Unpolarized states and hidden polarization

Hoz, P. de la; Björk, Gunnar; Klimov, A. B.; Leuchs, Gerd; Sánchez-Soto, Luis L.

doi:10.1103/physreva.90.043826

Cited by 19 publications

(12 citation statements)

References 34 publications

(57 reference statements)

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“…Possible continuations of this work include the consideration of angular and Cartesian expansions in higherdimensional spaces, in particular concerning the relations between four-dimensional symmetric traceless tensors and the biaxial expansions discussed here. Moreover, the formalism could be extended towards vector and higher-order tensor spherical harmonics [17,[50][51][52] or quantum state multipoles [39,53].…”

Section: Discussionmentioning

confidence: 99%

Relations between angular and Cartesian orientational expansions

Vrugt

Wittkowski

2020

AIP Advances

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Orientational expansions, which are widely used in the natural sciences, exist in angular and Cartesian form. Although these expansions are orderwise equivalent, it is difficult to relate them in practice. In this article, both types of expansions and their relations are explained in detail. We give explicit formulas for the conversion between angular and Cartesian expansion coefficients for functions depending on one, two, and three angles in two and three spatial dimensions. These formulas are useful, e.g., for comparing theoretical and experimental results in liquid crystal physics. The application of the expansions in the definition of orientational order parameters is also discussed.

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Section: Discussionmentioning

confidence: 99%

Relations between angular and Cartesian orientational expansions

Vrugt

Wittkowski

2020

AIP Advances

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“…[20]. The tensor operators (33) can be expressed in terms of the spin operator ⃗ S. [64,[108][109][110][111][112] The transformation rules (for sharp angular momentum s) read [64] T (s)…”

Section: Application To Spinsmentioning

confidence: 99%

Orientational Order Parameters for Arbitrary Quantum Systems

Vrugt

Wittkowski

2020

Annalen der Physik

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The concept of quantum-mechanical nematic order, which is important in systems such as superconductors, is based on an analogy to classical liquid crystals, where order parameters are obtained through orientational expansions. This method is generalized to quantum mechanics based on an expansion of Wigner functions. This provides a unified framework applicable to arbitrary quantum systems. The formalism recovers the standard definitions for spin systems. For Fermi liquids, the formalism reveals the nonequivalence of various definitions of the order parameter used in the literature. Moreover, new order parameters for quantum molecular systems with low symmetry are derived, which cannot be properly described with the usual nematic tensors.

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“…Therefore, the idea of construction of the polarization measures by using second-order moments of the Stokes operators occured [15,16]. Moreover, a provisionally improved characterization of polarization has recently been obtained * iulia.ghiu@g.unibuc.ro † paulina.marian@g.unibuc.ro ‡ tudor.marian@g.unibuc.ro with the help of higher-order moments [17][18][19][20][21][22]. Collaterally, it was recently proved that the Stokes-operator measurements have great importance for the estimation of the covariance matrix of macroscopic quantum states [23].…”

Section: Introductionmentioning

confidence: 99%

Modification of polarization through de-Gaussification

Ghiu

Marian

2018

Phys. Rev. A

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We analyze the polarization of a quantum radiation field under a de-Gaussification process. Specifically, we consider the addition of photons to a two-mode thermal state to get mixed non-Gaussian and nonclassical states which are still diagonal in the Fock basis. Stokes-operator-based degrees of polarization and two distance-type measures defined with Hilbert-Schmidt and Bures metrics are investigated. For a better insight we here introduce a polarization degree based on the relative entropy. Polarization of the thermal states is fully investigated and simple closed expressions are found for all the defined degrees. The evaluated degrees for photon-added states are then compared to the corresponding ones for the two-mode thermal states they originate from. We present interesting findings which tell us that some popular degrees of polarization are not fully consistent. However, the most solidly defined degrees, which are based on the Bures metric and relative entropy, clearly indicate an enhancement of polarization through de-Gaussification. This conclusion is supported by the behavior of the degrees of polarization of the Fock states, which are finally discussed as a limit case.

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Unpolarized states and hidden polarization

Cited by 19 publications

References 34 publications

Relations between angular and Cartesian orientational expansions

Relations between angular and Cartesian orientational expansions

Orientational Order Parameters for Arbitrary Quantum Systems

Modification of polarization through de-Gaussification

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