Ultracold Bosons in Optical Superlattices
List of publications
If you want to have a look at the long and impressive history of this experiment. Look at its citation history on google scholar following this link!
Experiments with ultracold bosons in optical superlattices
In our experiments with ultracold bosonic rubidium atoms in optical superlattices, we are studying quantum phases and phase transitions in specific condensed matter models as well as questions of quantum manybody dynamics (more). Every experimental run starts out with the creation of a BoseEinstein condensate of Rb78 using a magnetooptical trap (MOT) and forced evaporation in a magnetic trap and, later, in an optical dipole trap.
Beyond this initial step, our main tool is an optical superlattice formed by overlapping two standingwave laser fields with a commensurate wavelength ratio of 2 (more). Two perpendicular optical lattices complete the setup of a regular threedimensional lattice with a unit cell of two sites. Full dynamical control over the individual laserbeam intensities as well as over the relative phase between the two standing waves forming the superlattice allows us to set all relevant parameters of the atomic manybody system. We are currently extending this system by replacing one of the transverse lattice by another superlattice, thus obtaining a unit cell of four sites – a plaquette.
The past
Some examples of experiments performed with the single superlattice potential – still in Mainz – include the direct observation of atom cotunneling of repulsively interacting atoms, the observation and control of superexchange interactions between neighboring atoms and the controlled creation and detection of spincorrelations in the optical lattice. In terms of dynamics, we have investigated the relaxation of strongly correlated bosons in onedimensional chains following a quantum quench. Another experiment dealt with manybody LandauZener sweeps with onedimensional quantum gases and a drastic breakdown of adiabaticity far from equilibrium.
Even before the implementation of our first superlattice, the machine went through a long history of experiments with singlewavelength optical lattices. Prominent examples from the list of results are the observation of the quantum phase transition from a superfluid to a bosonic Mott insulator, the measurement of the collapseandrevival dynamics of a matterwave field and the realization of a TonksGirardeau gas. More recently, we could also demonstrate the storage of light in a Mott insulator by means of electrically induced transparency and determine a quantitative phase diagram of the BoseHubbard model at finite temperatures.
With the extension to the twoaxes superlattices, we aimed at, for example, realizing minimal versions of topologically ordered quantum phases of bosons. Such phases with topological order cannot be classified by an order parameter and represent a new class of manybody systems without any local order. Only by carrying globals measurements on the system, one can reveal the hidden order in the system.
Furthermore, we are able to create, control and detect spincorrelated states in two dimensions in analogy to 2D valence bond solid states, and to follow their dynamics. Such states are of general interest in the context of quantum magnetism and hightemperature superconductivity.
Recent projects
Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
The plateaux of the Hall conductivity observed in the quantum Hall effect can be attributed to a topological invariant characterizing Bloch bands: the Chern number. Until now, topological transport associated with nonzero Chern numbers has only been observed in electronic systems. In the context of artificial gauge fields for ultracold atoms, however, the implementation of experimental probes revealing the nontrivial topology of energy bands is one of the most challenging goals. In this work, the Chern number of artificially generated Hofstadter bands in an optical lattice was measured by looking at the transverse deflection of an atomic cloud in response to an external gradient. When applying a force, the atoms acquire an anomalous transverse velocity which is caused by the nontrivial topology of the band structure and for a uniformly populated band it can be be related to its Chern number. The Chern number could thus be determined by measuring the centerofmass position of the atom cloud in situ. In addition to this, a novel bandmapping technique for determining the populations of the Hofstadter bands as well as a new alloptical scheme for generating uniform artificial gauge fields in optical superlattices were developed. This experiment constitutes the first measurement of a Chern number in a nonelectronic systems and the applied method can easily be generalized to a wide range of physical systems. For the experimental parameters, the lowest band of the Hofstadter model is very flat and thus a good candidate for the realization of novel topological states of matter like fractional Chern insulators.
A Thouless quantum pump with ultracold bosonic atoms in an optical superlattice
The concept of a topological charge pump was first introduced by David Thouless more than 30 years ago. It would enable the robust transport of charge through an adiabatic cyclic evolution of the underlying Hamiltonian. In contrast to classical transport, the charge that is transported per cycle is quantized and purely determined by the topology of the pump cycle, making it robust to perturbations. On a fundamental level, the quantized charge transport can be connected to a topological invariant, the Chern number, and a Thouless quantum pump may therefore be regarded as a 'dynamical' version of the integer quantum Hall effect. In this work, such a pump was realized using ultracold bosonic atoms forming a Mott insulator in a dynamically controlled optical superlattice. By taking in situ images of the cloud, a quantized deflection per pump cycle was observed for the first time and its robustness against external perturbations could be shown by comparing the deflection for different pump parameters. The pump's genuine quantum nature was revealed by showing that, in contrast to groundstate particles, a counterintuitive reversed deflection occurs for particles in the first excited band. Furthermore it was directly demonstrated that this system undergoes a controlled topological transition in higher bands when tuning the superlattice parameters. These results open a route to the implementation of more complex pumping schemes. By adding a spin degree of freedom, a Z2 spin pump could be implemented in a spindependent superlattice. Moreover, extending the Thouless pump to 2D systems would enable the realization of an analogon of the 4D integer quantum Hall effect.
Spin pumping and measurement of spin currents in optical superlattices
Exposing materials to strong magnetic fields has led to remarkable discoveries, most prominently the observation of the integer and fractional quantum Hall effect. These quantum phenomena surprise due to their robustness and independence of material properties, arising from their topological nature. More recently, a fundamentally different quantum state was observed, the topological insulator, which preserves timereversal symmetry. Such timereversal symmetric systems in 2D that also conserve spin, exhibit the quantum spin Hall effect. It is characterized by a quantized spin but vanishing charge conductance. Analogous to topological charge pumps proposed by Thouless 1983, a dynamical version of a topological insulator can be designed: a quantum spin pump. We report on an experimental implementation of a spin pump with ultracold bosonic atoms in an optical superlattice.
Starting from an antiferromagnetically ordered spin chain, we periodically vary the underlying spindependent Hamiltonian by changing a global magnetic gradient. We show, that in the limit of isolated double wells the system is a dynamical version of the quantum spin Hall effect and observe the associated response: a spin current without charge current. The response was detected by both a direct verification of spin transport through insitu measurements of the spins' center of mass displacement and the measurement of local spin currents. To observe these spin currents in optical lattices, we demonstrate a novel detection method using the amplitude of superexchange oscillations emerging after a projection onto static double wells.
Exploring 4D quantum Hall physics with a 2D topological charge pump
The quantum Hall effect  a prominent example for topological states of matter in 2D  can be generalized to 4D systems. In 4D, a novel quantized Hall response appears, which is nonlinear and described by a 4D topological invariant  the second Chern number. We realize a dynamical version of the 4D quantum Hall effect by implementing a 2D topological charge pump for ultracold bosonic atoms in an angled optical superlattice. We observe a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number.
Floquet approach to Z2 lattice gauge theories
Stronglyinteracting gauge theories are extremely challenging to access with conventional numerical techniques. Here, we take a first step towards quantum simulation of gauge theories by implementing a Floquetbased method with twocomponent ultracold bosons in a doublewell potential. For resonant periodic driving at the onsite interaction strength and an appropriate choice of the modulation parameters, the effective Floquet Hamiltonian exhibits Z_{2} symmetry. We study the dynamics of the system for different initial states, reveal challenges that arise due to symmetrybreaking terms and outline potential pathways to overcome them.
People
Phone: +49 89 2180 6143 

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Phone: +49 89 2180 6133 
Former Members
Josselin Bernardoff  Internship student 
Simon Hertlein  Bachelor student 
Philip Zupancic  Bachelor student 
Moritz Berngruber  Master student 
Dipl. Phys. Ute Schnorrberger  PhD Student 
Dipl.Phys. Stefan Trotzky  PhD Student 
Dr. Simon Fölling  PhD Student 
Dr. Marcos Atala  PhD Student 
Dr. Michael Lohse  PhD Student 
Prof. Sylvain Nascimbène  Postdoc 
Prof. Julio T. Barreiro  Postdoc 
Prof. YuAo Chen  Postdoc 