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Gaining a better understanding of quantum control strategies is arguably the most urgent theoretical challenge toward the realisation of functional quantum technologies. Within the broad paradigm of quantum continuous variables, that allows one to describe a wide range of physical systems - such as light, trapped ions, atomic ensembles and superconducting devices - a powerful theoretical framework, combining elements of group theory and quantum stochastic calculus, has been developed to address the mathematical problem of quantum control, and allows one to address far reaching theoretical questions with remarkable practical impact.
Quantum control is typically divided into open-loop control, where the operations applied on the system are pre-determined, and closed-loop ("feedback") control, where the operations applied depend on the state of the system. Usually, the latter is enacted by letting future control operations on the system depend on the outcome of measurements on a part of it.
However, a new paradigm for feedback control, proper to quantum systems and with no classical analogue, has emerged, where the control operations are not parametrised by the classical outcome of measurement processes but rather by the full, "coherent" quantum state of the system. This paradigm has been termed "coherent feedback" and, for continuous variables, admits a clear-cut definition by means of the introduction of the so called input-output formalism in the Langevin equations, which models interfaces between static, localised degrees of freedom and travelling continua of modes (that would populate free space or, typically, a long optical fibre in the case of quantum light).
Although suspected to be superior to measurement-based feedback to accomplish certain tasks, such as cooling, no systematic analysis of the ultimate limits of coherent feedback, nor any reliable comparison with measurement-based strategies, has been carried out yet. This would be an extremely timely contribution, since experimental techniques are now ripe for the efficient implementation of such methods. This PhD project, which will blend a general mathematical treatment and its application to concrete physical systems, intends to fill this gap and obtain a systematic understanding of the ultimate limits of coherent feedback control under varying practical constraints.
Optimal coherent feedback schemes for the cooling (as quantified by the achieved reduction in entropy), squeezing (i.e., the compression of noise in one degree of freedom) and for the creation of stable quantum entanglement will be identified, first for Gaussian systems (which allow for a description in terms of finite dimensional matrices, and hence for the application of techniques from matrix analysis) and then for general quantum systems approached in the Heisenberg picture through the Langevin equations. Such schemes will then be applied to the optimisation of specific technological tasks, such as metrology and quantum teleportation. Direct interaction with experimentalists will also be pursued whenever relevant. This project will present the opportunity for acquiring both analytical and numerical skills, as well as training in both quantum physics and advanced algebra.
If interested, please contact Dr Alessio Serafini a.serafini@ucl.ac.uk for further details.