Prof Dieter Jaksch

Abstract:

We show that the macroscopic magnetic and electronic properties of strongly correlated electron systems can be manipulated by coupling them to a cavity mode. As a paradigmatic example we consider the Fermi-Hubbard model and find that the electron-cavity coupling enhances the magnetic interaction between the electron spins in the ground-state manifold. At half filling this effect can be observed by a change in the magnetic susceptibility. At less than half filling, the cavity introduces a next-nearest-neighbor hopping and mediates a long-range electron-electron interaction between distant sites. We study the ground-state properties with tensor network methods and find that the cavity coupling can induce a phase characterized by a momentum-space pairing effect for electrons.

Abstract:

Polar molecules offer a new platform for quantum simulation of systems with long-range interactions, based on the electrostatic interaction between their electric dipole moments. Here, we report the development of coherent quantum state control using microwave fields in $^{40}$Ca$^{19}$F and $^{87}$Rb$^{133}$Cs molecules, a crucial ingredient for many quantum simulation applications. We perform Ramsey interferometry measurements with fringe spacings of $\sim 1~\rm kHz$ and investigate the dephasing time of a superposition of $N=0$ and $N=1$ rotational states when the molecules are confined. For both molecules, we show that a judicious choice of molecular hyperfine states minimises the impact of spatially varying transition-frequency shifts across the trap. For magnetically trapped $^{40}$Ca$^{19}$F we use a magnetically insensitive transition and observe a coherence time of 0.61(3)~ms. For optically trapped $^{87}$Rb$^{133}$Cs we exploit an avoided crossing in the AC Stark shifts and observe a maximum coherence time of 0.75(6)~ms.

Abstract:

We show that strong parametric driving of a quantum harmonic oscillator coupled to a thermal bath allows one to distinguish between different microscopic models for the oscillator-bath coupling. We consider a bath with an Ohmic spectral density and a model where the system-bath interaction can be tuned continuously between position and momentum coupling via the coupling angle α. We derive a master equation for the reduced density operator of the oscillator in Born-Markov approximation and investigate its quasisteady state as a function of the driving parameters, the temperature of the bath and the coupling angle α. We find that the driving introduces a strong dependence of the time-averaged variance of position and momentum on these parameters. In particular, we identify parameter regimes that maximize the α dependence and provide an intuitive explanation of our results.

Abstract:

The $t$–$J$ model is a standard model of strongly correlated electrons, often studied in the context of high-$T_c$ superconductivity. However, most studies of this model neglect three-site terms, which appear at the same order as the superexchange $J$. As these terms correspond to pair-hopping, they are expected to play an important role in the physics of superconductivity when doped sufficiently far from half-filling. In this paper we present a density matrix renormalisation group study of the one-dimensional $t$–$J$ model with the pair hopping terms included. We demonstrate that these additional terms radically change the one-dimensional ground state phase diagram, extending the superconducting region at low fillings, while at larger fillings, superconductivity is completely suppressed. We explain this effect by introducing a simplified effective model of repulsive hardcore bosons.