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Quantum-optical state engineering

About a century ago, Max Planck introduced quantization of light to explain the spectrum of blackbody radiation. The first experimental confirmation of non-classical features of the light field came almost 60 years later with measurements of photon correlations, and over 20 more years passed before we learned to controllably generate first nonclassical states of light, such as single photons and squeezed vacuum. After these observations, over the past two and a half decades, the field of quantum optics grew rapidly. Optics has become a playground for testing fundamental concepts of quantum mechanics, such as entanglement, measurement, nonlocality and decoherence. With the beginning of the present century, quantum optics has given rise to applications in quantum information technology, such as quantum communication, metrology and computation.

Still, our ability to generate quantum states of light is strongly limited. Until recently, we could only produce very basic states: single photons, entangled photon pairs, squeezed and quadrature entangled states. However, the past few years have seen a technology boom, resulting in a plethora of new quantum optical states produced and measured: single- and dual-rail optical qubits, displaced Fock states, photon-added states, "Schrödinger cats", and many others. Yet the "holy grail" – an ability to synthesize any arbitrary state of the electromagnetic field is not yet achieved. This is a primary vision of the present project. At the same time, we are working on various other tasks in continuous-variable quantum-information processing, such as entanglement purification, simulation of optical nonlinearity as well as heralded linear-optical quantum computation.

How do we generate quantum states of light? We begin with parametric down-conversion – a nonlinear optical effect that can produce single- or two-mode squeezed light. This state, which is only weekly nonclassical and/or weekly entangled, is our "primitive", which we process further to shape the state we need. The additional tools we use at this stage,

allow us to gain access to the entire optical Hilbert space. For example, in order to obtain a single photon from a spontaneously generated photon pair, we detect one photon in a pair, and then we know the other photon has been generated as well. Increasingly complex optical states can be engineered by more complicated measurements, such as, for example, in our recent work on preparing arbitrary superpositions of 0-, 1-, and 2-photon states for the first time.

Of course, it is important to not only to prepare complex optical states, but also use them for practical purposes. For example, when a part of an entangled state is sent over a long distance (in a quantum communication setup, for example), the entanglement tends to degrade because of losses in a line. By using our quantum engineering techniques, we can undo this loss, bringing the entanglement back to the original level.

A closely related line of our research is quantum engineering of spin states in atomic ensembles. The primary process enabling such engineering is Raman scattering, which creates entanglement between the scattered light and the long-lived collective spin excitation stored in the ensemble. The Hamiltonian of this process is mathematically identical to that of parametric down-conversion, so it allows us to apply the well-developed toolbox of optical quantum state engineering to the Hilbert space of atomic spin excitations. The vision is to gain as much control over quantum states of atomic ensembles and light-atom entanglement as we now have over pure optical systems. This extension will not only permit combining discrete- and continuous-variable techniques in light-atom interfacing and quantum communications, but also present new opportunities in quantum metrology.

Our review paper on quantum state engineering and continuous-variable tomography