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Entanglement creation and detection in quantum optical systems

Final Activity Report Summary - ENTANGLEMENT CREATIO (Entanglement creation and detection in quantum optical systems)

The basics of quantum mechanics have already been known for half a century, however, it has become possible only quite recently to study many-body quantum dynamics experimentally. For such an experiment one must be able to control very well the quantum system, and be able to measure its state at least at the end of the dynamics. Moreover, the quantum system must also be well isolated from the environment. The main difficulty arises since these two requirements must be fulfilled at the same time.

Several quantum optical systems offer the possibility of studying many-body quantum dynamics, such as optical lattices of bosonic two-state atoms, trapped cold ions or photonic systems obtained from parametric down-conversion. The development of the necessary technical tools were in the centre of the efforts of the quantum optics community in the last decade.

One of the notions introduced relatively late in quantum theory is entanglement. The word itself is from Schrodinger, however, a modern definition is from 1989. If a two-particle system is in an entangled state then it exhibits several phenomena which could not be obtained from classical physics. Beside fundamental quantum theory, it also has connections to quantum information processing applications: Entangled states can be used for quantum information processing tasks which could not be done without entanglement.

My project aimed at studying multipartite entanglement in quantum optical systems. I intended to develop methods which make it possible to study entanglement in physical systems, such as optical lattices of two-state atoms, in which full control of the system is not possible for the experimenter. That is, only collective quantities are accessible or only local measurements are possible.

Our first result was showing that the detection of true multipartite entanglement in the vicinity of the so called cluster state is possible with few measurements. These ideas have already been used in an experiment in a photonic system. Before it was not at all clear that the number of measurements needed does not scale exponentially with the size of the system. If this were the case then entanglement detection in many-body systems with local measurements would not be possible even for modest size systems.

Our other main result was about detecting entanglement with collective measurements in optical lattices of two-state atoms. Our criterion detects entanglement in the vicinity of the so-called many-body singlet states. Such states can be created, for example, as ground states of Heisenberg spin chains. Our proposal is relevant to experiments with colds atoms trapped in optical lattices. These ideas will certainly be used in an experiment in the not-so-far future.

Our third main result was about detecting entanglement in spin chain with correlation measurements. We showed that in one- or two-dimensional spin lattices with various type of interactions (Heisenberg, xy, etc.) entanglement can be detected by measuring average two-point correlations. These results are again quite general, can be used in many physical systems such as optical lattices of two-state atoms or trapped cold ions.