Effect of an incoherent pump on two-mode entanglement in optical parametric generation

Abstract

Pumping a nonlinear crystal by an intense radiation results in the optical parametric generation of photons in two modes (the signal and the idler). Quantized electromagnetic field in these modes is described by a continuous-variable quantum state, which is entangled if the pump is a coherent state produced by a laser. The signal and the idler modes remain populated by photons even if the pump becomes incoherent (dephased by a medium, mixed with a thermal state, or produced by an alternative source such as the superluminescent diode). However, the incoherent pump does effect the entanglement and purity of the signal and the idler modes, which is of vital importance for the quantum information applications and the interferometry. Here we develop an approach to infer the signal-idler entanglement and purity for a general quantum incoherent pump with the given Glauber-Sudarshan function. We show that the signal-idler entanglement is extremely sensitive to the phase distribution of the pump and illustrate our findings by physically relevant examples of the incoherent pump: thermal and displaced thermal states, slightly dephased and phase-averaged coherent states, and states modulated by the Kerr medium. arXiv:1905.05756v1 [quant-ph]

Towards Quantum Telescopes: Demonstration of a Two-Photon Interferometer for Quantum-Assisted Astronomy

“…Moreover, this description can be extended further by employing the Quantum Continuous Variable (CV) formalism [40]. The CV formalism will play an important role in expanding the presented technique to multiple observing stations assisted by auxiliary ground-based quantum states such as squeezed states and non-trivial quantum channels [41][42][43][44][45][46], providing novel opportunities in astronomy for extraction of valuable information. At the same time, the complexity of analytical descriptions and data processing would grow tremendously with an increased number of stations and auxiliary quantum states involved in the measurements, including entangled ones [3,25,26], so an important future research goal is to provide a theoretical description of such expansions based on both entities, the Gaussian states and quantum channels, powered by machine-learning methods [47,48].…”

Dependence of the photon statistics of down-converted field-modes on the photon statistics of pump field-mode

“…The interaction time t is defined by the length of the crystal [39]. The state of the signal and idler field-modes can be calculated from ρ(t) = |Ψ(t) Ψ(t)| by tracing over the pump field-mode.…”

“…It is valid for arbitrary pump field-mode states with any down-conversion strength n p η 2 t 2 . A wide range of down-conversion strength is achievable experimentally using continuous-wave laser in non-degenerate optical parametric amplifier [39,[61][62][63]. However, many experiments fall under the category of being in the weak downconversion limit, that is, n p η 2 t 2 ≪ 1.…”

“…In this paper, we treat the pump as a quantized field-mode and investigate how the photon statistics of the pump fieldmode affects the statistics of the down-converted field-modes. As the PDC is a unitary process, the state of the down-converted field-modes is calculated by solving the unitary time-dynamics of the pump field-mode governed by the Hamiltonian that describes the PDC process [4,[38][39][40]. We characterize the photon statistics of the pump and the down-converted field-modes using the second-order correlation function, which is defined as [41][42][43]…”