© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Physical Review A

Quantum versus stochastic or hidden-variable fluctuations in two-photon interference effects

C. Su, K. Wódkiewicz

Published Nov 1, 1991• 20 citations

Abstract

In a series of experiments performed by Mandel and co-workers, nonclassical effects have been demonstrated in the interference of two photons generated in a process of parametric down-conversion. The nonclassical effects in the two-photon interference effects can be discussed in the framework of two different descriptions. In the first description, a stochastic theory of electromagnetic field fluctuations can be used in order to calculate the interference pattern. In the second description, a theory of hidden-variable fluctuations can be applied in order to calculate correlations of the interference pattern. A stochastic theory leads to statistical inequalities for the light intensities, while a local hidden-variable theory leads to Bell's inequalities. Using the Schwinger-boson representation of the angular momentum, we show that the two-photon interference effects can be described in terms of spin-correlated states. In particular, we show that the action of a beam splitter on the photons in a parametric down-conversion is equivalent to the production of an entangled state that is very similar to the well-known Einstein, Podolsky, and Rosen spin-singlet state. We show that the stochastic theory of two-photon fluctuations is not equivalent to a hidden-variable theory of photon correlations. We establish a range for which the stochastic theory fails but the hidden-variable theory is still possible. We compare our theoretical predictions with the experimental results and conclude that a violation of the stochastic theory has been clearly observed, while the violation of the hidden-variable theory is less pronounced.

DOI: 10.1103/physreva.44.6097

Related papers

Quantum theory of fourth-order interference

Z. Y. Ou

The quantum theory of fourth-order interference of light is presented in a general format and compared with classical wave theory. The conditions under which nonclassical phenomena occur are discussed. In particular, the interference between the quantum field and classical field may give rise to a nonclassical effect. For some special states of light, the interference pattern does not disappear even though one field is much stronger than the other, for which no classical analog exists. Fourth-order effects in the interference between two independent fields are analyzed in detail. It is pointed out that the fourth-order interference between independent fields will not disappear when the integration time of detection is of the order of the reciprocal bandwidth of the two light fields as long as the spectra of the two fields are symmetric around the same center frequency, and for some correlated fields, the interference does not vanish even if the detection time is much larger than the reciprocal bandwidth of the fields. A new type of fourth-order interference experiment involving a beam splitter is proposed in which local realism of the Einstein-Podolsky-Rosen form is violated for quantum mechanics. This general argument is then applied to the interference between two photons generated in the parametric down-conversion process. The possibility of violations of Bell's inequalities in interference experiments is investigated.

Physical Review A•Mar 1, 1988•81 citations

Nonclassical Photon Interference Effects

C K Hong, Z. Y. Ou, L. Mandeļ

This chapter discusses two reported experiments in which the interference between signal and idler photons generated in the process of parametric down-conversion were investigated. Although two-photon interference effects have been treated theoretically before, it analyzes the two experiments in some detail to show how differences between the predictions of classical and quantum theories appear. The chapter compares the predictions of classical and quantum theories with the experimental results obtained. As practically all detectors of light rely on the photoelectric effect, in which a free electron is produced at the expense of a photon, the photon annihilation operator plays a key role in describing the measurement of light in the quantum theory. The time correlation between signal and idler photons produced in the parametric down-conversion process was first measured with a resolving time of about 10 nanoseconds. The interference effect can be made the basis of a measurement of the length of a photon wave packet with femtosecond time resolution.

CRC Press eBooks•Aug 12, 2020•2 citations

Reexamining the Einstein-Podolsky-Rosen experiment, photon correlation and Bell's inequality

L. Fritsche, M. Haugk

The purpose of this article is to show that the introduction of hidden variables to describe individual events is fully consistent with the statistical predictions of quantum theory. We illustrate the validity of this assertion by discussing two fundamental experiments on correlated photons which are believed to behave ``violently non-classical''. Our considerations carry over to correlated pairs of neutral particles of spin one-half in a singlet state. Much in the spirit of Einstein's conviction we come to the conclusion that the state vector of a system does not provide an exhaustive description of the individual physical system. We also briefly discuss an experiment on ``quantum teleportation'' and demonstrate that our completely local approach leads to a full understanding of the experiment indicating the absence of any teleportation phenomenon. We caution that the indiscriminated use of the term ``Quantum Theory'' tends to obscure distinct differences between the quantum mechanics of massive particles and the propagation of photons. It is emphasized that the properties of polarizers, beam splitters, halfwave plates etc. used in photon-correlation experiments are defined by the laws of classical optics. Hence, understanding the outcome of those experiments requires a well-founded interconnection between classical and quantum electrodynamics free from unnecessary hypotheses.

arXiv:0705.2568•May 17, 2007•0 citations

Four-photon entanglement from down-conversion

Harald Weinfurter, Marek Żukowski

Double-pair emission from type-II parametric down-conversion results in a highly entangled four-photon state. Due to interference, which is similar to bunching from thermal emission, this state is not simply a product of two pairs. The observation of this state can be achieved by splitting the two emission modes at beam splitters and subsequent detection of a photon in each output. Here we describe the features of this state and construct a Bell-type inequality, which gives a necessary and sufficient condition for a four-photon test of local realistic hidden variable theories.

arXiv:quant-ph/0103049•Physical Review A•Jun 7, 2001•183 citations

Einstein-Podolsky-Rosen state for space-time variables in a two-photon interference experiment

Yanhua H. Shih, Alexander V. Sergienko, Morton H. Rubin

A pair of correlated photons generated from parametric down-conversion was sent to two independent Michelson interferometers. Second-order interference was studied by means of a coincidence measurement between the outputs of two interferometers. The reported experiment and analysis studied this second-order interference phenomenon from the point of view of the Einstein-Podolsky-Rosen (EPR) paradox. The experiment was done in two steps. The first step of the experiment used 50-psec and 3-nsec coincidence time windows simultaneously. The 50-psec window was able to distinguish a 1.5-cm optical path difference in the interferometers. The interference visibility was measured to be 38% and 21% for the 50-psec time window and 22% and 7% for the 3-nsec time window, when the optical path differences of the interferometers were 2 cm and 4 cm, respectively. By comparing the visibilities between these two windows, the experiment showed the nonclassical effect which resulted from an EPR state. The second step of the experiment used a 20-psec coincidence time window, which was able to distinguish a 6-mm optical path difference in the interferometers. The interference visibilities were measured to be 59% for an optical path difference of 7 mm. This is an observation of visibility greater than 50% for a two-interferometer EPR experiment which demonstrates nonclassical correlation of space-time variables.

Physical Review A•Feb 1, 1993•70 citations

Numerical simulation of Einstein-Podolsky-Rosen experiments in a local hidden variables model

Werner A. Hofer

We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. In our model correlations arise from a phase, connecting the electromagnetic fields of the two photons at their separate points of measurement. We sum up coincidences for each pair individually and model the operation of a polarizer beam splitter numerically. The results thus obtained differ substantially from the classical results. In addition, we analyze the effects of decoherence and non-ideal beam splitters. It is shown that under realistic experimental conditions the Bell inequalities are violated by more than 30 standard deviations.

arXiv:quant-ph/0108141•Aug 31, 2001•2 citations

In a series of experiments performed by Mandel and co-workers, nonclassical effects have been demonstrated in the interference of two photons generated in a process of parametric down-conversion. The nonclassical effects in the two-photon interference effects can be discussed in the framework of two different descriptions. In the first description, a stochastic theory of electromagnetic field fluctuations can be used in order to calculate the interference pattern. In the second description, a theory of hidden-variable fluctuations can be applied in order to calculate correlations of the interference pattern. A stochastic theory leads to statistical inequalities for the light intensities, while a local hidden-variable theory leads to Bell's inequalities. Using the Schwinger-boson representation of the angular momentum, we show that the two-photon interference effects can be described in terms of spin-correlated states. In particular, we show that the action of a beam splitter on the photons in a parametric down-conversion is equivalent to the production of an entangled state that is very similar to the well-known Einstein, Podolsky, and Rosen spin-singlet state. We show that the stochastic theory of two-photon fluctuations is not equivalent to a hidden-variable theory of photon correlations. We establish a range for which the stochastic theory fails but the hidden-variable theory is still possible. We compare our theoretical predictions with the experimental results and conclude that a violation of the stochastic theory has been clearly observed, while the violation of the hidden-variable theory is less pronounced.

The quantum theory of fourth-order interference of light is presented in a general format and compared with classical wave theory. The conditions under which nonclassical phenomena occur are discussed. In particular, the interference between the quantum field and classical field may give rise to a nonclassical effect. For some special states of light, the interference pattern does not disappear even though one field is much stronger than the other, for which no classical analog exists. Fourth-order effects in the interference between two independent fields are analyzed in detail. It is pointed out that the fourth-order interference between independent fields will not disappear when the integration time of detection is of the order of the reciprocal bandwidth of the two light fields as long as the spectra of the two fields are symmetric around the same center frequency, and for some correlated fields, the interference does not vanish even if the detection time is much larger than the reciprocal bandwidth of the fields. A new type of fourth-order interference experiment involving a beam splitter is proposed in which local realism of the Einstein-Podolsky-Rosen form is violated for quantum mechanics. This general argument is then applied to the interference between two photons generated in the parametric down-conversion process. The possibility of violations of Bell's inequalities in interference experiments is investigated.

This chapter discusses two reported experiments in which the interference between signal and idler photons generated in the process of parametric down-conversion were investigated. Although two-photon interference effects have been treated theoretically before, it analyzes the two experiments in some detail to show how differences between the predictions of classical and quantum theories appear. The chapter compares the predictions of classical and quantum theories with the experimental results obtained. As practically all detectors of light rely on the photoelectric effect, in which a free electron is produced at the expense of a photon, the photon annihilation operator plays a key role in describing the measurement of light in the quantum theory. The time correlation between signal and idler photons produced in the parametric down-conversion process was first measured with a resolving time of about 10 nanoseconds. The interference effect can be made the basis of a measurement of the length of a photon wave packet with femtosecond time resolution.

The purpose of this article is to show that the introduction of hidden variables to describe individual events is fully consistent with the statistical predictions of quantum theory. We illustrate the validity of this assertion by discussing two fundamental experiments on correlated photons which are believed to behave ``violently non-classical''. Our considerations carry over to correlated pairs of neutral particles of spin one-half in a singlet state. Much in the spirit of Einstein's conviction we come to the conclusion that the state vector of a system does not provide an exhaustive description of the individual physical system. We also briefly discuss an experiment on ``quantum teleportation'' and demonstrate that our completely local approach leads to a full understanding of the experiment indicating the absence of any teleportation phenomenon. We caution that the indiscriminated use of the term ``Quantum Theory'' tends to obscure distinct differences between the quantum mechanics of massive particles and the propagation of photons. It is emphasized that the properties of polarizers, beam splitters, halfwave plates etc. used in photon-correlation experiments are defined by the laws of classical optics. Hence, understanding the outcome of those experiments requires a well-founded interconnection between classical and quantum electrodynamics free from unnecessary hypotheses.

Double-pair emission from type-II parametric down-conversion results in a highly entangled four-photon state. Due to interference, which is similar to bunching from thermal emission, this state is not simply a product of two pairs. The observation of this state can be achieved by splitting the two emission modes at beam splitters and subsequent detection of a photon in each output. Here we describe the features of this state and construct a Bell-type inequality, which gives a necessary and sufficient condition for a four-photon test of local realistic hidden variable theories.

A pair of correlated photons generated from parametric down-conversion was sent to two independent Michelson interferometers. Second-order interference was studied by means of a coincidence measurement between the outputs of two interferometers. The reported experiment and analysis studied this second-order interference phenomenon from the point of view of the Einstein-Podolsky-Rosen (EPR) paradox. The experiment was done in two steps. The first step of the experiment used 50-psec and 3-nsec coincidence time windows simultaneously. The 50-psec window was able to distinguish a 1.5-cm optical path difference in the interferometers. The interference visibility was measured to be 38% and 21% for the 50-psec time window and 22% and 7% for the 3-nsec time window, when the optical path differences of the interferometers were 2 cm and 4 cm, respectively. By comparing the visibilities between these two windows, the experiment showed the nonclassical effect which resulted from an EPR state. The second step of the experiment used a 20-psec coincidence time window, which was able to distinguish a 6-mm optical path difference in the interferometers. The interference visibilities were measured to be 59% for an optical path difference of 7 mm. This is an observation of visibility greater than 50% for a two-interferometer EPR experiment which demonstrates nonclassical correlation of space-time variables.

We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. In our model correlations arise from a phase, connecting the electromagnetic fields of the two photons at their separate points of measurement. We sum up coincidences for each pair individually and model the operation of a polarizer beam splitter numerically. The results thus obtained differ substantially from the classical results. In addition, we analyze the effects of decoherence and non-ideal beam splitters. It is shown that under realistic experimental conditions the Bell inequalities are violated by more than 30 standard deviations.