Experimental determination of number–phase uncertainty relations

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

doi:10.1364/ol.18.001259

Cited by 65 publications

(26 citation statements)

References 14 publications

(12 reference statements)

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“…37 Nonetheless, various ingenious techniques have been suggested in the attempt to identify at least an approximate value for optical phase, [38][39][40] and one of them has achieved notable success.…”

Section: Kz Lφ +mentioning

confidence: 99%

Quantum issues with structured light

Williams

Andrews

2016

SPIE Proceedings

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Descriptions of optical beams with structured wavefronts or vector polarizations are widely cast in terms of classical field theory. The corresponding fully quantum counterparts often present new insights into what is physically observed, and they are especially of interest when tackling issues such as entanglement. Similarly, when determining angular momentum densities, it appears that the separate roles of photon spin and beam topological charge can only be satisfactorily addressed within a quantum framework. In some such respects, the quantum versions of theory might be considered to introduce an additional layer of complexity; in others, they can clearly and very substantially simplify the theoretical representation. At the photon level, the fully quantized descriptions of topologically structured and singular beams nonetheless raise important fundamental questions and puzzles, whose resolution continue to invite attention. Many of the mechanistic interpretations and predictions (those that appear to be supported by a true congruence between classic and quantum optical descriptions, essentially conflating electromagnetic field and state wavefunction concepts) can lead to theoretical pitfalls. This paper highlights some physical implications that emerge from a fully quantum treatment of theory.

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Section: Kz Lφ +mentioning

confidence: 99%

Quantum issues with structured light

Williams

Andrews

2016

SPIE Proceedings

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“…Several modifications of the 'classical' balanced homodyne detection scheme have been proposed in order to measure the discrete WDF characterizing quantum states of finitedimensional systems like atoms or spins ), or for the tomography of a beam of identically prepared charged particles, entering into an electric field which causes harmonic oscillations in t ransverse direction (Tegmark [1996]). Optical homodyne tomography was also used to measure the number-phase uncertainty relations (Beck, Smithey, Cooper and Raymer [1993]) or the ultrafast (sub-ps) time-resolved photon statistics of arbitrary single-mode w eak fields from phase-averaged quadrature amplitude distributions (Munroe, Boggavarapu, Anderson and Raymer [1995]). …”

Section: Measurement Procedures Of Phase Space Distribution Functionsmentioning

confidence: 99%

“…Since time and frequency are also non-commuting variables for nonstationary signals, a time-frequency joint probability density cannot be measured directly, but can only be obtained from marginal distributions along rotated directions in the ) , ( ω t plane (Man'ko and Vilela Mendes [1999]). The setup of Beck, Raymer, Walmsley and Wong [1993], consists of a s uccession of dispersive elements and time lenses (Kolner [1994], Godil, Auld and Bloom [1994]), which mix ω and t.…”

Section: Measurement Procedures Of Phase Space Distribution Functionsmentioning

confidence: 99%

Phase space correspondence between classical optics and quantum mechanics

Dragoman

2002

Progress in Optics

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The paper scrutinizes both the similarities and the differences between the classical optics and quantum mechanical theories in phase space, especially between the Wigner distribution functions (WDF) defined in the respective phase spaces. Classical optics is able to provide an understanding of either the corpuscular or wave aspects of quantum mechanics, reflected in phase space through the classical limit of the quantum WDF or the WDF in classical optics, respectively. However, classical optics, as any classical theory, cannot mimic the w ave-particle duality that is at the heart of quantum mechanics. Moreover, it is never enough underlined that, although the mathematical phase space formalisms in classical optics and quantum mechanics are very similar, the main difference between these theories, evidenced in the results of measurements, is as deep as it can get even in phase space. On the other hand, the phase space treatment allows an unexpected similar treatment of interference phenomena, although quantum and classical superpositions of w avefunctions and fields, respectively, have a completely different behavior. This similarity originates in the bilinear character of the WDF in both quantum mechanics and classical optical wave theory. Actually, the phase space treatment of the quantum and classical wave theory is identical from the mathematical point of view, if the Planck's constant is replaced by the wavelength of light. Even WDFs of particular quantum states, such as the Schrödinger cat state, can be mimicked by classical optical means, but not the true quantum character, which resides in the probability significance of the wavefunction, in comparison to the physical 'realness' of classical wave fields. 2 1. INTRODUCTION Quantum mechanics was born from the need to quantify the energy of the emitted or absorbed electromagnetic radiation in order to explain the black body spectrum and the photoelectric effect. Light was thus considered, from the beginning of the quantum revolution, either as an extended wave or as a bunch of particles with definite energy. The subsequent evolution of quantum mechanics has not succeeded to settle the century old controversy regarding the corpuscular or wave-like nature of light, but rather deepened the mystery, extending the wave-corpuscle controversy to material particles. Quantum mechanics, and more recently quantum optics, is able to correctly calculate the essential characteristics of a quantum system, such as its energy levels, quantum statistics and so on, but still longs for a proper interpretation of its calculations. The widely accepted probabilistic interpretation of quantum mechanics is still an open question, the meaning and even existence of a wavefunction for photons, for example, being still subject to debate.One of the main reasons for this paradoxical situation of the most successful recent theory in physics is that although it has initially borrowed a lot of concepts from classical physics, in particular from classical optics, the subsequent evolu...

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“…Results have been obtained for vacuum, coherent, squeezed, and other states [3,4]. Given the measured density matrix, we can experimentally obtain (infer) any of the various quantum distributions of optical phase, in particular the Pegg-Barnett phase distribution [10], the Shapiro-Shepard positive-operator measure (ΡOM) phase [11], the marginal Wigner distribution [12], and the Vogel-Schleich operational phase distribution [13].…”

Section: Determination Of Optical Phase Distributionsmentioning

confidence: 99%

“…Further, we discuss the kinds of information, (71) such as phase and photon number distributions, which are available from such a state measurement [3]. From such distributions the number-phase uncertainty relations can be studied experimentally [4].…”

Section: Introductionmentioning

confidence: 99%

Quantum States and Number-Phase Uncertainty Relations Measured by Optical Homodyne Tomography

et al. 1994

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Experiments have been performed to determine the Wigner distribution and the density matrix (and for pure states the wave function) of a light mode, by using tomographic inversion of a set of measured probability distributions for quadrature amplitudes. From these measurements the quantum distributions of optical phase and photon number have been obtained. The measurements of quadrature-amplitude distributions for a temporal mode of the electromagnetic field are carried out using balanced homodyne detection. We refer to this new method as optical homodyne tomography. Given the measured density matrix, one can experimentally infer any of the various quantum distributions of optical phase, in particular the Pegg-Barnett (or, equivalently, Shapiro-Shepard) phase distribution, the marginal Wigner distribution, and the Vogel-Schleich operational phase distribntion. We have used this approach to make measurements of the number-plase uncertainty relation for coherent-state fields. The coherent states do not attain the minimum value for the number-phase uncertainty product, as set by the expectation value of the commutator of the number and phase operators; this is true theoretically and experimentally.

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Experimental determination of number–phase uncertainty relations

Cited by 65 publications

References 14 publications

Quantum issues with structured light

Quantum issues with structured light

Phase space correspondence between classical optics and quantum mechanics

Quantum States and Number-Phase Uncertainty Relations Measured by Optical Homodyne Tomography

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