Quantum State Engineering in Open Systems: Harnessing Dissipation and Measurement

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Weak measurement (WM) is an alternative to the dogma of von Neumann’s “collapse” of a quantum wave function. WM avoids a complete destruction of the wave function while being capable of extracting partial information from the measured system. Concomitantly, measurement is associated with the back-action of the detector on the system state. The core idea of the present theoretical proposal is to exploit the almost non-destructive nature of WM and, at the same time, harness its back-action for the purpose of quantum engineering of non-trivial states. This advance will be accomplished through three key steps: (i) The WM-induced generation of states, (ii) state stabilization, and (iii) state manipulation. We will apply this idea to topological systems with few quasi-particles as well as for many-body systems. In certain limits, WM-defined protocols give rise to dynamics closely related to that of open dissipative systems. In that context, instead of employing WM protocols, it is also possible to achieve state generation, stabilization, and manipulation by subjecting the system to a combination of time-dependent driving forces and dissipation due to an external environment. While such drive-and-dissipation protocols have been extensively studied and employed for generating exotic states in the past, the new element in our proposal is the emergence of a dark space, i.e., a manifold of degenerate dark states. In particular, engineering a dark space opens the door to robust quantum state manipulation in devices harboring topological zero modes, e.g., Majorana states or parafermions. Starting with systems hosting only a few topological quasiparticles, we will target strongly correlated many-body states. We will design on-demand few-quasiparticle states, manipulate them (resulting, e.g., in geometric phases and braiding protocols), and develop WM-based or driven-dissipative protocols to engineer a host of correlated many-body states, including non-trivial ground and excited states as well as novel non-equilibrium states. The successful completion of this project will result in several key advances: (1) We will introduce a new paradigm of many-body physics vis-à-vis generation and manipulation of quantum states. (2) We will elucidate crucial facets of the measurement operation not known before. (3) We expect an impact on the field of quantum information processing through our novel qubit manipulation techniques.