Shifting the quantum-classical boundary: theory and experiment for statistically classical optical fields

Abstract

The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schrödinger's famous remark about it [Proc. Camb. Phil. Soc. 31, 555 (1935)], prompts examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments, and report here values of the Bell parameter greater than B = 2.54. This is many standard deviations outside the limit B = 2 established by the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit B = 2.828.... These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it.Introduction: For many decades the term "entanglement" has been attached to the world of quantum mechanics [1]. However, it is true that non-quantum optical entanglement can exist (realized very early by Spreeuw [2]) and its applications have concrete consequences. These are based on entanglements between two, or more than two, degrees of freedom, which are easily avalable classically [2][3][4][5][6]. Multi-entanglements of the same kind are also being explored quantum mechanically [7]. Applications in the classical domain have included, for example, resolution of a long-standing issue concerning Mueller matrices [8], an alternative interpretation of the degree of polarization [9], introduction of the Bell measure as a new index of coherence in optics [10], and innovations in polarization metrology [11]. Here we present theoretical and experimental results extending these results by showing that probabilistic classical optical fields can exhibit violations of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [12] of quantum strength. This is evidence of a new kind that asks for reconsideration of the common understanding that Bell violation signals quantum physics. We emphasize that our discussion focuses on non-quantum entanglement of nondeterministic classical optical fields, and does not engage issues such as non-locality that are important for some applications in quantum information.The observations and applications of non-quantum wave entanglement noted above [2-6, 8-11] exploited nonseparable correlations among two or more modes or degrees of freedom (DOF) of optical wave fields. Nonseparable correlations among modes are an example of entanglement [13], but are not enough for our present purpose. In addition, we want to conform to three criteria that Shimony has identified for Bell tests [1], facts of quantum Nature that must be satisfied when examining possible tests of the quantum-classical border. Fortuitously, the ergodic stochastic optical fields of the classical theory of partial coherence and partial polarization (see Wolf [15]) satisfy these criteria fully (see Suppl. Materials [16]), and we have used such fields as our test bed. Background Theory: We will deal here only wit...

Quantum Rayleigh Annihilation of Entangled Photons

“…Spontaneously emitted photons with ± φ e m polarization angles relative to the pump polarization ep , will be amplified through the optically linear parametric gain coefficient [10,11] which will include a polarization dependence in the factor e p • e k µ , bringing about a correlation between the state of polarization and its number of amplified photons as found in [5]. For e k µ • x = cos φ e m and x • y = 0 , a non-vanishing value along the y -polarization is obtained by blocking off either  φ or  φ polarized photons as, for a large number of photons, the y -polarized photons cancel each other out..…”

“…For some particular reason though, another report [5] of high levels of correlations between classical and entangled functions of optical polarization was totally ignored. The latter reference [5] suggests that the violations of Bell inequalities "has less to do with quantum theory than previously thought, but everything to do with entanglement. "…”

“…Nevertheless, the interpretation of the experimental results of [1][2][3][4][5] failed to take into account the role played by the quantum Rayleigh conversion of photons [7][8][9][10][11] in their propagation through the dielectric media of optical fibers, beam splitters, polarization rotating devices and other dielectric elements comprising the experimental setups. While the classical Rayleigh scattering induced by perturbations of the refractive index is the major loss factor in optical fibers [12], the quantum Rayleigh conversion of photons has been practically ignored although documented in early textbooks [7,8].…”

“…The two types of experimental results [2 -4] and [5] can be linked by recalling that a large number of photons carried by an optical wavefront emerge from either spontaneous emission or stimulated emission [9][10][11]. In the case of only one photon propagating through a dielectric medium, the only process occurring is that of absorption of the photon by an oscillating dipole and spontaneous emission of one photon, which corresponds to the quantum Rayleigh conversion of photons (QRCP).…”

Spin–orbit laser mode transfer via a classical analogue of quantum teleportation

“…This investigation was also later taken up in the single photon regime by other groups [5,6]. Recently, the role of Bell inequalities in classical optics has drawn a fair amount of attention, being addressed in a series of papers [7][8][9]. This new understanding of classical non-separability resulted in new optical applications inspired by quantum information [10][11][12][13][14][15][16][17].…”