Since the first Bose Einstein condensates (BECs) of neutral atoms were achieved in 1995,
the ongoing research into using such many-body quantum states of matter as a **quantum simulator**
has tremendously expanded the scope of research on strongly correlated quantum matter.

For lattice models of strongly correlated quantum particles, quantum simulation works the following way: confine ultracold bosonic or fermionic atoms inside the lowest Bloch band(s) of an optical lattice, which is formed by (a) standing laser wave(s).

As such systems can realize many of the important and difficult-to-solve models of condensed matter physics, like e.g. the 2D Hubbard model doped away from unit filling, the equilibrium state of this system could reveal the models ground state -**thus ''quantum simulation'': solving a model for which theory cannot yet compute the ground state reliably,
via precise and controlled **__experimental__ realization of the model at low entropy/temperature.

My work in the domain of quantum simulation is concerned with three key topics:

**
(1) Static and dynamic phenomena in quantum matter, such as disordered systems,
dissipatively driven phases and mobile quantum impurities in 1D.
**

(2) Obtaining lattice-confined atoms at low entropies for quantum simulation.

(3) Measuring the properties of the realized state inside the lattice.

For lattice models of strongly correlated quantum particles, quantum simulation works the following way: confine ultracold bosonic or fermionic atoms inside the lowest Bloch band(s) of an optical lattice, which is formed by (a) standing laser wave(s).

As such systems can realize many of the important and difficult-to-solve models of condensed matter physics, like e.g. the 2D Hubbard model doped away from unit filling, the equilibrium state of this system could reveal the models ground state -

My work in the domain of quantum simulation is concerned with three key topics:

(2) Obtaining lattice-confined atoms at low entropies for quantum simulation.

(3) Measuring the properties of the realized state inside the lattice.

New insight and new physics from correlated ultracold atoms: disordered systems, dissipatively
driven phases and mobile quantum impurities

(back to top)

My earliest published work was concerned with showing the capabilities of interacting atoms moving inside purposefully disordered optical lattices to**quantum-simulate hard-to-solve problems in quantum percolation and spin glass theory**
[Phys. Rev. Lett 93 40401 (2004),
Phys. Rev. A 72 63616 (2005),
J. Phys. B - Atom. Mol. Opt. Phys. 39, 121 (2006),
Acta. Phys. Pol. A 109, 89 (2006)].

Later revisiting this topic showed how the creation of two physically identical replicas of the same disordered system and measuring their cross-system overlap would allow to**probe for the Bose glass phase**,
one of the basic models in the study of disordered quantum many-body systems
[New J. Phys. 10, 073032 (2008)].

My first direct involvement in using the potential of lattice-confined ultracold atoms to create completely new many-body states of quantum matter came in the theory-experiment collaboration with the group of J. Hecker-Denschlag (Innsbruck) on**metastable repulsively bound pairs** [Nature 441, 853 (2006)].
This work was the start of an ongoing line of my work in modelling and thus understanding many-body experiments through strong
DMRG numerics.

I was further involved in an influential collaborative project to design**dissipatively driven many-body phases** of correlated atoms,
such as a lattice BEC of bosons or η-paired states of superfluid fermion pairs.
[Nat. Phys. 4, 878 (2008)].
This scheme is based on engineering couplings of the lattice confined atoms to many disconnected local dissipative reservoirs.

It could then be shown under which conditions many such local actions drive the system collectively towards a well-defined global state [Phys. Rev. A 78, 42307 (2008)].

Afterwards,**mobile quantum impurities inside a 1D quantum liquid** became a major focus of my work.

I could show that any impurity newly injected into the system belongs to a**new dynamical universality class**, in which the
impurity loses all quasiparticle properties and is characterized by subdiffusive motion, i.e. logarithmically slow
motion, slower than any power law, instead
[Phys. Rev. Lett. 113, 70601 (2014);
c.f. figure].

Flanking this work was a collaboration on the**full non-equilibrium dynamics of a 'kicked' impurity** oscillating inside
a parabolically confined 1D quantum liquid
[New J. Phys. 15, 045018 (2013)].

These theoretical works were complemented by research as lead theorist on two high-impact collaborations with experimental groups.

With the group of F. Minardi at LENS (Firenze) we studied the**polaronic mass shift** of an impurity oscillating inside a 1D mass
and its dependence on the bath-impurity interaction
[Phys. Rev. A 85 23623 (2012)].

And with the group of I. Bloch at MPQ Garching (München) we provided an unprecedented look at the**quantum-coherent propagation
of both spin waves and polarons**, resolved in time and space
[Nat. Phys. 9, 235 (2013); c.f. figure].

(back to top)

(back to top)

My earliest published work was concerned with showing the capabilities of interacting atoms moving inside purposefully disordered optical lattices to

Later revisiting this topic showed how the creation of two physically identical replicas of the same disordered system and measuring their cross-system overlap would allow to

My first direct involvement in using the potential of lattice-confined ultracold atoms to create completely new many-body states of quantum matter came in the theory-experiment collaboration with the group of J. Hecker-Denschlag (Innsbruck) on

I was further involved in an influential collaborative project to design

It could then be shown under which conditions many such local actions drive the system collectively towards a well-defined global state [Phys. Rev. A 78, 42307 (2008)].

Afterwards,

I could show that any impurity newly injected into the system belongs to a

Flanking this work was a collaboration on the

These theoretical works were complemented by research as lead theorist on two high-impact collaborations with experimental groups.

With the group of F. Minardi at LENS (Firenze) we studied the

And with the group of I. Bloch at MPQ Garching (München) we provided an unprecedented look at the

(back to top)

(back to top)

Even though lattice-confined ultracold atoms excel at precisely mimicking those Hubbard-type models to be quantum simulated, they struggle against one drawback: as the near-total isolation of the atoms from the environment is indispensable for bringing them to ultracold temperatures, it is a

This is a major hurdle for quantum simulation of e.g. the main candidate model to explain high-T

To solve this problem, and provide methods to future experiments for producing very-low entropy states for quantum simulation,

Adiabatic state preparation exploits the available high degree of control over the optical lattice to load the atoms initially into a 'trivial' product state, with e.g. one atom in every second site of a superlattice. Removing the optical superlattice adiabatically would then see this state cross over smoothly into the exact non-trivial ground state of the Hamiltonian of which the ground state is sought.

In my work I have described how this approach can be used to

Previously, I had shown that adiabatic state preparation could be used to form the optical lattice analogue of a

Further work with M. Dolfi and M. Troyer quantified the degree of heating the atoms incur when being loaded into the lattice in the standard manner, and provided prescriptions as to

For the other approach, entropy shifting, I have shown together with S. Langer and A. J. Daley, when and how

(back to top)

Measuring observables

(back to top)

The concept of quantum simulation requires measuring the properties of any state prepared in the lattice - i.e. to ''read out'' the result.

With the field of quantum simulation increasingly being advanced by experiments using confocal microscope-based optical lattice setups, which offer unprecedented single-site resolution and manipulation of atoms,**previous measuring schemes that offer
frequency/time and spatial/momentum resolution are reaching their limits**,
due to the generally low number of atoms in these setups.

I was part of a wider collaboration to show how the newly available single-site resolution provides a way out of this dilemma, being the basis of a novel in-lattice approach for**measuring practically any time- and space-dependent
spin-spin correlation function** of any effective spin-Hamiltonian that can be realized in such experiments
[Phys. Rev. Lett. 111, 147205 (2013)].

I further proposed and theoretically validated a much more**general scheme of lattice-assisted spectroscopy
applicable to practically any Hamiltonian** that could provide frequency-resolved local particle- and hole-spectra
[Phys. Rev. Lett. 115, 165301 (2015); c.f. figure].
This scheme can then be generalized further to provide momentum-resolved and higher-order spectral functions.

(back to top)

The concept of quantum simulation requires measuring the properties of any state prepared in the lattice - i.e. to ''read out'' the result.

With the field of quantum simulation increasingly being advanced by experiments using confocal microscope-based optical lattice setups, which offer unprecedented single-site resolution and manipulation of atoms,

I was part of a wider collaboration to show how the newly available single-site resolution provides a way out of this dilemma, being the basis of a novel in-lattice approach for

I further proposed and theoretically validated a much more

(back to top)