More than a century ago, pioneeringworks carried out by Poynting (1909) and other physicists have provided the evidence of the validity of Marxwell equations for an electromagnetic field, showing how a beam of light carries energy and momentum, both in the linear and angular components. In particular the angular momentum of light, related to the generator of rotations in quantum mechanics, has been typically associated with its polarization, and more specifically with its circular polarization components. An optical beam traveling in the positive direction of the z axis that is circularly polarized, carries a z-component angular momentum content σ = ±h per photon, which is positive if the circular polarization is left-handed and negative if it is right-handed. This angular momentum content is not just a formal property, but a very concrete one that can have significant mechanical effects as for example an observable induced rotation by absorption to amaterial particle Beth (1936); Friese et al. (1998)
More than a century ago, pioneeringworks carried out by Poynting (1909) and other physicists have provided the evidence of the validity of Marxwell equations for an electromagnetic field, showing how a beam of light carries energy and momentum, both in the linear and angular components. In particular the angular momentum of light, related to the generator of rotations in quantum mechanics, has been typically associated with its polarization, and more specifically with its circular polarization components. An optical beam traveling in the positive direction of the z axis that is circularly polarized, carries a z-component angular momentum content σ = ±h per photon, which is positive if the circular polarization is left-handed and negative if it is right-handed. This angular momentum content is not just a formal property, but a very concrete one that can have significant mechanical effects as for example an observable induced rotation by absorption to amaterial particle Beth (1936); Friese et al. (1998)
The angular momentum of light is a useful resource for many applications. In specific physical architectures it can be considered as the sum of two independent terms, the spin and the orbital components, in analogy to particle systems. The spin angular momentum is related to the polarization of the optical beam, that is the direction of the oscillating electric field, whereas the orbital angular momentum is associated with the spatial distribution of the field. Being independent, spin and orbital angular momenta have been discovered and explored in separate contexts for many years, while only recently it has been considered the possibility to address both quantities on the same beam (or individual photons). The interaction between these two quantities gives rise to complex structures of the electromagnetic field, or to the so called classical entanglement in the domain of single photons. The research presented in this work aimed to show that combining spin and orbital angular momenta in light beams or single photons may be a useful tool for a variety of applications, with particular interest to the case of architectures characterized by spin-orbit interaction. This concept was made concrete through the design and the realization of several experiments, in the framework of singular optics, foundations of quantum mechanics, quantum information theory and quantum simulation.
Photons are an ideal candidate for encoding both classical and quantum information. Besides spin angular momentum associated with circular polarization, single photon can also carry other fundamentally new degree of freedom of orbital angular momentum related to the spiral phase structure of light. The key significance of orbital angular momentum lies in its potential in realizing a high-dimensional Hilbert space and in encoding a high-dimensional quantum information. Since Allen et al. [Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185] recognized the physical reality of photon orbital angular momentum in 1992, rapidly growing interest has been aroused in orbital angular momentum (OAM) from both classical and quantum points of view. Here we present an overall review on the high-order orbital angular momentum of photon, including its preparation and manipulation based on some specific techniques and also its applications. The spatial light modulator is a commercial device that has been widely employed to generate the OAM beams. We make and identify the optical OAM superposition with very high quantum numbers up to l=360. Recently, the metallic spiral phase mirrors were also developed to produce high-order OAM beams up to l=5050. In addition, the Q-plates made of anisotropic and inhomogeneous liquid crystals were invented to generate high-order OAM beams in a polarization-controllable manner, and the OAM superposition of l=± 50 were achieved. Owing to high rotational symmetry, these high OAM beams have been found to have more and more important applications in the fields of high-sensitivity sensing and high-precision measurements. Two fascinating examples are discussed in detail. The first example is that the research group led by Prof. Zeilinger has prepared and observed the quantum entanglement of high orbital angular momenta up to l=±300 by the technique of polarization-OAM entanglement swapping, and they demonstrated that the angular resolution could be significantly improved by a factor of l. Their result was the first step for entangling and twisting even macroscopic, spatially separated objects in two different directions. The second example is that the research group led by Prof. Padgett has demonstrated an elegant experiment of rotational Doppler effects for visible light with l=±20 OAM superposition. They showed that a spinning object with an optically rough surface might induce a Doppler effect in light reflected from the direction parallel to the rotation axis, and the frequency shift was proportional to both the disk's angular speed and the optical OAM. The potential applications in noncontact measurement of angular speed and in significant improvement of angular resolution for remote sensing will be particularly fascinating.
A photon can be considered both a particle and a wave in quantum mechanics. Quantum optics deals with such quantum mechanical properties of a photon. One such property that has been of particular interest recently is that of light’s momentum, specifically its linear momentum and orbital angular momentum (OAM). Light carrying both types of momentum are of particular utility to the life sciences. Linear momentum (LM) photons have the ability to directly manipulate particles. For example, photons with these properties can be used to separate one specific particle from a group. One can then more closely observe its properties. OAM photons have the potential to unravel DNA strands using the torque of the photons to further observe certain specific physical properties. Light carrying OAM has also shown promise in the field of information technology as a new means of sending large amounts of data over long distances securely and extremely quickly. Because photons behave quantum mechanically, the encryptions are much more difficult to decode, and since the information is being sent as light it clearly travels at the speed of light. This paper will provide background on the quantum optics of particle manipulation and the results from experimental studies performed on this topic. The results show evidence of light with both types of momentum being created and used to manipulate particles. We generated light with both types of momentum, trapped particles with optical tweezers, and measured the force on the particles with a high speed video camera, optical tweezers, and computer programs that we used to track the particles.
Abstract A century ago Einstein introduced the notion of the linear momentum of a photon, h k, and analyzed its transfer to an atom (and back) in the establishment of thermodynamic equilibrium between black-body radiation and matter. In addition to a linear momentum, the photon also possesses an angular momentum, ħ, directed parallel (or antiparallel) to its propagation direction (the OZ axis in Fig. 4.1), depending on its polarization direction (left- or right-handed). This angular momentum is due to the spin of the photon, equal to 1. Half a century later, Kastler (1950) considered the use of the transfer of the angular momentum of a polarized photon to the angular momentum of an atom as a method of optical orientation of atoms. In essence, this was the first method to control atomic motion by means of low-intensity light, developed even before the advent of the laser; it which found widespread application in investigating and then using spin polarization effects in atomic physics. But even after lasers had made their appearance, the method of optical orientation of atoms (or pumping of certain magnetic sublevels in atoms) proved very important, specifically in the laser cooling of atoms (Chapter 5).
This presentation first reviews the historical development of the field of nonlinear optics, starting from its inception in 1961. It then reviews some of its more recent developments, including especially how nonlinear optics has become a crucial tool for the developing field of quantum technologies. Fundamental quantum processes enabled by nonlinear optics, such as the creation of squeezed and entangled light states, are reviewed. We then illustrate these concepts by means of specific applications, such as the development of secure communication systems based on the quantum states of light. We are also interested in studying the properties of structured light fields. These structured light beams have recently been shown to possess exotic properties of their own, such as vacuum propagation velocities differing from the light velocity c for plane waves. These beams can also be tailored in such a way that they carry orbital angular momentum, which can be used to apply a torque to mechanical objects and as a carrier of information in a classical and quantum telecommunication system. Light can carry angular momentum both by means of its spin angular momentum (as manifested for example in circular polarization) and by means of its orbital angular momentum (OAM), whose origin is a helical structure of its wavefront. The orbital angular momentum of light has recently been recognized to constitute a crucial attribute for many photonic technologies, including the trapping and manipulation of small particles and for multiplexing in optical telecommunication. In this presentation we review some of the fundamental properties of OAM including its quantum features such as entanglement. We then go on to describe a secure telecommunication system in which information is encoded in OAM, and which can carry more than one bit of information per photon.
Angular momentum plays an iniport,aiit role in both classical and quantum physics. Historically the angular momentum content of a photon was divided into spin or polarization angular momentum (PAM), which relies in the vectorial structure of the field, and orbital angular momentum (OAM), which is usually related with the spatial structure of the beam. It has been experimeiitally demonstrated that, under the paraxial approximation, one can manipulate independently the PAM and the OAM. While the former is a classical tool in quantum information experiments, only recently the potential of the OAM has been explored. In particular, it was demonstrated recently that the idler and signal photons produced in the process of spontaneous parametxic downconversion constitute an entangled state of OAM [l]. The experiment showed that when the beam that pumps the nonlinear crystal is an eigenstate of the OAM, the quantum state of the down converted photons can in principle be described as IQ