Spectral structure and decompositions of optical states, and their applications

Abstract

We discuss the spectral structure and decomposition of multi-photon states. Ordinarily 'multiphoton states' and 'Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of 'multi-photon' states is much broader than the class of 'Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states. This representation allows us to work in bases imposed by experimental constraints, simplifying calculations in many situations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong-Ou-Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schrödinger Kitten and Fock states. Our techniques allow for very simple descriptions of each of these examples.

Quantum estimation of the Schwarzschild spacetime parameters of the Earth

“…While in [13] it was shown that the effects can have an impact on quantum communications in space, the main aim of this work is to take advantage of these effects to measure space-time parameters of interest, such as the Schwarzschild radius (mass of the Earth [25].…”

Quantum trajectories for a system interacting with environment in a single-photon state: Counting and diffusive processes

“…(15) and (16),which ends the proof of (13). Note that knowing the initial state |ψ of S, single photon state |1 ξ of the environment, and the results of measurements (η j , .…”

“…One of them is a single photon state [12][13][14]. About the methods of its generation and application in quantum of computing and communication one can read in [15][16][17][18][19][20][21][22].…”

“…The state |1 ξ is a discrete analogue of a single-photon state in the model of continuous modes discussed in [13,14]. Now, let us describe the evolution of the composed E + S system.…”

“…Sooner or later, it depends in the profile ξ k of the environment state |1 ξ , the system S meets the qubit prepared in the excited state, so finally only the second term gives non-zero contribution to (13), and |Ψ j|η η ηj becomes separable.…”