevLett.107.175301 doi:10.1103/PhysRevLett.107.175301 (ID: 717718)
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We perform precision measurements on a Mottinsulator quantum state of ultracold atoms with tunable interactions. We probe the dependence of the superfluidtoMottinsulator transition on the interaction strength and explore the limits of the standard BoseHubbard model description. By tuning the onsite interaction energies to values comparable to the interband separation, we are able to quantitatively measure numberdependent shifts in the excitation spectrum caused by effective multibody interactions.

M. J. Mark, E. Haller, J. Danzl, K. Lauber, M. Gustavsson, H. C. Nägerl Demonstration of the temporal matterwave Talbot effect for trapped matter waves,
New J. Phys. 13 85005 (20110810),
http://dx.doi.org/10.1088/13672630/13/8/085008 doi:10.1088/13672630/13/8/085008 (ID: 717720)
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We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially noninteracting matter waves and observe matterwave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with subrecoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.

H. C. Nägerl, M. J. Mark, E. Haller, M. Gustavsson, R. Hart, J. Danzl Optimal trapping wavelengths of Cs2 molecules in an optical lattice.,
Eur. Phys. J. D 65 250 (20110804),
http://dx.doi.org/10.1140/epjd/e2011200854 doi:10.1140/epjd/e2011200854 (ID: 717829)
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The present paper aims at finding optimal parameters for trapping of Cs2 molecules in optical
lattices, with the perspective of creating a quantum degenerate gas of groundstate molecules. We have
calculated dynamic polarizabilities of Cs2 molecules subject to an oscillating electric field, using accurate
potential curves and electronic transition dipole moments. We show that for some particular wavelengths
of the optical lattice, called “magic wavelengths”, the polarizability of the groundstate molecules is equal
to the one of a Feshbach molecule. As the creation of the sample of groundstate molecules relies on
an adiabatic population transfer from weaklybound molecules created on a Feshbach resonance, such a
coincidence ensures that both the initial and final states are favorably trapped by the lattice light, allowing
optimized transfer in agreement with the experimental observation.

H. C. Nägerl, M. J. Mark, E. Haller, M. Gustavsson, R. Hart, J. Danzl Ultracold and dense samples of groundstate molecules in lattice potentials,
J. Phys. Conf. Ser. 264 012015 (20110101),
http://dx.doi.org/10.1088/17426596/264/1/012015 doi:10.1088/17426596/264/1/012015 (ID: 717722)
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We produce an ultracold and dense sample of rovibronic ground state Cs2 molecules close to the regime of quantum degeneracy, in a single hyperfine level, in the presence of an optical lattice. The molecules are individually trapped, in the motional ground state of an optical lattice well, with a lifetime of 8 s. For preparation, we start with a zerotemperature atomic Mottinsulator state with optimized doublesite occupancy and efficiently associate weaklybound dimer molecules on a Feshbach resonance. Despite extremely weak FranckCondon wavefunction overlap, the molecules are subsequently transferred with >50% efficiency to the rovibronic ground state by a stimulated fourphoton process. Our results present a crucial step towards the generation of BoseEinstein condensates of groundstate molecules and, when suitably generalized to polar heteronuclear molecules such as RbCs, the realization of dipolar manybody quantumgas phases in periodic potentials.

E. Haller, R. Hart, M. J. Mark, J. Danzl, L. Reichsöllner, M. Gustavsson, M. Dalmonte, G. Pupillo, H. C. Nägerl Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons,
Nature 466 600 (20100729),
http://dx.doi.org/10.1038/nature09259 doi:10.1038/nature09259 (ID: 717204)
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Quantum manybody systems can have phase transitions even at zero temperature; fluctuations arising from Heisenberg’s uncertainty principle, as opposed to thermal effects, drive the system from one phase to another. Typically, during the transition the relative strength of two competing terms in the system’s Hamiltonian changes across a finite critical value. A wellknown example is the Mott–Hubbard quantum phase transition from a superfluid to an insulating phase, which has been observed for weakly interacting bosonic atomic gases. However, for strongly interacting quantum systems confined to lowerdimensional geometry, a novel type of quantum phase transition may be induced and driven by an arbitrarily weak perturbation to the Hamiltonian. Here we observe such an effect—the sine–Gordon quantum phase transition from a superfluid Luttinger liquid to a Mott insulator—in a onedimensional quantum gas of bosonic caesium atoms with tunable interactions. For sufficiently strong interactions, the transition is induced by adding an arbitrarily weak optical lattice commensurate with the atomic granularity, which leads to immediate pinning of the atoms. We map out the phase diagram and find that our measurements in the strongly interacting regime agree well with a quantum field description based on the exactly solvable sine–Gordon model. We trace the phase boundary all the way to the weakly interacting regime, where we find good agreement with the predictions of the onedimensional Bose–Hubbard model. Our results open up the experimental study of quantum phase transitions, criticality and transport phenomena beyond Hubbardtype models in the context of ultracold gases.
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M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, R. Hart, A. J. Daley, H. C. Nägerl Interference of interacting matter waves,
New J. Phys. 12 065029 (20100628),
http://dx.doi.org/10.1088/13672630/12/6/065029 doi:10.1088/13672630/12/6/065029 (ID: 717260)
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The phenomenon of matterwave interference lies at the heart of quantum physics. It has been observed in various contexts in the limit of noninteracting particles as a singleparticle effect. Here we observe and control matterwave interference whose evolution is driven by interparticle interactions. In a multipath matterwave interferometer, the macroscopic manybody wave function of an interacting atomic Bose–Einstein condensate develops a regular interference pattern, allowing us to detect and directly visualize the effect of interactioninduced phase shifts. We demonstrate control over the phase evolution by inhibiting interactioninduced dephasing and by refocusing a dephased macroscopic matter wave in a spinechotype experiment. Our results show that interactions in a manybody system lead to a surprisingly coherent evolution, possibly enabling narrowband and highbrightness matterwave interferometers based on atom lasers.
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E. Haller, R. Hart, M. J. Mark, J. Danzl, L. Reichsöllner, H. C. Nägerl Inducing Transport in a DissipationFree Lattice with Super Bloch Oscillations,
Phys. Rev. Lett. 104 200403 (20100521),
http://dx.doi.org/10.1103/PhysRevLett.104.200403 doi:10.1103/PhysRevLett.104.200403 (ID: 717107)
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Particles in a perfect lattice potential perform Bloch oscillations when subject to a constant force, leading to localization and preventing conductivity. For a weaklyinteracting BoseEinstein condensate (BEC) of Cs atoms, we observe giant centerofmass oscillations in position space with a displacement across hundreds of lattice sites when we add a periodic modulation to the force near the Bloch frequency. We study the dependence of these \"super\" Bloch oscillations on lattice depth, modulation amplitude, and modulation frequency and show that they provide a means to induce linear transport in a dissipationfree lattice. Surprisingly, we find that, for an interacting quantum system, super Bloch oscillations strongly suppress the appearance of dynamical instabilities and, for our parameters, increase the phasecoherence time by more than a factor of hundred.
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E. Haller, M. J. Mark, R. Hart, J. G. Danzl, L. Reichsöllner, V. Melezhik, P. Schmelcher, H. C. Nägerl ConfinementInduced Resonances in LowDimensional Quantum Systems,
Phys. Rev. Lett. 104 153203 (20100414),
http://dx.doi.org/10.1103/PhysRevLett.104.153203 doi:10.1103/PhysRevLett.104.153203 (ID: 717461)
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We report on the observation of confinementinduced resonances in strongly interacting quantumgas systems with tunable interactions for one and twodimensional geometry. Atomatom scattering is substantially modified when the swave scattering length approaches the length scale associated with the tight transversal confinement, leading to characteristic loss and heating signatures. Upon introducing an anisotropy for the transversal confinement we observe a splitting of the confinementinduced resonance. With increasing anisotropy additional resonances appear. In the limit of a twodimensional system we find that one resonance persists.
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J. G. Danzl, M. J. Mark, E. Haller, M. Gustavsson, R. Hart, J. Aldegunde, J. M. Hutson, H. C. Nägerl An ultracold highdensity sample of rovibronic groundstate molecules in an optical lattice,
Nature Phys. 6 270 (20100221),
http://dx.doi.org/10.1038/nphys1533 doi:10.1038/nphys1533 (ID: 717459)
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Control over all internal and external degrees of freedom of molecules at the level of single quantum states will enable a series of fundamental studies in physics and chemistry1, 2. In particular, samples of groundstate molecules at ultralow temperatures and high number densities will facilitate new quantumgas studies3 and future applications in quantum information science4. However, high phasespace densities for molecular samples are not readily attainable because efficient cooling techniques such as laser cooling are lacking. Here we produce an ultracold and dense sample of molecules in a single hyperfine level of the rovibronic ground state with each molecule individually trapped in the motional ground state of an optical lattice well. Starting from a zerotemperature atomic Mottinsulator state5 with optimized doublesite occupancy6, weakly bound dimer molecules are efficiently associated on a Feshbach resonance7 and subsequently transferred to the rovibronic ground state by a stimulated fourphoton process with >50% efficiency. The molecules are trapped in the lattice and have a lifetime of 8 s. Our results present a crucial step towards Bose–Einstein condensation of groundstate molecules and, when suitably generalized to polar heteronuclear molecules, the realization of dipolar quantumgas phases in optical lattices8, 9, 10.
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E. Haller, M. Gustavsson, M. J. Mark, J. Danzl, R. Hart, G. Pupillo, H. Nägerl Realization of an Excited, Strongly Correlated Quantum Gas Phase,
Science 325 12241227 (20090904),
http://dx.doi.org/10.1126/science.1175850 doi:10.1126/science.1175850 (ID: 717095)
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Ultracold atomic physics offers myriad possibilities to study strongly correlated manybody systems in lower dimensions. Typically, only groundstate phases are accessible. Using a tunable quantum gas of bosonic cesium atoms, we realized and controlled in onedimensional geometry a highly excited quantum phase that is stabilized in the presence of attractive interactions by maintaining and strengthening quantum correlations across a confinementinduced resonance. We diagnosed the crossover from repulsive to attractive interactions in terms of the stiffness and energy of the system. Our results open up the experimental study of metastable, excited, manybody phases with strong correlations and their dynamical properties.
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J. Danzl, M. J. Mark, E. Haller, M. Gustavsson, R. Hart, A. Liem, H. Zellmer, H. Nägerl Deeply bound ultracold molecules in an optical lattice,
New J. Phys. 11 055036 (20090514),
http://dx.doi.org/10.1088/13672630/11/5/055036 doi:10.1088/13672630/11/5/055036 (ID: 717101)
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We demonstrate efficient transfer of ultracold molecules into a deeply bound rovibrational level of the singlet ground state potential in the presence of an optical lattice. The overall molecule creation efficiency is 25%, and the transfer efficiency to the rovibrational level v=73,J=2> is above 80%. We find that the molecules in v=73,J=2> are trapped in the optical lattice, limited by optical excitation by the lattice light. The molecule trapping time for a lattice depth of 15 atomic recoil energies is about 20 ms. We determine the trapping frequency by the lattice phase and amplitude modulation technique. It will now be possible to transfer the molecules to the rovibrational ground state v=0,J=0> in the presence of the optical lattice.
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J. Danzl, M. J. Mark, E. Haller, M. Gustavsson, N. Bouloufa, O. Dulieu, H. Ritsch, R. Hart, H. Nägerl Precision molecular spectroscopy for ground state transfer of molecular quantum gases,
PhyDid A 142 283295 (20090512),
http://dx.doi.org/10.1039/b820542f doi:10.1039/b820542f (ID: 660699)
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One possibility for the creation of ultracold, highphasespacedensity quantum gases of molecules in the rovibrational ground state relies on first associating weaklybound molecules from quantumdegenerate atomic gases on a Feshbach resonance and then transfering the molecules via several steps of coherent twophoton stimulated Raman adiabatic passage (STIRAP) into the rovibronic ground state. Here, in ultracold samples of Cs_2 Feshbach molecules produced out of ultracold samples of Cs atoms, we observe several optical transitions to deeply bound rovibrational levels of the excited 0_u^+ molecular potentials with high resolution. At least one of these transitions, although rather weak, allows efficient STIRAP transfer into the deeply bound vibrational level v=73> of the singlet X ^1Sigma_g^+ ground state potential, as recently demonstrated. From this level, the rovibrational ground state level v=0, J=0> can be reached with one more transfer step. In total, our results show that coherent ground state transfer for Cs_2 is possible using a maximum of two successive twophoton processes or one single fourphoton STIRAP process.
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M. J. Mark, J. Danzl, E. Haller, M. Gustavsson, N. Bouloufa, O. Dulieu, H. Salami, T. Bergeman, H. Ritsch, R. Hart, H. Nägerl Dark resonances for ground state transfer of molecular quantum gases,
Appl. Phys. B Las. Opt. 95 09462171 (20090219),
http://dx.doi.org/10.1007/s0034000934071 doi:10.1007/s0034000934071 (ID: 660715)
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One possible way to produce ultracold, highphasespacedensity quantum gases of molecules in the rovibronic ground state is given by molecule association from quantumdegenerate atomic gases on a Feshbach resonance and subsequent coherent optical multiphoton transfer into the rovibronic ground state. In ultracold samples of Cs2 molecules, we observe twophoton dark resonances that connect the intermediate rovibrational level v=73,J=2⟩ with the rovibrational ground state v=0,J=0⟩ of the singlet X 1 Σ g + groundstate potential. For precise dark resonance spectroscopy we exploit the fact that it is possible to efficiently populate the level v=73,J=2⟩ by twophoton transfer from the dissociation threshold with the stimulated Raman adiabatic passage (STIRAP) technique. We find that at least one of the twophoton resonances is sufficiently strong to allow future implementation of coherent STIRAP transfer of a molecular quantum gas to the rovibrational ground state v=0,J=0⟩.
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