The control of quantum systems is at the core of many groundbreaking scientific advancements. These quantum technologies often rely on state preparation that may require the generation of entanglement between specific elements of the system which is, in effect, quantum state engineering. This has become possible with the use of ultracold atoms, molecules, and ions, and the use of state-of-the laser technologies that drive highly controlled light-matter interactions. However, these experiments are, in reality, never entirely decoupled with the surrounding environment. Therefore, the performance of quantum state engineering protocols is often significantly reduced by dissipative effects, such as the electron’s interaction with the free-space electromagnetic modes leading to spontaneous emission.

To combat these issues, our research group studies quantum state engineering in the context of open quantum systems. Our work in this area explores two distinct pathways to deal with dissipative effects. For one, we are interested in schemes that speed up the system dynamics such that the state engineering occurs on a timescale much faster than that of the main dissipative effects. In the context of spin squeezing, exploring schemes in higher dimensional systems offer this possibility as it can avoid the coarse-graining criteria of adiabatic elimination calculations that reduce the system to highly studied two-level models. Another avenue for speeding up system dynamics is to avoid the requirement of adiabaticity which is usually employed to dynamically follow the eigenstates of time-dependent Hamiltonians. Such schemes are studied in the emerging field of adiabatic shortcuts, which our group has explored in the context of speeding up adiabatic passage. These shortcuts aim to transform systems from an initial quantum state to the same final quantum state as an ideal adiabatic process, but in much less time. They have also been shown to be more robust to other imperfections in experimental implementations such as intensity of frequency fluctuations of a driving laser. We have used an adiabatic shortcut based on Lewis-Riesenfeld invariant theory to construct the laser frequency and intensity profiles for a quick and robust particle slowing scheme.

The other pathway in dealing with decoherence is the exciting prospect of engineering the dissipative processes to damp the system into a useful entangled state. We have used this idea to speed up the dissipative creation of a ring state for the use in quantum metrology. Here, two opposing Raman transitions mediated through oppositely polarized lasers and a bad-cavity mode is the main source of decoherence, and so the dissipation can be controlled by varying the relative intensity between the driving lasers. The use of controlled dissipation allowed us to damp into a state in a specific decoherence-free subspace using a cavity drive that perfectly destructively interferes with emission pattern of the atoms in the desired state. We could then adiabatically transform this state into the ring state while remaining in the decoherence-free subspace. An adiabatic shortcut in this system unfortunately cannot create the desired entangled state, and so we are exploring the use of higher dimensional models with extra degrees of freedom to find systems with this kind of decoherence-free subspace shortcut. Higher dimensional dissipative systems also offer the possibility of entangling different degrees of freedom with one another and expanding the parameter range in which metrologically useful interparticle entanglement is generated. This is explored in a SU(4) superradiant lasing model in which there is a continuous generation of spin-momentum and particle-particle entanglement in a fully dissipative system.