Effect of the pump state on the dynamics of the parametric amplifier

Hillery, Mark; Yu, Deng‐Guang; Bergou, János A.

doi:10.1103/physreva.52.3209

Cited by 7 publications

(5 citation statements)

References 15 publications

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“…The Hamiltonian (113) describes the two-photon down-conversion process in the crystal (one photon of frequency ω a is absorbed, and two photons of frequencies ω b , ω c are emitted), and the sum-frequency generation (two photons of frequencies ω b , ω c are absorbed and one photon of frequency ω a is emitted). Several aspects of model (113) have been thoroughly studied in the literature [143,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161]. The first description of the parametric amplifier and frequency converter, without the classical approximation for the pumping field, was performed by Walls and Barakat [147], who solved exactly the quantum-mechanical problem by the technique of the integrals of motion.…”

Section: Three-wave Mixing and The Trilinear Hamiltonianmentioning

confidence: 99%

“…Other approaches have been used to analyze the dynamics of the system (113): Jurčo found exact solutions using the Bethe ansatz [153]; Gambini and Carusotto solved the coupled nonlinear equations of motion by using iteration methods [149,154]; McNeil and Gardiner have studied the process in a cavity by finding the solution of a Fokker-Planck equation [152]; Hillery et al determined exact relations between the number fluctuations of the three modes [158].…”

Section: Three-wave Mixing and The Trilinear Hamiltonianmentioning

confidence: 99%

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Multiphoton quantum optics and quantum state engineering

2006

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We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter–radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry.A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms that are relevant for the conceptual investigations as well as for the practical applications of forefront aspects of modern quantum mechanics. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states.We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromagnetic field, either in discrete or in continuous variables, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information

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Section: Three-wave Mixing and The Trilinear Hamiltonianmentioning

confidence: 99%

Section: Three-wave Mixing and The Trilinear Hamiltonianmentioning

confidence: 99%

Multiphoton quantum optics and quantum state engineering

2006

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“…or any linear combination of them, commute with H. As in the degenerate case we can find a relation between the number fluctuations in the pump and those in either of the other two modes [18]. We find that…”

Section: χ (2) Interactionsmentioning

confidence: 52%

“…More recently the parametric approximation has been extended to cover pumps which are not in coherent states [31,34,35]. In particular, pumps which have a large coherent amplitude but are squeezed so that their phase fluctuations are reduced have been treated.…”

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confidence: 99%

An introduction to the quantum theory of nonlinear optics

Hillery¹

2009

Acta Physica Slovaca. Reviews and Tutorials

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An introduction to the quantum theory of nonlinear opticsThis article is provides an introduction to the quantum theory of optics in nonlinear dielectric media. We begin with a short summary of the classical theory of nonlinear optics, that is nonlinear optics done with classical fields. We then discuss the canonical formalism for fields and its quantization. This is applied to quantizing the electromagnetic field in free space. The definition of a nonclassical state of the electromagnetic field is presented, and several examples are examined. This is followed by a brief introduction to entanglement in the context of field modes. The next task is the quantization of the electromagnetic field in an inhomogeneous, linear dielectric medium. Before going on to field quantization in nonlinear media, we discuss a number of commonly employed phenomenological models for quantum nonlinear optical processes. We then quantize the field in both nondispersive and dispersive nonlinear media. Flaws in the most commonly used methods of accomplishing this task are pointed out and discussed. Once the quantization has been completed, it is used to study a multimode theory of parametric down conversion and the propagation of quantum solitons.

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“…The effect of the squeezed pump on the properties of the signal and idler modes is studied in Refs. [60][61][62][63] and the effect of the pump depletion is analyzed in the degenerate OPG in Refs. [64,65].…”

Section: Introductionmentioning

confidence: 99%

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

2019

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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]

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Effect of the pump state on the dynamics of the parametric amplifier

Cited by 7 publications

References 15 publications

Multiphoton quantum optics and quantum state engineering

Multiphoton quantum optics and quantum state engineering

An introduction to the quantum theory of nonlinear optics

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

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