We derive the complete photon count statistics of an interferometer based on two beam splitters. As a special case we consider a joint intensity–electric field measurement. Our approach is based on the transformation properties of state vectors as well as field operators at a beam splitter
We demonstrate experimentally a phase measurement using general two-photon superposition states in a multiport interferometer shown schematically. A pair of photons, produced in the process of spontaneous parametric down-conversion, is transformed into the desired superposition state using beam splitters BS1 and BS2, provided that no photon escapes through the unmonitored port of BS2. In the signal arm, the photon pair experiences losses introduced by the beam splitter BS3 and monitored by a detector C, and subsequently probes the phase shift phi. The phase information is read out by sending the photons onto the beam splitter BS4, whose output ports are monitored by detectors A and B.
A quantum mechanical description of a non-absorbing electromagnetic (em) beam splitter (BS) transformation is given by the use of momentum creation operators, which also include momentum shift operators operating on the BS. This BS transformation is used for analysing photon-statistics effects in the em Mach-Zehnder interferometer. Also the relation between this BS transformation and Welcher-Weg measurements is discussed. The analogy between em and atom interferometers is described with an emphasis on the use of high-order correlation functions. The entanglement between the interfering beams in these interferometers and the BS is taken into account in our analysis for treating special effects.
Two-photon-counting interferometry has been realized by measuring the electrical current due to two-photon absorption in the space-charge layer of a semiconductor detector located at the output port of an interferometer. We apply this technique to study the correlation properties of twin beams issued from parametric fluorescence. We describe in detail how the different second-order correlation functions (interbeam, intrabeam) can be extracted at the femtosecond time scale from raw data. The values of these correlation functions determined by our experiments are in excellent agreement with theory. More precisely, extrabunching in twin beams is unambiguously demonstrated and theoretically described using two models: a comprehensive multimode quantum optics model and a simpler classical stochastic approach. Given the high brightness of our twin-beam source, both theories yield similar results. Finally, convenient analytical expressions of the correlation functions were derived from both theories, expressions in which we have been able to relate specific terms to accidental and exact coincidences between photons. Two-photon interferometry thus determines to which extent twin photons are twin. This technique should become a useful tool for future quantum optics developments.
It is well known that photoelectric measurements yield information about the statistical behavior of fluctuating light beams. The probability of n photoelectrons being ejected, in a fixed time interval, from the photosensitive surface of the photoelectric detector, upon which the light beam is normally incident, is a linear (Poisson) transform of the probability density for the intensity of the beam. With the help of some plausible assumptions, the present analysis provides solutions to the problem of inverting the Poisson transform, thus determining the probability density for the intensity from experimentally obtained photocounting distributions. The effectiveness of the method is demonstrated by an actual inversion of a typical experimental counting distribution. The technique is of particular interest in connection with efforts to understand the statistical behavior of optical fields, especially of laser fields.
We propose an experimentally feasible scheme to generate various types of entangled states of light fields by using beam splitters and single-photon detectors. Two beams of light fields are incident on two beam splitters respectively with each beam being asymmetrically split into two parts in which one part is supposed to be so weak that it contains at most one photon. We let the two weak output modes interfere at a third beam splitter. A conditional joint measurement on both weak output modes may result in an entanglement between the other two output modes. The conditions for the maximal entanglement are discussed based on the concurrence. Several specific examples are also examined.
In the recently proposed photonic de Broglie wave interferometer, sophisticated beam splitters are used to split the de Broglie wave of a set of photons. The photonic de Broglie or collective phase shift can, however, be found in conventional interferometry if the full photon statistics are recorded. We propose a variation of the original photonic de Broglie wave interferometer. We show that the collective phase shift can and has been found in interferometry using photon pairs and propose two new photonic de Broglie wave interferometers in which normal beam splitters are used. Both of these rely on conditioning to select the cases for which all the photons behave as a single object.