Photon statistics of two-mode squeezed states and interference in four-dimensional phase space

Caves, Carlton M.; Zhu, Chang Jun; Milburn, G. J.; Schleich, Wolfgang P.

doi:10.1103/physreva.43.3854

Cited by 104 publications

(74 citation statements)

References 14 publications

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“…This behavior is similar to the distribution function of a displaced two-mode squeezed state discussed in Ref. [7,8].…”

Section: Photon Statistics In the Individual Modessupporting

confidence: 63%

“…Only some particular cases have been considered (see for example Refs. [7] and [8]). In the present paper we therefore extend these considerations to an arbitrary two-mode squeezed vacuum and address the following questions: (i) What is the most general case of the squeezed vacuum of a two-mode oscillator, and how many independent parameters are needed to describe this state?…”

Section: Introductionmentioning

confidence: 99%

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Photon statistics of a two-mode squeezed vacuum

et al. 1993

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We i n v estigate the general case of the photon distribution of a two-mode squeezed vacuum and show that the distribution of photons among the two modes depends on four parameters: two squeezing parameters, the relative phase between the two oscillators and their spatial orientation. The distribution of the total number of photons depends only on the two squeezing parameters. We derive analytical expressions and present pictures for both distributions.

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“…This behavior is similar to the distribution function of a displaced two-mode squeezed state discussed in Ref. [7,8].…”

Section: Photon Statistics In the Individual Modessupporting

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Photon statistics of a two-mode squeezed vacuum

et al. 1993

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show abstract

“…11 and 12 we have plotted the PND for β 1 = β 2 = 0, and for different values of r; this corresponds to the two-mode fourphoton squeezed vacuum. As in the case of the standard two-mode squeezed vacuum [12], we obtain a diagonal, symmetric PND, in spite of the unbalanced choice on the phases.…”

Section: Photon Statisticssupporting

confidence: 51%

“…We compare it with the PND of the two-mode squeezed states, thoroughly studied in Ref. [12], and we show its strong dependence on the modulus and phases of the nonlinear couplings, and on the heterodyne mixing angles. We next show the behavior of the average photon numbers in the two modes as functions of |γ|.…”

Section: Photon Statisticsmentioning

confidence: 91%

Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

2004

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Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper "Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states", we introduce two-mode nonlinear canonical transformations depending on two heterodyne mixing angles. They are defined in terms of hermitian nonlinear functions that realize heterodyne superpositions of conjugate quadratures of bipartite systems. The canonical transformations diagonalize a class of Hamiltonians describing non degenerate and degenerate multiphoton processes. We determine the coherent states associated to the canonical transformations, which generalize the non degenerate two-photon squeezed states. Such heterodyne multiphoton squeezed are defined as the simultaneous eigenstates of the transformed, coupled annihilation operators. They are generated by nonlinear unitary evolutions acting on two-mode squeezed states. They are non Gaussian, highly non classical, entangled states. For a quadratic nonlinearity the heterodyne multiphoton squeezed states define two-mode cubic phase states. The statistical properties of these states can be widely adjusted by tuning the heterodyne mixing angles, the phases of the nonlinear couplings, as well as the strength of the nonlinearity. For quadratic nonlinearity, we study the higher-order contributions to the susceptibility in nonlinear media and we suggest possible experimental realizations of multiphoton conversion processes generating the cubic-phase heterodyne squeezed states.

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“…Pumping the PDC sources with spectrally broad ultrafast pump pulses further increases the repertoire of realizable quantum states, including the generation of genuine single-photon quantum pulses [5] or the creation of multimode quantum frequency combs [6,7]. Naturally, the experimental progress during recent years has been accompanied by elaborate theoretical considerations which aim for a complete understanding of the PDC process [8][9][10][11][12][13]. However, when it comes to the description of PDC output states, two at a first glance disparate methods are still prevailing.…”

Section: Introductionmentioning

confidence: 99%

Characterizing entanglement in pulsed parametric down-conversion using chronocyclic Wigner functions

Brecht

Silberhorn

2013

Phys. Rev. A

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Pulsed parametric downconversion (PDC) processes generate photon pairs with a rich spectraltemporal structure, which offer an attractive potential for quantum information and communication applications. In this paper, we investigate the four-dimensional chronocyclic Wigner function WPDC(ωs, ωi, τs, τi) of the PDC state, which naturally lends itself to the pulsed characteristics of these states. From this function we derive the conditioned time-bandwidth product of one of the pair photons, a quantity which is not only a valid measure of entanglement between the PDC photons but also allows to highlight a remarkable link between the discrete and continuous variable descriptions of PDC. We numerically analyze PDC processes with different conditions to demonstrate the versatility of our approach, which is applicable to a large number of current PDC sources.

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Photon statistics of two-mode squeezed states and interference in four-dimensional phase space

Cited by 104 publications

References 14 publications

Photon statistics of a two-mode squeezed vacuum

Photon statistics of a two-mode squeezed vacuum

Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

Characterizing entanglement in pulsed parametric down-conversion using chronocyclic Wigner functions

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