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All the previous studies on photonic tunneling are just based on a simple and directly analogy with a one-dimensional quantum-mechanical tunneling, without taking into account the horizontal structure of electromagnetic waves along the waveguide, such that they are oversimplified and incomplete. Here we present a more serious deliberation on photonic tunneling through cut-off waveguides, and obtain a strictly theoretical model with some new results., Comment: 22 pages, no figure

Guided waves and surface waves can be taken as two typical examples of structured optical fields with the transverse spin. Analytical derivations are developed to demonstrate that (i) guided waves also carry the transverse spin that depends on the mean direction of propagation, which may have important applications in spin-dependent unidirectional optical interfaces; (ii) the quantization form of the transverse spin is for the first time revealed, which is not obvious and related to an ellipticity; (iii) from a unified point of view, the transverse spin can be attributed to the presence of an effective rest mass of structured optical fields; (iv) the transverse spin can also be described by the spin matrix of the photon field; (v) unlike a free optical field whose spin projection on the propagation direction is the only observable, owing to the effective rest mass, the spin projection of structured optical fields on other directions is also an observable, such that one can develop an optical analogy of spintronics. A preliminary idea about the potential applications of the transverse spin is presented, but an in-depth and complete study will be presented in our next work., Comment: 30 pages, 7 figure

Because spatio-temporal tensors are associated with the Lorentz group, whereas spinors are associated with its covering group SL(2, C), one can associate with every tensor a spinor (but not vice versa). In particular, the (1,0)+(0,1) representation of SL(2, C) can provide a six-component spinor equivalent to the electromagnetic field tensor. The chief aim of this work is to develop the (1,0)+(0,1) description for the electromagnetic field in the absence of sources, rigorously and systematically, which should be useful if we are to deal with those issues involving with single-photon states and the angular momentum of light, etc. Based on our formalism, the quantum theory and some symmetries of the photon field can be discussed in a new manner, and the spin-orbit interaction of photons can be described in a form that is closely analogous to that of the Dirac electron. Moreover, in terms of the (1,0)+(0,1) description, one can treat the photon field in curved spacetime via spin connection and the tetrad formalism, which is of great advantage to study the gravitational spin-orbit coupling of photons., Comment: 60 pages, no figure. It will provide a comprehensive reference for some of our future works

In a recent interesting Letter [Phys. Rev. Lett. 108, 140401 (2012)] I. Bialynicki-Birula and his coauthor have derived the uncertainty relation for the photons in three dimensions. However, some of their arguments are problematical, and this impacts their conclusion., Comment: Detailed version of a Comment, 11 pages, no figure

Time operator is studied on the basis of field quantization, where the difficulty stemming from Pauli's theorem is circumvented by borrowing ideas from the covariant quantization of the bosonic string, i.e., one can remove the negative energy states by imposing Virasoro constraints. Applying the index theorem, one can show that in a different subspace of a Fock space, there is a different self-adjoint time operator. However, the self-adjoint time operator in the maximal subspace of the Fock space can also represent the self-adjoint time operator in the other subspaces, such that it can be taken as the single, universal time operator. Furthermore, a new insight on Pauli's theorem is presented., Comment: 13 pages, No figure, to be published in Physics Letters B

The cross-Kerr nonlinearity (XKNL) effect can induce efficient photon interactions in principle with which photonic multiqubit gates can be performed using far fewer physical resources than linear optical schemes. Unfortunately, it is extremely challenging to generate giant cross-Kerr nonlinearities. In recent years, much effort has been made to perform multiqubit gates via weak XKNLs. However, the required nonlinearity strengths are still difficult to achieve in the experiment. We here propose an XKNL-based scheme for realizing a two-photon polarization-parity gate, a universal two-qubit gate, in which the required strength of the nonlinearity could be orders of magnitude weaker than those required for previous schemes. The scheme utilizes a ring cavity fed by a coherent state as a quantum information bus which interacts with a path mode of the two polarized photons (qubits). The XKNL effect makes the bus pick up a phase shift dependent on the photon number of the path mode. Even when the potential phase shifts are very small they can be effectively measured using photon-number resolving detectors, which accounts for the fact that our scheme can work in the regime of tiny XKNL. The measurement outcome reveals the parity (even parity or odd parity) of the two polarization qubits., Comment: 8 pages, 5 figures; some revisions have been made

The Hawking radiation can be viewed from very different perspectives, not all of which can be proved to be rigorously equivalent to one another. On the other hand, an old interest in the zitterbewegung (ZB) of the Dirac electron has recently been rekindled by the investigations on spintronics and graphene, etc. In this letter, we show that, if particles emitted by black holes are electrons or positrons, one can also regard the Hawking radiation as a ZB process., Comment: 8 pages, 2 figures. Haitang Yang demands to take him away from the author list

In term of the volume-integrated Poynting vector, we present a quantum field-theory investigation on the zitterbewegung (ZB) of photons, and show that this ZB occurs only in the presence of virtual longitudinal and scalar photons. To present a heuristic explanation for such ZB, by assuming that the space time is sufficiently close to the flat Minkowski space, we show that the gravitational interaction can result in the ZB of photons., Comment: 9 pages, no figure, to be published in Chinese Physics B

Many theoretical and experimental investigations have presented a conclusion that evanescent electromagnetic modes can superluminally propagate. However, in this paper, we show that the average energy velocity of evanescent modes inside a cut-off waveguide is always less than or equal to the velocity of light in vacuum, while the instantaneous energy velocity can be superluminal, which does not violate causality according to quantum field theory: the fact that a particle can propagate over a space-like interval does preserve causality provided that here a measurement performed at one point cannot affect another measurement at a point separated from the first with a space-like interval., Comment: 12 pages, 1 figure, to be published in Physical Review A

We present a scheme for asymmetric quantum information splitting, where a sender distributes asymmetrically a qubit to distant agents in a network. The asymmetric distribution leads to that the agents have different powers to reconstruct the sender's qubit. In other words, the authorities of the agents for getting the quantum secret are hierarchized. The scheme does not need the agents to get together and make nonlocal operations. Our scheme can also be modified to implement controlled teleportation against uncooperation of part of supervisors., Comment: Introduction and Conclusion parts are improved

In terms of a photon wave function corresponding to the (1, 0)+(0, 1) representation of the Lorentz group, the radiation and Coulomb fields within a source-free region can be described unitedly by a Lorentz-covariant Dirac-like equation. In our formalism, the relation between the positive- and negative-energy solutions of the Dirac-like equation corresponds to the duality between the electric and magnetic fields, rather than to the usual particle-antiparticle symmetry. The zitterbewegung (ZB) of photons is studied via the momentum vector of the electromagnetic field, which shows that only in the presence of virtual longitudinal and scalar photons, the ZB motion of photons can occur, and its vector property is described by the polarization vectors of the electromagnetic field., Comment: 26 pages, no figure, to be published in Physical Review A

The validity of the work by Lamata et al [Phys. Rev. Lett. 98, 253005 (2007)] can be further shown by quantum field theory considerations., Comment: 5 pages, no figure, to be published in Physical Review A

Contrary to mechanical waves, the two-slit interference experiment of single photons shows that the behavior of classical electromagnetic waves corresponds to the quantum mechanical one of single photons, which is also different from the quantum-field-theory behavior such as the creations and annihilations of photons, the vacuum fluctuations, etc. Owing to a purely quantum effect, quantum tunneling particles including tunneling photons (evanescent modes) can propagate over a spacelike interval without destroying causality. With this picture we conclude that the superluminality of evanescent modes is a quantum mechanical rather than a classical phenomenon., Comment: Also as a Reply to the Comment by H. G. Winful [Phys. Rev. A 76, 057803 (2007)], to be published in Annalen der Physik

Via the proper-time eigenstates (event states) instead of the proper-mass eigenstates (particle states), free-motion time-of-arrival theory for massive spin-1/2 particles is developed at the level of quantum field theory. The approach is based on a position-momentum dual formalism. Within the framework of field quantization, the total time-of-arrival is the sum of the single event-of-arrival contributions, and contains zero-point quantum fluctuations because the clocks under consideration follow the laws of quantum mechanics., Comment: 15 pages, A detailed version with a appendix, to be published in Physics Letters B

In the paper, we show that there exists a close analogy between the behavior of de Broglie matter waves and that of electromagnetic waves inside a hollow waveguide, such that the guided photons can be treated as free massive particles subject to a relativistic quantum-mechanical equation. Inspired by the effective rest mass of guided photons and the zitterbewegung phenomenon of the Dirac electron, at variance with the well-known Higgs mechanism we present some different heuristic ideas on the origin of mass., Comment: 14 pages, no figure

Applying the fact that guided photons inside a waveguide can be treated as massive particles, one can study the superluminality of evanescent modes via showing that a massive particle can propagate over a spacelike interval, which corresponds to quantum tunneling effects. For this purpose, we treat the particle as a quantum reference frame, while attach an inertia observer to a classical reference frame, and then quantize the formulae for the Lorentz transformation between the quantum and classical reference frames, from which we obtain the conclusion that, owing to the Heisenberg's uncertainty relation, the particle can propagate over a spacelike interval., Comment: 15 pages, no figure

To investigate how quantum effects might modify special relativity, we will study a Lorentz transformation between classical and quantum reference frames and express it in terms of the four-dimensional (4D) momentum of the quantum reference frame. The transition from the classical expression of the Lorentz transformation to a quantum-mechanical one requires us to symmetrize the expression and replace all its dynamical variables with the corresponding operators, from which we can obtain the same conclusion as that from quantum field theory (given by Weinberg's formula): owing to the Heisenberg's uncertainty relation, a particle (as a quantum reference frame) can propagate over a spacelike interval., Comment: 14 pages, to be published in Physics Letters B

Relativistic free-motion time-of-arrival theory for massive spin-1/2 particles is systematically developed. Contrary to the nonrelativistic time-of-arrival operator studied thoroughly in previous literatures, the relativistic time-of-arrival operator possesses self-adjoint extensions because of the particle-antiparticle symmetry. The nonrelativistic limit of our theory is in agreement with the nonrelativistic time-of-arrival theory. By comparing the time-of-arrival operator with the Hamiltonian operator of a free Dirac particle, one can show a duality between position space and momentum space., Comment: 16 pages, no figure. Revised version

Though both theoretical and experimental investigations have revealed the superluminal behavior of evanescent electromagnetic waves, there are many disputes about the physical meaning and validity of such superluminal phenomenon, which is due to the fact that the traditional investigations are based on the theory of tunneling time, and concerned with the problem of what the group velocity of evanescent waves means. In this paper, by studying the quantum probability amplitude for photons to propagate over a spacelike interval along an undersized waveguide, we present theoretical evidence for such superluminality.

Traditionally, the zitterbewegung (ZB) of the Dirac electron has just been studied at the level of quantum mechanics. Seeing that the fact that an old interest in ZB has recently been rekindled by the investigations on spintronic, graphene, and superconducting systems, etc., in this paper we present a quantum-field-theory investigation on ZB and obtain the conclusion that, the ZB of an electron arises from the influence of virtual electron-positron pairs (or vacuum fluctuations) on the electron., Comment: 10 pages, no figure, to be published in Chinese Physics

A relativistic quantum-mechanical description of guided waves is given, based on which we present an alternative way to describe and interpret the propagation of electromagnetic wave packets through an undersized waveguide. In particular, we show that the superluminal phenomenon of evanescent modes is actually a known conclusion in quantum field theory, and it preserves a quantum-mechanical causality., Comment: 24 pages, Revised version based on PRA75,013813(2007)

A field-theoretical space-time position operator can be properly introduced for the Dirac field, it plays the role of a generalized Noether charge associated with a local symmetry, and its second-quantized form shows that quantum fields possess zero-point time, which implies that a zero-point fluctuation of energy must be accompanied with a zero-point fluctuation of time, and then in agreement with the time-energy uncertainty principle. In practice, some possible physical effects owing to zero-point time remain to be found., Comment: This paper has been withdrawn by the author due to a crucial error in this paper

Time operator can be introduced by three different approaches: by pertaining it to dynamical variables; by quantizing the classical expression of time; taken as the restriction of energy shift generator to the Hilbert space of a physical system., Comment: 17 pages, accepted to be published in Annals of Physics

Relativistic free-motion time-of-arrival theory for massive spin-1/2 particles is systematically developed. Contrary to the nonrelativistic time-of-arrival operator studied thoroughly in previous literatures, the relativistic time-of-arrival operator possesses self-adjoint extensions because of the particle-antiparticle symmetry. The nonrelativistic limit of our theory is in agreement with the nonrelativistic time-of-arrival theory., Comment: 16 pages, no figure, revised version

Traditionally, the theory related to the spatial angular momentum has been studied completely, while the investigation in the generator of Lorentz boost is inadequate. In this paper we show that the generator of Lorentz boost has a nontrivial physical significance, it endows a charged system with an electric moment, and has an important significance for the electrical manipulations of electron spin in spintronics. An alternative treatment and interpretation for the traditional Darwin term and spin-orbit coupling are given., Comment: 9 pages

In near-field optics and optical tunneling theory, photon wave mechanics, i.e., the first quantized theory of the photon, allows us to address the spatial field localization problem in a flexible manner which links smoothly to classical electromagnetics. In this letter, photon wave mechanics is developed in a rigorous and unified way, based on which field quantization is obtained in a new way., Comment: Detailed version by adding the last paragraph as well as Appendix A and B

The usual quantum mechanics describes the mass eigenstates. To describe the proper-time eigenstates, a duality theory of the usual quantum mechanics was developed. The time interval is treated as an operator on an equal footing with the space interval, and the quantization of the space-time intervals between events is obtained. As a result, one can show that there exists a zero-point time interval., Comment: 15 pages, No figure

In this article, we show that in the level of quantum mechanics, a photon position operator with commuting components can be obtained in a more natural way; in the level of quantum field theory, the photon position operator corresponds to the center of the photon number. It is most interesting for us to show that, a photon inside a waveguide can be localized in the same sense that a massive particle can be localized in free space, and just as that it is impossible to localize a massive particle with a greater precision than its Compton wavelength, one can also arrival at a similar conclusion: it is impossible to localize a photon inside a waveguide with a greater precision than its equivalent Compton wavelength, which owing to evanescent-wave or photon-tunneling phenomena., Comment: 22 pages, 1 figure

In contrast to wave functions in nonrelativistic quantum mechanics interpreted as probability amplitudes, wave functions in relativistic quantum mechanics have generalized meanings such as charge-density amplitudes, energy-density amplitudes as well as particle-number density amplitudes, etc. Applying electromagnetic field intensities we construct a photon wave function, it corresponds to the (1,0)+(0,1) spinor representation of the electromagnetic field, and can be interpreted as the energy-density amplitude of photons outside a source. In terms of photon wave functions we develop photon wave mechanics, which provides us with a new quantum-mechanical description for photons outside a source., Comment: Revised version based on Chin. Phys. Lett. 24, 418 (2007)