Properties of the nonclassical light (NCL) have been considered with an emphasis on experimentally-observed features, which are underlain by the well-known Mandel's formula connecting the statistics of photocounts with that of light falling on the detector. A systematic operational approach is presented to study the NCL using two parallel sets of numbers measured: probabilities of photocounts {pm} and normalised factorial moments of counts {gk}. Two particular examples are examined in detail: a 'heated' squeezed vacuum and a 'heated' one-photon state. An alternative method is proposed to discover the week nonclassicality using 'generalised' moments {ak(s)}. The effect of the linear absorption (amplification) and of the beam-splitting of the NCL, and the relation between the NCL and the absolute calibration of photodetectors are considered. The conditions are elucidated whereat the beam-splitter realises a mathematical operation of superposition of two one-mode fields useful in studying the NCL.
Properties of the nonclassical light (NCL) have been considered with an emphasis on experimentally-observed features, which are underlain by the well-known Mandel's formula connecting the statistics of photocounts with that of light falling on the detector. A systematic operational approach is presented to study the NCL using two parallel sets of numbers measured: probabilities of photocounts {pm} and normalised factorial moments of counts {gk}. Two particular examples are examined in detail: a 'heated' squeezed vacuum and a 'heated' one-photon state. An alternative method is proposed to discover the week nonclassicality using 'generalised' moments {ak(s)}. The effect of the linear absorption (amplification) and of the beam-splitting of the NCL, and the relation between the NCL and the absolute calibration of photodetectors are considered. The conditions are elucidated whereat the beam-splitter realises a mathematical operation of superposition of two one-mode fields useful in studying the NCL.
Antibunching, photon-number squeezing, and quadrature squeezing represent characteristics of nonclassical electromagnetic fields that have been observed in the laboratory. Experiments involving nonclassical light often make use of beam splitters to superimpose light beams. We discuss the photon statistics that arise from the superimposition of two arbitrary (not necessarily independent) quantum fields at a device such as a beam splitter. The photomixing density operator of the superimposition field is presented, and the behavior of the balanced mixer is examined in the general case.1 The failure of classical probability theory as a descriptor of the relationship between the photon statistics at the output and at the input of the beam splitter is elucidated.
Photon number resolving detectors can be highly useful for studying the statistics of multiphoton quantum states of light. In this work we study the counts statistics of different states of light measured on multiplexed on–off detectors. We put special emphasis on artificial nonclassical features of the statistics obtained. We show new ways to derive analytical formulas for counts statistics and their moments. Using our approach we are the first, to the best of our knowledge, to derive statistics moments for multimode thermal states measured on multiplexed on–off detectors. We use them to determine empirical Mandel parameters and recently proposed sub-binomial parameters suitable for tests of nonclassicality of the measured states. Additionally, we investigate sub-Poissonian and superbunching properties of the two-mode squeezed state measured on a pair of multiplexed detectors, and we present results of the Fano factor and second-order correlation function for these states.
Any single on-off photocounter, which can only detect the presence or absence of photons without discriminating their number, is not capable of identifying nonclassical nature of light. This limitation arises because any photocounting statistics obtained with such a detector can be easily reproduced with coherent states of a light mode. We show that a simple modification of an on-off detector -- introducing controlled attenuation as a tunable setting -- enables such detectors to reveal nonclassical properties of radiation fields.
Although light quanta were known since the works by Planck and Einstein, for several decades after these works, there was no need to treat light quantum mechanically, and all experiments could be well explained using the quantum description of matter and classical description of light (the semiclassical approach). The situation changed with the development of sources of so-called nonclassical light, i.e., light whose properties cannot be understood in the framework of the semiclassical approach. Two simple examples can be given here. The first one is the suppression of shot noise in optical detectors. Shot noise, i.e., fluctuations of photocurrent scaling as the square root of the photocurrent mean value, can be, in principle, attributed to the discrete nature of the charge generated by the detector. At the same time, the effect of shot-noise suppression, which is observed with certain light sources (squeezed light) is clearly related to the statistics of light, and quantum mechanics is completely necessary for its description. Another example, which brings us closer to the subject of the present paper, is two-photon light. This type of light contains only pairs of photons (often called biphotons), and hence, a pair of properly aligned photon-counting detectors registering two-photon light, in an ideal case, will produce only simultaneous photocounts. This behavior, again, can only be explained in terms of a quantum-mechanical description for the light.
Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multimode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beam splitters, in a transparent manner. For single-mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon by a beam splitter, these conditions turn exactly into signatures of negativity under partial transpose (NPT) entanglement of the output state. Since the classical moment problem does not generalize to two or more modes, we turn in these cases to other familiar sufficient but not necessary conditions for nonclassicality, namely the Mandel parameter criterion and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two-mode states we present a single test that can, if successful, simultaneously show nonclassicality as well as NPT entanglement. We also develop a test for NPT entanglement after beam-splitter action on a nonclassical state, tracing carefully the way in which it goes beyond the Mandel nonclassicality test. The result of three-mode beam-splitter action after coupling to an ancilla in the ground state is treated in the same spirit. The concept of genuine tripartite entanglement, and scalar measures of nonclassicality at the Mandel level for two-mode systems, are discussed. Numerous examples illustrating all these concepts are presented.
Numerous nonclassicality criteria based on the probabilities of experimental photocount or theoretical photon-number distributions are derived using several approaches. Relations among the derived criteria are revealed and the fundamental criteria are identified. They are grouped into parametric systems that allow the analysis of the nonclassicality from different points of view (``local'' nonclassicality, pairwise character of photon correlations, etc.). Considering their structure, the criteria may be divided into groups that differ in the power to resolve the nonclassicality. Quantification of the nonclassicality using the Lee nonclassicality depth and the nonclassicality counting parameter is discussed. The number of field modes used is identified as an important parameter that may cause unexpected results. An appropriate linear transformation of a photocount (photon-number) distribution into its s-ordered form, needed for the determination of the nonclassicality depth, is derived. For comparison, the derived criteria are applied both to an experimental photocount histogram of a twin beam and the reconstructed photon-number distributions with different levels of the noise.