The interplay of correlations that leads to electronic order in the Mott transition or Charge Density Wave state is one of the key challenges in correlated electron systems. It gives rise to a large variety of different ground states ranging from highly unconventional (“bad”) metals to charge density wave states or superconductivity. The case of the Mott insulator is due to high electronic correlations competing with the kinetic energy of the conducting electrons. Doping this Mott insulating state tunes the hierarchy of the competing interactions, where besides the pure electronic interactions also coupling to spin or lattice degrees of freedom are involved. This is especially true for the doped 2D Mott insulator which shows some of the most intriguing phenomena of correlated electron systems: High temperature superconductivity.
In our research we control the Mott state in various ways: Ultrafast photo-doping directly excites charges above the gap and allows investigating the peculiar properties of the photo-induced states. These do not show simple metallic properties but are still dominated by the strong electron-electron (or also electron-phonon) interactions. The photo-excited electron feels the Coulomb attraction by the hole that it leaves behind. Ultrafast optical probes allow us to directly measure such drag-back dynamics on timescales of the electron hopping while tuning with external parameters like temperature, pressure, electric or magnetic fields tune the relative strength of the electronic interactions and therefore control the recombination dynamics of the excited electrons back to the ground state.
Another way controlling effective interactions is to excite directly vibrational, spin, or orbital properties that are coupled to the ground state or the electronic properties of the system. In the organic charge transfer salts we use resonant excitations of local vibrational modes to alter the local molecular orbitals. That modulates the electronic on-site properties and makes the effective interactions in the Hubbard model time dependent. Such quantum modulation spectroscopy of a single degree of freedom in the solid state allows an experimental deconstruction of the Hubbard Hamiltonian by exposing couplings that otherwise would have vanishingly small contributions in equilibrium.
 M. Mitrano et al. Pressure-Dependent Relaxation in the Photoexcited Mott Insulator ET-F2TCNQ: Influence of Hopping and Correlations on Quasiparticle Recombination Rates. Phys. Rev. Lett. 112, 117801 (2014).
 S. Kaiser et al. Optical Properties of a Vibrationally Modulated Solid State Mott Insulator. Scientific Reports 4, 3823 (2014).
 R. Singla et al. THz-Frequency Modulation of the Hubbard U in an Organic Mott Insulator. Phys. Rev. Lett. 115 187401 (2015).