Quantum phase-space description of light polarization

Klimov, A. B.; Delgado, J.; Sánchez-Soto, Luis L.

doi:10.1016/j.optcom.2005.08.002

Cited by 11 publications

(15 citation statements)

References 64 publications

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“…Because of the lack of off-diagonal contributions of the form , n|ˆ| , n with ≠ , the total -function is an average of the -functions over the Fock layers. The role of the sum over is to remove the total intensity from the description of the state [182]. In all the density plots in the paper we use the same colormap that ranges from dark blue (corresponding to the numerical value 0) to bright red (corresponding to the numerical value 1).…”

Section: The Husimi -Functionmentioning

confidence: 99%

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Quantum concepts in optical polarization

et al. 2021

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We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincaré sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincaré space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored and their potential applications in quantum technologies are discussed.

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Section: The Husimi -Functionmentioning

confidence: 99%

“…Both Husimi functions ( + , − ) and (n) should be closely related. In fact, the latter can be understood as a marginal of the former, as has been worked out [72,182]. To this end, it is essential to realize that the two-mode quadrature coherent states are expressed in terms of the SU(2) coherent states by [189…”

Section: The Husimi -Functionmentioning

confidence: 99%

Quantum concepts in optical polarization

et al. 2021

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“…It is possible to turn the action of the Stokes operators discussed in the previous section into a very simple phase-space picture. To this end we introduce the parametrization [101] α = √ I e i ϕ a cos(θ/2) , β = √ I e i ϕ a e −iφ sin(θ/2), (5.1) where ϕ a appears now as a global phase and the pertinent relative phase is φ = ϕ a − ϕ b . The radial variable…”

Section: Mapping the Dynamics On The Spherementioning

confidence: 99%

Nonlinear cross-Kerr quasiclassical dynamics

et al. 2013

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We study the quasiclassical dynamics of the cross-Kerr effect. In this approximation, the typical periodical revivals of the decorrelation between the two polarization modes disappear and remain entangled. By mapping the dynamics onto the Poincaré space, we find simple conditions for polarization squeezing. When dissipation is taken into account, the shape of the states in such a space is not considerably modified, but their size is reduced.The optical Kerr effect refers to the intensity-dependent phase shift that a light field experiences during its propagation through a third-order nonlinear medium. This leads to a remarkable non-Gaussian operation that has sparked considerable interest due to potential applications in a variety of areas, such as quantum non-demolition measurements [1-9], generation of quantum superpositions [10][11][12][13][14][15][16][17][18][19], quantum teleportation [20][21][22], quantum logic [23-28] and single-particle detectors [29][30][31], to cite only a few. Enhanced Kerr nonlinearities have been observed in electromagnetically induced transparency [32-35], Bose-Einstein condensates [36], cold atoms [37] and Josephson junctions [38-40]. Additional arrangements involve the Purcell effect [41], Rydberg atoms [42], light-induced Stark shifts [43] and nanomechanical resonators [44].Special mention must be made of the role this cubic nonlinearity has played in the generation of squeezed light. The first proposals employed schemes involving a nonlinear interferometer [45] or degenerate four-wave mixing [46,47]. But quite soon optical fibers became the paradigm for that purpose [48][49][50][51][52][53]. However, due to the typically small values of the nonlinearity in silica glass [54], Kerr-based fibers need long propagation distances and high powers, which bring other unwanted effects [55,56].In this paper, we direct out attention on this limit of high intensities, in which one could expect a classical description to be pertinent. Under reasonable assumptions, Maxwell's equations lead to a set of coupled nonlinear Schrödinger equations that has long been a useful tool for depicting the behavior of optical fields in nonlinear dispersive media. It has proved valuable in the description of such diverse phenomena as pulse compression, dark soliton formation and self-focusing of ultrashort pulses [57]. However, there remain non-classical features that cannot be explained in this classical manner. To put it differently, at the most basic level, the propagation of light in a Kerr medium is accompanied by unavoidable quantum effects.The considerations so far indicate that the regime we wish to explore can be regarded as a problem at the boundary between classical and quantum worlds. Probably, the transition between both can be best scrutinized by exploiting phase-space methods [58][59][60]. This opens New Journal of Physics 15 (2013) 043038 (http://www.njp.org/)

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“…Similar calculation for quadrature coherent state of equal amplitudes is obtained by Klimov et.al. 22 . Considering s = 0 in Eq.…”

Section: Phase Space Description Of Bi-modal Quadrature Coherent Statesmentioning

confidence: 99%

Quasi-probability distribution functions for optical-polarization

Singh

Singh²,

Gupta

2010

SPIE Proceedings

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Cahill-Glauber C(s)-correspondence is employed to construct Quasi-Probability Distribution Functions (QPDFs) for optical-polarization in phase space following equivalent description of polarization in Classical Optics. The proposed scheme provides pragmatic insights as compared to obscure SU (2) quasi-distributions on Poincare sphere. QPDF (Wigner function) of bi-modal quadrature coherent states is evaluated and numerically investigated to demonstrate the application.

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Quantum phase-space description of light polarization

Cited by 11 publications

References 64 publications

Quantum concepts in optical polarization

Quantum concepts in optical polarization

Nonlinear cross-Kerr quasiclassical dynamics

Quasi-probability distribution functions for optical-polarization

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