Measurement of number-phase uncertainty relations of optical fields

Smithey, D. T.; Beck, M.; Cooper, J.; Raymer, Michael G.

doi:10.1103/physreva.48.3159

Cited by 184 publications

(52 citation statements)

References 37 publications

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“…They possess all properties of genuine probability densities and can be measured since recent time in quantum optics of the radiation field by homodyne detection [1][2][3][4]. The field of problems of the reconstruction of the density operator from such or similar data is called quantum tomography.…”

Section: Introductionmentioning

confidence: 99%

Radon transform and pattern functions in quantum tomography

Wünsche¹

1997

Journal of Modern Optics

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The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to displacement and squeezing of states are studied and it is shown that the last is equivalent to a symplectic transformation of the variables of the Radon transform with the contragredient matrix to the transformation of the variables in the Wigner quasiprobability. The reconstruction of the density operator from the Radon transform and the direct reconstruction of its Fock-state matrix elements and of its normally ordered moments are discussed. It is found that for finite-order moments the integration over the angle can be reduced to a finite sum over a discrete set of angles. The reconstruction of the Fock-state matrix elements from the normally ordered moments leads to a new representation of the pattern functions by convergent series over even or odd Hermite polynomials which is appropriate for practical calculations. The structure of the pattern functions as first derivatives of the products of normalizable and nonnormalizable eigenfunctions to the number operator is considered from the point of view of this new representation.

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Section: Introductionmentioning

confidence: 99%

Radon transform and pattern functions in quantum tomography

Wünsche¹

1997

Journal of Modern Optics

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“…Introduction -Homodyne detection (HD) is an effective tool to characterize the quantum state of light in either the time [1][2][3][4][5][6][7][8] or the frequency [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] domain. In a spectral homodyne detector, the signal under investigation interferes at a balanced beam splitter with a local oscillator (LO) with frequency ω 0 .…”

mentioning

confidence: 99%

Full quantum state reconstruction of symmetric two-mode squeezed thermal states via spectral homodyne detection and a state-balancing detector

et al. 2016

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We suggest and demonstrate a scheme to reconstruct the symmetric two-mode squeezed thermal states of spectral sideband modes from an optical parametric oscillator. The method is based on a single homodyne detector and active stabilization of the cavity. The measurement scheme have been successfully tested on different two-mode squeezed thermal states, ranging from uncorrelated coherent states to entangled states.PACS numbers: 03.65. Wj, 42.50.Lc, 42.50.Dv Introduction -Homodyne detection (HD) is an effective tool to characterize the quantum state of light in either the time [1][2][3][4][5][6][7][8] or the frequency [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] domain. In a spectral homodyne detector, the signal under investigation interferes at a balanced beam splitter with a local oscillator (LO) with frequency ω 0 . The two outputs undergo a photodetection process and their photocurrents are combined leading to a photocurrent continuously varying in time. The information about the spectral field modes at frequencies ω 0 ± Ω (sidebands) is then retrieved by electronically mixing the photocurrent with a reference signal with frequency Ω and phase Ψ. Upon varying the phase θ of the LO, we may access different field quadratures, whereas the phase Ψ can be adjusted to select the symmetric S or antisymmetric A balanced combinations of the upper and lower sideband modes.

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“…In this case the transformation is characterized by a single parameter θ that ranges from -π to +π. For a sufficiently large number of, say, position distributions, each with a different value of θ over this range, the discrete inverse Radon transform that is well known from computer-assisted tomography may be used to reconstruct the Wigner distribution of the field [4]. From this function it is straightforward to obtain the density matrix via a Fourier transform.…”

Section: Quantum and Classical Measurementsmentioning

confidence: 99%

“…The single mode problem has been solved using optical homodyne tomography, (OHT) [4] and partial reconstruction has been developed for the two-mode problem [46]. As Raymer has shown [48], a complete state reconstruction for even the two-mode problem using ΟHΤ is unpleasantly cumbersome.…”

Section: τEst-plus-reference Interferometry For Quantum State Reconstmentioning

confidence: 99%