Dicke state preparation with applications in metrology

In this thesis, we focus on three distinct strategies to prepare Dicke states for quantum enhanced metrology. First, we consider an ensemble of spins with dipole-dipole interactions where we apply pulses to selectively climb up the Dicke ladder. In a second approach, we use geometric phase gates in a Grover method to obtain the Dicke states which does not require dipole-dipole interactions, selective addressing or special detunings and can accommodate large numbers of spins. The method's built-in protection against dephasing and the use of the prepared state for quantum metrology are discussed. For the third method, we consider spins coupled linearly to a bosonic mode and state preparation is investigated numerically through optimal control techniques with a combination of linear and nonlinear controls. Our calculations largely focus on the preparation of the state in the middle of the Dicke ladder with half the spins excited and half de-excited, which is referred to as superradiant if emitting and superabsorptive when absorbing. Nonetheless, the methods can be applied to prepare any arbitrary Dicke state. This study will lead to the enrichment of knowledge regarding the theory of general Dicke state preparations and quantum control strategies while paving the way towards exciting applications in quantum precision metrology.