Classical evolution of quantum fluctuations in spin-like systems: squeezing and entanglement

Klimov, A. B.; Espinoza, P.

doi:10.1088/1464-4266/7/6/004

Cited by 28 publications

(37 citation statements)

References 39 publications

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“…To provide an appropriate phase-space description of states, we take advantage of the pioneering work of Stratonovich [38] and Berezin [39], who introduced quasi-probability distribution functions on the sphere satisfying all the proper requirements. This construction was later generalized by others [40][41][42][43][44][45] and has proved to be very useful in visualizing properties of spin-like systems [60][61][62][63][64][65].…”

Section: Polarization Wigner Functionmentioning

confidence: 99%

Quantum polarization tomography of bright squeezed light

et al. 2012

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We reconstruct the polarization sector of a bright polarization squeezed beam starting from a complete set of Stokes measurements. Given the symmetry that underlies the polarization structure of quantum fields, we use the unique SU(2) Wigner distribution to represent states. In the limit of localized bright states, the Wigner function can be approximated by an inverse threedimensional Radon transform. We compare this direct reconstruction with the results of a maximum likelihood estimation, thus finding excellent agreement. Figure 4. Sections of the isocontour of the Wigner function in figure 3 through the coordinate axes, for the three different reconstruction techniques used. In gray the direct Radon transform, in green the ML method with nine settings for the angles of the wave plates and in dotted lines the results of a Gaussian ML approximation are shown.

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Section: Polarization Wigner Functionmentioning

confidence: 99%

Quantum polarization tomography of bright squeezed light

et al. 2012

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“…(3.29) in [24] f ⋆ g [25] ∂W ρ ∂t a b N = 2 W(A) Eq. (30) in [26] (61) in [25] states the equation of motion for the limit of J → ∞ using only the Poisson bracket.…”

Section: Wigner Functions Of Infinite-dimensional Quantum Systemsmentioning

confidence: 99%

Time evolution of coupled spin systems in a generalized Wigner representation

2019

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Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinitedimensional quantum systems and have been widely used in quantum optics and beyond. Continuous phase spaces have also been studied for finite-dimensional quantum systems such as spin systems. However, much less is known for finite-dimensional, coupled systems, and we present a complete theory of Wigner functions for this case. In particular, we provide a self-contained Wigner formalism for describing and predicting the time evolution of coupled spins which lends itself to visualizing the high-dimensional structure of multi-partite quantum states. We completely treat the case of an arbitrary number of coupled spins 1 2, thereby establishing the equation of motion using Wigner functions. The explicit form of the time evolution is then calculated for up to three spins 1 2. The underlying physical principles of our Wigner representations for coupled spin systems are illustrated with multiple examples which are easily translatable to other experimental scenarios. Prior work on Wigner functions of finite-dimensional quantum systemsFundamental postulates for phase-space representations of finite-dimensional quantum systems were proposed by Stratonovich [21] (see Appendix C.1), and these build the foundations for Wigner functions of finite-dimensional quantum systems. Reflecting the translational covariance of Wigner functions of infinite-dimensional quantum systems, one of these postulates states that the Wigner function has to transform naturally under rotations. The rotational covariance constrains continuous Wigner representations of spins into a spherical coordinate systems. The resulting Wigner functions can then be given by linear combinations of spherical harmonics, which offers a convenient tool for visualizing spins (see Sec. 1.4).The Wigner transformation of single-spin operators was developed by Várilly and Gracia-Bondía [22] and was then further extended by Brif and Mann [23,24]. In particular, [22] provides an explicit formula for the Wigner transformation for a single spin J, which satisfies the Stratonovich postulates. This formula uses a rank-j-dependent kernel which is based on mapping transition operators Jm⟩⟨Jm ′ onto their corresponding Wigner functions W Jm⟩⟨Jm ′ ; the connection between tensor operators J T jm and spherical harmonics Y jm was also mentioned. A more general kernel for the continuous phase-space representation of a single spin was stated in [23,24]. It defines Wigner functions of tensor operators J T jm of single spins as the corresponding spherical harmonics Y jm . We build on these results in Sec. 3.2 while also unifying normalization factors.Parallel to our work, a general approach for phase-space representations was proposed in [27] which is based on the so-called displaced parity operator [28]. The explicit form of the transformation kernel is computed for the special cases of a single spin J (see Eq. (8) in ...

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“…The above expressions allow us to evaluate the quasiclassical evolution of W (σ) ̺ in a simple way (see also [29]). This is an alternative to the spin coherent path integral formalism used in [30], [31].…”

Section: Large Smentioning

confidence: 99%

Bopp operators and phase-space spin dynamics: application to rotational quantum Brownian motion

Zueco

Calvo²

2007

J. Phys. A: Math. Theor.

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Abstract. For non-relativistic spinless particles, Bopp operators give an elegant and simple way to compute the dynamics of quasiprobability distributions in the phase space formulation of Quantum Mechanics. In this work, we present a generalization of Bopp operators for spins and apply our results to the case of open spin systems. This approach allows to take the classical limit in a transparent way, recovering the corresponding Fokker-Planck equation.

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Classical evolution of quantum fluctuations in spin-like systems: squeezing and entanglement

Cited by 28 publications

References 39 publications

Quantum polarization tomography of bright squeezed light

Quantum polarization tomography of bright squeezed light

Time evolution of coupled spin systems in a generalized Wigner representation

Bopp operators and phase-space spin dynamics: application to rotational quantum Brownian motion

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