Quantum states of light show characteristics beyond the classical properties of the electromagnetic field. In particular, non-classical states such as single photon Fock states or entangled states can be seen as resources for many quantum information tasks. In our group, we use photon number resolving measurements. These enable us to generate, on the one hand, highly non-lassical states and, on the other hand, offer promising new methods for quantum state characterization.
Phase space representation of light
Every quantum state can be described as an expansion in the photon number basis |n〉. Alternatively, the phase space representation of light is an equivalent description that incorporates all quantum effects, but resembles the classical concept of amplitude and phase. Starting from the creation and annihilation operators â† and â, one can define quadrature operators x̂ = (1 / 2) (â + â†) andŷ = (-i / 2) (â - â†). They obey the Heisenberg commutation relation and can be interpreted as position and momentum. The quantum state in phase space can then be characterized by their quasi-probability distribution, such as the Wigner function W(x, y).
The Wigner function becomes a classical distribution of amplitude and phase in the limit of bright fields. Weak fields have a blurred distribution in accordance with the Heisenberg uncertainty. It is possible to narrow the distribution in one quadrature, at the cost of widening the other. Light states which feature these distributions are called squeezed states. Moreover, the Wigner function can, for certain non-classical states, have negative values.