Complete experimental characterization of the quantum state of a light mode via the Wigner function and the density matrix: application to quantum phase distributions of vacuum and squeezed-vacuum states

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

doi:10.1088/0031-8949/1993/t48/005

Cited by 163 publications

(58 citation statements)

References 35 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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“…The Wigner function was rst reconstructed experimentally for quantum states of light [5] and, thereafter, heavily used within quantum optics in the study and applications of the quantum nature of light. Today, the Wigner function has been also reconstructed for modes of molecular vibrations [6], the motion of trapped atomic ions [7], the spatial superposition state of atoms [8] and very recently for the thermal mechanical states of a harmonic oscillator in pulsed optomechanics [9].…”

Section: Introductionmentioning

confidence: 99%

Wigner Function Reconstruction in Levitated Optomechanics

Rashid¹,

Toroš²

2017

Quantum Measurements and Quantum Metrology

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Abstract:We demonstrate the reconstruction of the Wigner function from marginal distributions of the motion of a single trapped particle using homodyne detection. We show that it is possible to generate quantum states of levitated optomechanical systems even under the e ect of continuous measurement by the trapping laser light. We describe the opto-mechanical coupling for the case of the particle trapped by a free-space focused laser beam, explicitly for the case without an optical cavity. We use the scheme to reconstruct the Wigner function of experimental data in perfect agreement with the expected Gaussian distribution of a thermal state of motion. This opens a route for quantum state preparation in levitated optomechanics.

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“…By measuring the quadrature operators of the input signal state, the balanced homodyne detector can then obtain the quasi probability distribution or in other words, the Wigner function after kinds of quantum state tomography [1]. The first experiment determining the quantum state of light field was proposed by Smithy, Beck, Cooper, Raymer, et al in 1993 [1,2]. Nowadays, the quantum state tomography with balanced homodyne detector has become a standard method in quantum information field.…”

Section: Introductionmentioning

confidence: 99%

High-speed Balanced Homodyne Detector for Quantum Information Applications

Wang¹,

Chen²,

Zhang

2017

J. Phys.: Conf. Ser.

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Abstract.We have developed a balanced homodyne detector capable of working with femtosecond pulsed light at a 76MHz repetition rate and 800nm wavelength. It exhibits a common mode rejection ratio of 55dB, and can achieve the shot-noise limit. Provided with good performance, our detector can be used in high speed quantum information applications. IntroductionWith the powerful ability of demonstrating complete characterization of a quantum light state, highspeed balanced homodyne detection is essential for foundational analysis of quantum optics on many areas, such as quantum process tomography, quantum key distribution and quantum precision measurement. By measuring the quadrature operators of the input signal state, the balanced homodyne detector can then obtain the quasi probability distribution or in other words, the Wigner function after kinds of quantum state tomography [1]. The first experiment determining the quantum state of light field was proposed by Smithy, Beck, Cooper, Raymer, et al in 1993 [1,2]. Nowadays, the quantum state tomography with balanced homodyne detector has become a standard method in quantum information field.Over the past decades, remarkable effort has been made to make a balanced homodyne detector with satisfactory performance applying to various applications [3]. Conventionally, researchers use a circuit with a dual-stage amplifier to gain higher magnification and stability, but this design will bring extra noise as well. In our experiments, a single-stage simple-construct amplifier homodyne detector was also found able to satisfy the performance requirements of homodyne detectors: (a) low enough electrical noise competent to beat the shot-noise limit which is the key requirement to make a quantum measurement; (b) high enough bandwidth to distinguish 76 MHz repetition rate femtosecond optical pulse; (c) high common mode rejection ratio (CMRR) to make a balance between the two photodiodes [1].

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Complete experimental characterization of the quantum state of a light mode via the Wigner function and the density matrix: application to quantum phase distributions of vacuum and squeezed-vacuum states

Cited by 163 publications

References 35 publications

Radon transform and pattern functions in quantum tomography

Radon transform and pattern functions in quantum tomography

Wigner Function Reconstruction in Levitated Optomechanics

High-speed Balanced Homodyne Detector for Quantum Information Applications

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