of Laserphysics

# Publications

### 2018

### Observation of dynamical vortices after quenches in a system with topology

* N. Fläschner, D. Vogel, M. Tarnowski, B. S. Rem, D.-S. Lühmann, M. Heyl, J. C. Budich, L. Mathey, K. Sengstock, C. Weitenberg*

Topological phases constitute an exotic form of matter characterized by non-local properties rather than local order parameters. The paradigmatic Haldane model on a hexagonal lattice features such topological phases distinguished by an integer topological invariant known as the first Chern number. Recently, the identification of non-equilibrium signatures of topology in the dynamics of such systems has attracted particular attention. Here, we experimentally study the dynamical evolution of the wavefunction using time- and momentum-resolved full state tomography for spin-polarized fermionic atoms in driven optical lattices. We observe the appearance, movement and annihilation of dynamical vortices in momentum space after sudden quenches close to the topological phase transition. These dynamical vortices can be interpreted as dynamical Fisher zeros of the Loschmidt amplitude, which signal a so-called dynamical phase transition. Our results pave the way to a deeper understanding of the connection between topological phases and non-equilibrium dynamics.

Nature Physics 14, 265 (2018)

https://arxiv.org/abs/1608.05616

### 2016

### Twisted superfluid phase in the extended one-dimensional Bose-Hubbard

* D.-S. Lühmann*

### Experimental Reconstruction of the Berry Curvature in a Floquet Bloch Band

* N. Fläschner, B. Rem, M. Tarnowski, D. Vogel, D.-S. Lühmann, K. Sengstock, C. Weitenberg*

Topological properties lie at the heart of many fascinating phenomena in solid-state systems such as quantum Hall systems or Chern insulators. The topology of the bands can be captured by the distribution of Berry curvature, which describes the geometry of the eigenstates across the Brillouin zone. Using fermionic ultracold atoms in a hexagonal optical lattice, we engineered the Berry curvature of the Bloch bands using resonant driving and show a full momentum-resolved measurement of the ensuing Berry curvature. Our results pave the way to explore intriguing phases of matter with interactions in topological band structures

### Symmetry-broken momentum distributions induced by matter-wave diffraction during time-of-flight expansion of ultracold atoms

* M. Weinberg, O. Jürgensen, C. Ölschläger, D.-S. Lühmann, K. Sengstock, J. Simonet*

We study several effects which lead to symmetry-broken momentum distributions of quantum gases released from optical lattices. In particular, we demonstrate that interaction within the first milliseconds of the time-of-flight expansion can strongly alter the measurement of the initial atomic momentum distribution. For bosonic mixtures in state-dependent lattices, inter-species scattering processes lead to a symmetry breaking in momentum space. The underlying mechanism is identified to be diffraction of the matter wave from the total density lattice, which gives rise to a timedependent interaction potential. Our findings are of fundamental relevance for the interpretation of time-of-flight measurements and for the study of exotic quantum phases such as the twisted superfluid. Beyond that, the observed matter-wave diraction can also be used as an interferometric probe. In addition, we report on diffraction from the state-dependent standing light field, which leads to the same symmetry-broken momentum distributions, even for single component condensates.

### 2015

### Emulating molecular orbitals and electronic dynamics with ultracold atoms

*D.-S. Lühmann, C. Weitenberg, K. Sengstock*

In the recent years, ultracold atoms in optical lattices have proven their great value as quantum simulators for studying strongly-correlated phases and complex phenomena in solid-state systems. Here we reveal their potential as quantum simulators for molecular physics and propose a technique to image the three-dimensional molecular orbitals with high resolution. The outstanding tunability of ultracold atoms in terms of potential and interaction offer fully-adjustable model systems for gaining deep insight into the electronic structure of molecules. We study the orbitals of an artificial benzene molecule and discuss the effect of tunable interactions in its conjugated pi electron system with special regard to localization and spin order. The dynamical timescale of ultracold atom simulators are on the order milliseconds which allow for the time-resolved monitoring of a broad range of dynamical processes. As an example, we compute the hole dynamics in the conjugated pi system of the artificial benzene molecule.

Phys. Rev. X 5, 031016 (2015)

### Twisted complex superfluids in optical lattices

*O. Jürgensen, K. Sengstock, D.-S. Lühmann*

We show that correlated pair tunneling drives a phase transition to a twisted superfluid with a complex order parameter. This unconventional superfluid phase spontaneously breaks the time-reversal symmetry and is characterized by a twisting of the complex phase angle between adjacent lattice sites. We discuss the entire phase diagram of the extended Bose--Hubbard model for a honeycomb optical lattice showing a multitude of quantum phases including twisted superfluids, pair superfluids, supersolids and twisted supersolids. Furthermore, we show that the nearest-neighbor interactions breaks the inversion symmetry of the lattice and gives rise to dimerized density-wave insulators, where particles are delocalized on dimers. For two components, we find twisted superfluid phases with strong correlations between the species already for surprisingly small pair-tunneling amplitudes. Interestingly, this ground state shows an infinite degeneracy ranging continuously from a supersolid to a twisted superfluid.

### Non-standard Hubbard models in optical lattices: a review

* O. Dutta, M. Gajda, P. Hauke, M. Lewenstein, D.-S. Lühmann, B. A. Malomed, T. Sowiński, J. Zakrzewski*

Originally, the Hubbard model has been derived for describing the behaviour of strongly-correlated electrons in solids. However, since over a decade now, variations of it are also routinely being implemented with ultracold atoms in optical lattices. We review some of the rich literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighboring sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation on the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, also the effects related to higher Bloch bands become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher p-orbitals, as well as models that couple dynamically spin and orbital degrees of freedom. Finally, we review mean-field nonlinear-Schrödinger models of the Salerno type that share with the non-standard Hubbard models the nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of the consideration. We conclude by listing some future open problems.

Originally, the Hubbard model was derived for describing the behavior of strongly correlated electrons in solids. However, for over a decade now, variations of it have also routinely been implemented with ultracold atoms in optical lattices, allowing their study in a clean, essentially defect-free environment. Here, we review some of the vast literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After giving an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so-called extended Bose–Hubbard models, that include interactions between neighboring sites, next-neighbor sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation for the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, the effects related to higher Bloch bands also become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis, Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher p orbitals, as well as models that dynamically couple spin and orbital degrees of freedom. Finally, we review mean-field nonlinear Schrödinger models of the Salerno type that share with the non-standard Hubbard models nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of consideration. We conclude by listing some open problems, to be addressed in the future.

### 2014

### Observation of Density-Induced Tunneling

* O. Jürgensen, F. Meinert, M. J. Mark, H.-C. Nägerl, D.-S. Lühmann*

We study the dynamics of bosonic atoms in a tilted one-dimensional optical lattice and report on the first direct observation of density-induced tunneling.We show that the interaction affects the time evolution of the doublon oscillation via density-induced tunneling and pinpoint its density and interaction dependence. The experimental data for different lattice depths are in good agreement with our theoretical model. Furthermore, resonances caused by second-order tunneling processes are studied, where the density-induced tunneling breaks the symmetric behavior for attractive and repulsive interactions predicted by the Hubbard model.

### Dimerized Mott insulators in hexagonal optical lattices

*O. Jürgensen, D.-S. Lühmann*

We study bosonic atoms in optical honeycomb lattices with anisotropic tunneling and find dimerized Mott insulator (MI) phases with fractional filling. These incompressible insulating phases are characterized by an interaction-driven localization of particles in respect to the individual dimers and large local particle-number fluctuations within the dimers. We calculate the ground-state phase diagrams and the excitation spectra using an accurate cluster mean-field method. The cluster treatment enables us to probe the fundamental excitations of the dimerized MI where the excitation gap is dominated by the intra-dimer tunneling amplitude. This allows the distinction from normal Mott insulating phases gapped by the on-site interaction. In addition, we present analytical results for the phase diagram derived by a higher-order strong-coupling perturbative expansion approach. By computing finite lattices with large diameters the influence of a harmonic confinement is discussed in detail. It is shown that a large fraction of atoms forms the dimerized MI under experimental conditions. The necessary anisotropic tunneling can be realized either by periodic driving of the optical lattice or by engineering directly a dimerized lattice potential. The dimers can be mapped to their antisymmetric states creating a lattice with coupled p-orbitals.

### Quantum phases in tunable state-dependent hexagonal optical lattices

* D.-S. Lühmann, O. Jürgensen, M. Weinberg, J. Simonet, P. Soltan-Panahi, K. Sengstock*

We study the ground-state properties of ultracold bosonic atoms in a state-dependent graphene-like honeycomb optical lattice, where the degeneracy between the two triangular sublattices A and B can be lifted. We discuss the various geometries accessible with this lattice setup and present a novel scheme to control the energy offset with external magnetic fields. The competition of the on-site interaction with the offset energy leads to Mott phases characterized by population imbalances between the sublattices. For the definition of an optimal Hubbard model, we demonstrate a scheme that allows for the efficient computation of Wannier functions. Using a cluster mean-field method, we compute the phase diagrams and provide a universal representation for arbitrary energy offsets. We find good agreement with the experimental data for the superfluid to Mott insulator transition.

### 2013

### Large-Amplitude Superexchange of High-Spin Fermions in Optical Lattices

* O. Jürgensen, J. Heinze, D.-S. Lühmann*

We show that fermionic high-spin systems with spin-changing collisions allow to monitor superexchange processes in optical superlattices with large amplitudes and strong spin fluctuations. By investigating the non-equilibrium dynamics, we find a superexchange dominated regime at weak interactions. The underlying mechanism is driven by an emerging tunneling-energy gap in shallow few-well potentials. As a consequence, the interaction-energy gap that is expected to occur only for strong interactions in deep lattices is reestablished. By tuning the optical lattice depth, a crossover between two regimes with negligible particle number fluctuations is found: first, the common regime with vanishing spin-fluctuations in deep lattices and, second, a novel regime with strong spin fluctuations in shallow lattices. We discuss the possible experimental realization with ultracold 40K atoms and observable quantities in double wells and two-dimensional plaquettes.

New J. Phys. 15, 113017 (2013)

http://arxiv.org/abs/1306.1330

### Cluster Gutzwiller method for bosonic lattice systems

*D.-S. Lühmann*

A versatile and numerically inexpensive method is presented allowing the accurate calculation of phase diagrams for bosonic lattice models. By treating clusters within the Gutzwiller theory, a surprisingly good description of quantum fluctuations beyond the mean-field theory is achieved approaching quantum Monte Carlo predictions for large clusters. Applying this powerful method to the Bose-Hubbard model, we demonstrate that it yields precise results for the superfluid to Mott-insulator transition in square, honeycomb, and cubic lattices. Due to the exact treatment within a cluster, the method can be effortlessly adapted to more complicated Hamiltonians in the fast progressing field of optical lattice experiments. This includes state- and site-dependent superlattices, large confined atomic systems, and disordered potentials, as well as various types of extended Hubbard models. Furthermore, the approach allows an excellent treatment of systems with arbitrary filling factors. We discuss the perspectives that allow for the computation of large, spatially varying lattices, low-lying excitations, and time evolution.

### 2012

### Density-induced processes in quantum gas mixtures in optical lattices

*O. Jürgensen, K. Sengstock, D.-S. Lühmann*

We show that off-site processes and multi-orbital physics have a crucial impact on the phase diagram of quantum gas mixtures in optical lattices. In particular, we discuss Bose-Fermi mixtures where the intra- and interspecies interactions induce competing density-induced hopping processes, the so-called bond-charge interactions. Furthermore, higher bands strongly influence tunneling and on-site interactions. The resulting decrease of the tunneling competes with a decrease of the total on-site interaction energy both affecting the critical lattice depth of the superfluid to Mott insulator transition. In contrast to the standard Bose-Fermi-Hubbard model, we predict a large shift of the transition to shallower lattice depths with increasing Bose-Fermi attraction.

### Multi-orbital and density-induced tunneling of bosons in optical lattices

* D.-S. Lühmann, O. Jürgensen, K. Sengstock*

We show that multi-orbital and density-induced tunneling have significant impact on the phase diagram of bosonic atoms in optical lattices. Off-site interactions lead to density-induced hopping, so-called bond-charge interactions and can reach the same order of magnitude as conventional tunneling. In addition, interaction-induced higher-band processes also give rise to strongly modified tunneling, on-site, and bond-charge interactions. The derived phase diagram deviates substantially from the single-band Bose-Hubbard predictions indicating strong changes of the SF-MI transition point.

### Coherent multi-flavour spin dynamics in a fermionic quantum gas

* J. S. Krauser, J. Heinze, N. Fläschner, S. Götze, O. Jürgensen, D.-S. Lühmann, C. Becker, K. Sengstock*

We demonstrate the first experimental realization of a well‐controlled fermionic spinor gas with interaction‐driven spin oscillations. By properly choosing the initial spin states we can change the effective length of the atomic spin from 1/2 to 9/2. The control over the magnetic field allows to initialize and stop spin dynamics and to select the number of involved levels. We extract the microscopic interaction parameters and find excellent agreement with a two particle model including all spin‐dependent interactions. By tuning the depth of the optical lattice, we investigated the transition from on‐site dominated to quantum manybody spin dynamics, where spins diffuse throughout the lattice producing highly entangled states. For this case, we observe a new form of melting of a band insulator.

Nature Physics 8, 813–818 (2012)

http://arxiv.org/abs/1203.0948v1

### Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices

* P. Soltan-Panahi, D.-S. Lühmann, J. Struck, P. Windpassinger, K. Sengstock*

Orbital physics plays a significant role for a vast number of important phenomena in complex condensed matter systems such as high-Tc superconductivity and unconventional magnetism. In contrast, phenomena in superfluids - especially in ultracold quantum gases - are commonly well described by the lowest orbital and a real order parameter. Here, we report on the observation of a novel multi-orbital superfluid phase with a complex order parameter in binary spin mixtures. In this unconventional superfluid, the local phase angle of the complex order parameter is continuously twisted between neighboring lattice sites. The nature of this twisted superfluid quantum phase is an interaction-induced admixture of the p-orbital favored by the graphene-like band structure of the hexagonal optical lattice used in the experiment. We observe a second-order quantum phase transition between the normal superfluid (NSF) and the twisted superfluid phase (TSF) which is accompanied by a symmetry breaking in momentum space. The experimental results are consistent with calculated phase diagrams and reveal fundamentally new aspects of orbital superfluidity in quantum gas mixtures. Our studies might bridge the gap between conventional superfluidity and complex phenomena of orbital physics.

Nature Physics 8, 71–75 (2012)

http://arxiv.org/abs/1104.3456v1

### 2011

### Multi-band spectroscopy of ultracold fermions: Observation of reduced tunneling in attractive Bose-Fermi mixtures

* J. Heinze, S. Götze, J. S. Krauser, B. Hundt, N. Fläschner, D.-S. Lühmann, C. Becker, K. Sengstock*

We perform a detailed experimental study of the band excitations and tunneling properties of ultracold fermions in optical lattices. Employing a novel multi-band spectroscopy for fermionic atoms we can measure the full band structure and tunneling energy with high accuracy. In an attractive Bose-Fermi mixture we observe a significant reduction of the fermionic tunneling energy, which depends on the relative atom numbers. We attribute this to an interaction-induced increase of the lattice depth due to self-trapping of the atoms.

Phys. Rev. Lett. 107, 135303 (2011)

http://arxiv.org/abs/1107.2322v1

### 2010

### Time-resolved observation of coherent multi-body interactions in quantum phase revivals

* S. Will, T. Best, U. Schneider, L. Hackermüller, D.-S. Lühmann, and I. Bloch*

Interactions lie at the heart of correlated many-body quantum phases. Typically, the interactions between microscopic particles are described as two-body interactions. However, it has been shown that higher-order multi-body interactions could give rise to novel quantum phases with intriguing properties. So far, multi-body interactions have been observed as inelastic loss resonances in three-and four-body recombinations of atom-atom and atom-molecule collisions. Here we demonstrate the presence of effective multi-body interactions in a system of ultracold bosonic atoms in a three-dimensional optical lattice, emerging through virtual transitions of particles from the lowest energy band to higher energy bands. We observe such interactions up to the six-body case in time-resolved traces of quantum phase revivals, using an atom interferometric technique that allows us to precisely measure the absolute energies of atom number states at a lattice site. In addition, we show that the spectral content of these time traces can reveal the atom number statistics at a lattice site, similar to foundational experiments in cavity quantum electrodynamics that yield the statistics of a cavity photon field. Our precision measurement of multi-body interaction energies provides crucial input for the comparison of optical-lattice quantum simulators with many-body quantum theory.

### Probing superfluids in optical lattices by momentum-resolved Bragg spectroscopy

* Philipp T. Ernst, Sören Götze, Jasper S. Krauser, Karsten Pyka, Dirk-Sören Lühmann, Daniela Pfannkuche, and Klaus Sengstock*

The fundamental concept of superfluidity gives rise to fascinating effects and collective behaviour such as vortex creation and second sound. Using quantum gases in optical lattices, superfluids can be realized over a wide range of tunable parameters, with a continuous connection to the regime of strong correlation. However, for full experimental access and a comprehensive comparison with condensed-matter systems, there is a need for new detection techniques to probe their essential physics. Here we report on a comprehensive study of superfluids in optical lattices by Bragg spectroscopy. We present fully momentum-resolved measurements of the band structure and associated interaction effects at several lattice depths. In addition, we directly study the composition of excitations and observe strong indications for Bogoliubov backscattering. Our measurements demonstrate the applicability and limits of the Bogoliubov theory to describe excitation properties of superfluids in periodic potentials and should pave the way for detailed studies of strongly correlated phases.

Kronjaeger2009-Spontaneous-pattern-formation-XXX-0904.2339v1-02 (PDF)

### 2009

### Role of Interactions in 87Rb-40K Bose-Fermi Mixtures in a 3D Optical Lattice

* T. Best, S. Will, U. Schneider, L. Hackermüller, D. van Oosten, I. Bloch, and D.-S. Lühmann*

We investigate the effect of interspecies interaction on a degenerate mixture of bosonic Rb-87 and fermionic K-40 atoms in a three-dimensional optical lattice potential. Using a Feshbach resonance, the Rb-87-K-40 interaction is tuned over a wide range. Through an analysis of the Rb-87 momentum distribution, we find a pronounced asymmetry between strong repulsion and strong attraction. In the latter case, we observe a marked shift in the superfluid to Mott insulator transition, which we attribute to a renormalization of the Bose-Hubbard parameters due to self-trapping.

### 2008

### Self-Trapping of Bosons and Fermions in Optical Lattices

* D.-S. Lühmann, K. Bongs, K. Sengstock, and D. Pfannkuche*

We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with Rb-87-K-40 mixtures, where a large shift of the critical point has been found.

### Localization and delocalization of ultracold bosonic atoms in finite optical lattices

* D.-S. Lühmann, K. Bongs, K. Sengstock, and D. Pfannkuche*

We study bosonic atoms in small optical lattices by exact diagonalization and observe a striking similarity to the superfluid to Mott insulator transition in macroscopic systems. The momentum distribution, the formation of an energy gap, and the pair correlation function show only a weak size dependence. For noncommensurate filling we reveal in deep lattices a mixture of localized and delocalized particles, which is sensitive to lattice imperfections. Breaking the lattice symmetry causes a Bose-glass-like behavior. We discuss the nature of excited states and orbital effects by using an exact diagonalization technique that includes higher bands.