Canonical transformations and multipartite coupled parametric processes

Tlyachev, T. V.; Chebotarev, A. M.; Chirkin, A. S.

doi:10.1088/0031-8949/2014/t160/014041

Cited by 9 publications

(4 citation statements)

References 10 publications

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“…It should be noted that the considered process was recently implemented in the scheme with two consistently located nonlinear photon crystals out of the resonator (cascade processes) [16], where the photon-pair spectrum at a frequency over the pump frequency was investigated. Quantum properties of the process under consideration were comprehensively studied in [17][18][19], where the existence of four-partite entanglement was established. It should be noted that quantum correlations exist not only between photons at low frequencies and between photons at the highest frequencies with respect to the pump frequency but also between low-frequency and high-frequency photons.…”

Section: Multiplexing Ghost Imagingmentioning

confidence: 99%

“…Quantum properties of the process under consideration were comprehensively studied in works [17][18][19], where existence of four-partite entanglement was established. It should be noted that quantum correlations exist not only between photons at low frequencies and between photons at the highest frequencies in relation to pump frequency, but also between low-frequency and high-frequency photons.…”

Section: Multiplexing Ghost Imagingmentioning

confidence: 99%

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Correlations of Multiplexed Quantum Ghost Images and Improvement of the Quality of Restored Image

2017

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The currently used ghost-image schemes traditionally involve two-mode entangled light states or incoherent radiation. Here, we consider the application of four-mode entangled light states and show that multiplexed ghost images (MGI) formed by four-mode entangled quantum light states have mutual spatial correlations determined by the eighth-order field correlation functions. We develop a special algorithm to calculate high-order correlations of Bose operators. We also demonstrate that accounting of the MGI correlations allows us to improve the quality of the restored image of an object while processing the MGI by the measurement reduction method. We carry out computer modeling of the image recovery from the MGI. We establish that in the considered example the signal-to-noise ratio of the reduced ghost image is 4.6 times higher than the best signal-to-noise ratio for the ghost images themselves.

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Section: Multiplexing Ghost Imagingmentioning

confidence: 99%

Section: Multiplexing Ghost Imagingmentioning

confidence: 99%

Correlations of Multiplexed Quantum Ghost Images and Improvement of the Quality of Restored Image

2017

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“…[13]. Modern applications could be found in works by A. S. Chirkin et al [14,15,16,17,18,19]. Also quadratic Hamiltonians arise in opto-mechanical problems [20,21].…”

Section: Historical and Literature Reviewmentioning

confidence: 99%

“…[62], p. 21), so we prefer the term above. The symmetric part of D is defined by CARs (18) as D +D T = E, then D = A+E/2.…”

Section: Gaussian Statesmentioning

confidence: 99%

Irreversible quantum evolution with quadratic generator: Review

Teretenkov

2019

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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We review results on GKSL-type equations with multi-modal generators which are quadratic in bosonic or fermionic creation and annihilation operators. General forms of such equations are presented. The Gaussian solutions are obtained in terms of equations for the first and the second moments. Different approaches for their solutions are discussed.was developed in the works by I. A. Malkin, V. I. Man'ko and V. V. Dodonov [3,4,5]. Some modern studies on unitary dynamics with quadratic Hamiltonians could be found in works by A. M. Chebotraev and T. V. Tlyachov [7,8,9]. One of the main areas of application of quadratic multi-modal Hamiltonians is quantum optics, especially in case of parametric approximation (see Ref.[10], Ch. II, Ref. [11], Ch. 16, or Ref. [12], Sec. 7.1.2). Coherent states for multi-modal parametric systems were considered in Ref. [13]. Modern applications could be found in works by A. S. Chirkin et al [14,15,16,17,18,19]. Also quadratic Hamiltonians arise in opto-mechanical problems [20,21]. Another source of such Hamiltonians is the approximate quantization method by N. N. Bogolyubov [22]. (See also Ref. 80 for contemporary discussion.) Discussion of the unitary dynamics with non-stationary (time-dependent) Hamiltonians could be found in Refs.[24]- [26]. Physical applications of such Hamiltonians were discussed in Ref. [27]. Quantum evolution with a quadratic generator is also closely related to the classical one, which was studied in the general case by J. Williamson [28,29,30]. The quasi-classical approximation for squeezed states was discussed in Ref. [31]. More detailed bibliography for bosonic unitary evolution could be found in Refs. [5] and [32]. The fermionic case without dissipation was considered in Ref.[2] by F. A. Berezin. The unified approach both for the bosonic reversible dynamics and the fermionic one was considered by V. I. Man'ko and V. V. Dodonov.[33] We consider reversible (non-unitary) evolution with quadratic generators. From the historical point of view one should mention Ref.[34] by L. D. Landau, which is famous for the first appearance of the concept of the density matrix. What is interesting for this review is that equations for irreversible quantum evolution of the density matrix were also introduced there. As it was mentioned on p. 183 in Ref.[5] and in Sec. 23.1 of Ref. [35] in the harmonic oscillator case one has (in modern notation)ρ

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Quantum spatial dynamics of high-gain parametric down-conversion accompanied by cascaded up-conversion

Rasputnyi

Копылов

2021

Phys. Rev. A

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Canonical transformations and multipartite coupled parametric processes

Cited by 9 publications

References 10 publications

Correlations of Multiplexed Quantum Ghost Images and Improvement of the Quality of Restored Image

Correlations of Multiplexed Quantum Ghost Images and Improvement of the Quality of Restored Image

Irreversible quantum evolution with quadratic generator: Review

Quantum spatial dynamics of high-gain parametric down-conversion accompanied by cascaded up-conversion

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