Coherent states with complex frequency

L. Mandeļ, E. Wolf

Introduction In our discussion of the classical electromagnetic field we found it convenient to describe the field by a complex amplitude, both in the frequency and in the time domains. The complex representation is convenient partly because it contains information about the magnitude and about the phase of the electromagnetic disturbance, and partly because of its analytic properties. These features turn out to be particularly useful for the description of the optical coherence properties of the field. We shall see that an analogous quantum state of the field exists, leading to an interesting representation that is also particularly useful for the treatment of optical coherence. This coherent-state representation leads to a close correspondence between the quantum and classical correlation functions. The coherent states of the field come as close as possible to being classical states of definite complex amplitude. We shall find that coherent states turn out to be particularly appropriate for the description of the electromagnetic fields generated by coherent sources, like lasers and parametric oscillators; indeed it turns out that the field produced by any deterministic current source is in a coherent state. In the following sections we shall examine some of the properties of coherent states, and then go on to discuss representations based on these states. Coherent states were first discovered in connection with the quantum harmonic oscillator by Schrödinger (1926), who referred to them as states of minimum uncertainty product.

K. Thirulogasanthar, G. Honnouvo, G. Honnouvo

Stefania Sciara, Michael Kues, Christian Reimer +11 more

The investigation and use of integrated frequency comb sources (i.e. featured by equally-spaced discrete spectral modes) have recently provided a unique framework to address the challenges of generation and coherent manipulation of complex quantum states in on-chip devices. We exploit integrated frequency combs for generating entangled photon pairs, as well as multi-photon states, and high-dimensional (D-level, i.e. quDit) entangled photons. In particular, we manage to coherently manipulate such complex quantum systems by using telecommunications components (standard fiber telecom).

S. Twareque Ali, Jean-Pierre Antoine, Jean‐Pierre Gazeau

Stefania Sciara, Christian Reimer, Piotr Roztocki +8 more

We exploit integrated quantum frequency combs for the practical generation and coherent manipulation of complex entangled photon states, by using only standard silicon-based chips and fiber telecommunications components.

S. Twareque Ali, Jean-Pierre Antoine, Jean‐Pierre Gazeau