Experimental determination of quantum-phase distributions using optical homodyne tomography

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

doi:10.1103/physreva.48.r890

Cited by 87 publications

(53 citation statements)

References 18 publications

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“…We emphasize, however, that the method presented here also applies to a signal field described by a density operator. In contrast to the method of quantum state tomography [8][9][10][11] based on homodyne detection, the present technique does not couple the signal field out of the resonator. In order to measure the signal field we couple it in a linear way to a meter field.…”

Section: Introductionmentioning

confidence: 99%

“…This was indeed performed in Refs. [9,10] by methods which are standard in tomographic imaging [32].…”

Section: B Tomographic Measurementsmentioning

confidence: 99%

“…Optical homodyne tomography [8][9][10][11]28] is a method for obtaining the Wigner function (or, more generally [29][30][31], the matrix elements of the density operator in some representation) of the electromagnetic field, preparing the field again in the same state after each measurement. It therefore consists of an ensemble of repeated measurements of one quadrature operator for different phases relative to the local oscillator of the homodyne detector.…”

Section: B Tomographic Measurementsmentioning

confidence: 99%

“…[8] and implemented experimentally in Refs. [9][10][11] does not work, since by coupling the field out of the resonator we change the field state. In the present paper we propose to couple the field via a quantum-non-demolition (QND) interaction [12] to a meter field on which we then perform tomography using a balanced homodyne detector.…”

Section: Introductionmentioning

confidence: 99%

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Endoscopic tomography and quantum nondemolition

1999

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We propose to measure the quantum state of a single mode of the radiation field in a cavitythe signal field-by coupling it via a quantum-non-demolition Hamiltonian to a meter field in a highly squeezed state. We show that quantum state tomography on the meter field using balanced homodyne detection provides full information about the signal state. We discuss the influence of measurement of the meter on the signal field.

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Section: Introductionmentioning

confidence: 99%

“…This was indeed performed in Refs. [9,10] by methods which are standard in tomographic imaging [32].…”

Section: B Tomographic Measurementsmentioning

confidence: 99%

Section: B Tomographic Measurementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Endoscopic tomography and quantum nondemolition

1999

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“…Among the many state reconstruction techniques suggested in the literature [10][11][12][13][14][15][16][17][18][19], quantum homodyne tomography (QHT) [11][12][13]18] of radiation field have been received much attention [1], being the only method which has been implemented in quantum optical experiments [4,5,11], and recently being extended to estimation of the expectation value of any operator of the field [18], which makes the method the first universal detectors for radiation.…”

Section: Introductionmentioning

confidence: 99%

Adaptive quantum homodyne tomography

D’Ariano

Paris

1999

Phys. Rev. A

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An adaptive optimization technique to improve precision of quantum homodyne tomography is presented. The method is based on the existence of so-called null functions, which have zero average for arbitrary state of radiation. Addition of null functions to the tomographic kernels does not affect their mean values, but changes statistical errors, which can then be reduced by an optimization method that "adapts" kernels to homodyne data. Applications to tomography of the density matrix and other relevant field-observables are studied in detail.

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7 Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling

Raymer

Beck

2004

Quantum State Estimation

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We review experimental work on the measurement of the quantum state of optical fields, and the relevant theoretical background. The basic technique of optical homodyne tomography is described with particular attention paid to the role played by balanced homodyne detection in this process. We discuss some of the original single-mode squeezed-state measurements as well as recent developments including: other field states, multimode measurements, array detection, and other new homodyne schemes. We also discuss applications of state measurement techniques to an area of scientific and technological importance-the ultrafast sampling of time-resolved photon statistics. Please cite as: M. G. Raymer and M. Beck, "Experimental quantum state tomography of optical fields and ultrafast statistical sampling," in Quantum State Estimation, Vol. 649, edited by M. G. A. Paris and J. Rehacek (Springer-Verlag, Berlin, 2004), pp. 235-295.function [13][14][15]. However, in the case of mixed states, even for one-dimensional systems, more than two distributions are needed for state reconstruction.Because some of the first experimental work on quantum state measurement [16] analyzed the collected data using a mathematical technique that is very similar to the tomographic reconstruction technique used in medical imaging, and because all techniques are necessarily indirect, a generally accepted term for quantum state measurement has become quantum state tomography(QST.) Systems measured have included angular momentum states of electrons [17], the field [16,[18][19][20] and polarization [21] states of photon pairs, molecular vibrations [22], trapped ions [23], atomic beams [24], and nuclear spins [25]. Indeed, QST has become so prevalent in modern physics that it has been given its own Physics and Astronomy Classification Scheme (PACS) code by the American Institute of Physics: 03.65.Wj, State Reconstruction and Quantum Tomography.The purpose of this article is to review some of the theoretical and experimental work on quantum state measurement. Prior reviews can be found in [1,8,9,26]. We will concentrate here on measurements of the state of the field of an optical beam with an indeterminate number of photons in one or more modes. Measurement of the polarization state of beams with fixed photon number is discussed in the article by Altepeter, James and Kwiat in this volume. Nearly all field-state measurements are based on the technique of balanced homodyne detection, and hence fall under the category of optical homodyne tomography (OHT.) This technique was first suggested by Vogel and Risken [10] and first demonstrated by Smithey et al. [16]. A reasonably complete list of experiments that have measured the quantum states (or related quantities) of optical fields is presented in Table 1.Here we will describe balanced homodyne detection, and its application to OHT. We emphasize pulsed, balanced homodyne detection at zero frequency (DC) in order to model experiments on "wholepulse" detection. Such detection provides information on, for exampl...

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Experimental determination of quantum-phase distributions using optical homodyne tomography

Cited by 87 publications

References 18 publications

Endoscopic tomography and quantum nondemolition

Endoscopic tomography and quantum nondemolition

Adaptive quantum homodyne tomography

7 Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling

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