arXiv subjects
Publications and source records attributed to Bing He.
In this paper, applying the spinor representation of the electromagnetic field, we present a quantum-mechanical description of waveguides. As an example of application, a potential qubit generated via photon tunneling is discussed.
The general transformation of the product of coherent states $\prod_{i=1}^N|α_i>$ to the output state $\prod_{i=1}^M|β_i>$ ($N=M$ or $N\neq M$), which is realizable with linear optical circuit, is characterized with a linear map from the vector $(α^{\ast}_1,...,α^{\ast}_N)$ to $(β^{\ast}_1,...,β^{\ast}_M)$. A correspondence between the transformations of a product of coherent states and those of a single photon state is established with such linear maps. It is convenient to apply this linear transformation method to design any linear optical scheme working with coherent states. The examples include message encoding and quantum database searching. The limitation of manipulating entangled coherent states with linear optics is also discussed.
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.
We propose an experimental setup that is capable of unambiguously discriminating any pair of linearly independent single photon polarization qubits, about which we don't have any knowledge except that an extra pair of these unknown states are provided as the reference. This setup, which is constructed with optical CNOT gates, weak cross Kerr non-linearities, Bell state analysers and other linear optical elements, transforms the unknown triple photon input states to the corresponding single photon states to be deterministically processed by linear optics circuit. The optimal discrimination of the unknown states is achieved by this setup.
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.
We show that a general linear transformation from one single photon qudit to another, the dimension of which can be either equal or unequal to that of the first one, can be implemented by linear optics. As an application of the scheme we elaborate a method to deterministically realize any finite-element Positive Operator Value Measure (POVM) on single photon signals, which is also generalizable to any quantum system in principle.
The discrimination of any pair of unknown quantum states is performed by devices processing three parts of inputs: copies of the pair of unknown states we want to discriminate are respectively stored in two program systems and copies of data, which is guaranteed to be one of the unknown states, in a third system. We study the efficiency of such programmable devices with the inputs prepared with $n$ and $m$ copies of unknown qubits used as programs and data, respectively. By finding a symmetry in the average inputs, we apply the Jordan basis method to derive their optimal unambiguous discrimination and the minimum-error discrimination schemes. The dependence of the optimal solutions on the a prior probabilities of the mean input states is also demonstrated.
We present a general scheme to realize the POVMs for the unambiguous discrimination of quantum states. For any set of pure states it enables us to set up a feasible linear optical circuit to perform their optimal discrimination, if they are prepared as single-photon states. An example of unknown states discrimination is discussed as the illustration of the general scheme.
The Euclidean-time hadronic current correlation functions, $G_P(τ, T)$ and $G_V(τ, T)$, of pseudoscalar and vector currents have recently been calculated in lattice simulations of QCD and have been used to obtain the corresponding spectral functions. We have used the Nambu-Jona-Lasinio (NJL) model to calculate such spectral functions, as well as the Euclidean-time correlators, and have made a comparison to the lattice results for the correlators. We find evidence for the type of temperature dependence of the NJL coupling parameters that we have used in previous studies of the mesonic confinement-deconfinement transition. We also see that the spectral functions obtained when using the maximum-entropy-method (MEM) and the lattice data differ from the spectral functions that we calculate in our chiral model. However, our results for the Euclidean-time correlators are in general agreement with the lattice results, with better agreement when our temperature-dependent coupling parameters are used than when temperature-independent parameters are used for the NJL model. We also discuss some additional evidence for the utility of temperature-dependent coupling parameters for the NJL model. For example, if the constituent quark mass at T=0 is $352 {MeV}$ in the chiral limit, the transition temperature is $T_c=208 {MeV}$ for the NJL model with a standard momentum cutoff parameter. (If a Gaussian momentum cutoff is used, we find $T_c=225 {MeV}$ in the chiral limit, with $m=368 {MeV}$ at T=0.) The introduction of a weak temperature dependence for the coupling constant will move the value of $T_c$ into the range 150-170 MeV, which is more in accord with what is found in lattice simulations of QCD with dynamical quarks.
We make use of the Nambu-Jona-Lasinio (NJL) formalism and real-time finite-temperature field theory to calculate hadronic current correlation functions in the deconfined phase of quantum chromodynamics (QCD). We consider both pseudoscalar and vector currents and compare our results with those obtained in lattice simulations of QCD. Our results are similar to those obtained in the lattice simulations for $T=1.5 T_c$, where $T_c$ is the temperature of the confinement-deconfinement transition. For $T=3.0 T_c$ our results do not exhibit the resonances obtained from the lattice simulations. However, the errors presented for the lattice results are large and it is possible that our results at $T=3.0 T_c$ are consistent with the lattice results when these errors are taken into account. Since the method used in the lattice analysis to obtain the spectral functions requires assumptions about the likelihood of a particular form for the spectral function, we believe our calculations will be useful to researchers who wish to calculate hadronic current correlation functions at finite temperature using lattice-based methods. Our model makes use of temperature-dependent coupling constants for the NJL model. We present an argument that such temperature dependence is necessary, if the results of the model are to be consistent with what is known concerning QCD thermodynamics.
Recently there has been a great deal of interest in studying the properties of dense quark matter, with particular reference to diquark condensates and color superconductivity. In the present work we report calculations made for the excitations of quark matter for relatively low densities of the deconfined phase and in the absence of meson or diquark condensation. Here, we are interested in elucidating the role of "Pauli blocking", as such blocking affects the calculation vector, scalar and pseudoscalar $q\bar q$ excitations. As a byproduct of our analysis, we extend our calculations to higher densities and explore some consequences of the use of density-dependent coupling parameters for the Nambu--Jona-Lasinio model. (Such density-dependent parameters have been used in some of our previous work.) For our analysis made at large values of the matter density, we assume that at about 13 times nuclear matter density quark matter has only minimal nonperturbative interactions. At that high density we compare the result for hadronic current correlation functions calculated with density-dependent and density-independent NJL coupling constants. We find evidence for the use of density-dependent parameters, since the results with the density-independent constants do not go over to the perturbative description which we assume to be correct for $ρ\simeq 6ρ_c$, where $ρ_c$ is the matter density for the finite-density confinement-deconfinement transition. The use of density-dependent coupling constants in the study of diquark condensates and color superconductivity has not been explored as yet, and is a topic requiring further investigation, particularly given the strong interest in the properties of dense quark matter and color superconductivity.
We report the results of calculations of pseudoscalar-isoscalar hadronic current correlators using the Nambu--Jona-Lasinio model and the real-time finite-temperature formalism. Results are presented for the temperatures range 1.2 $\leq T/T_c\leq$ 6.0, where $T_c$ is the temperature of the confinement-deconfinement transition, which we take to be $T_c=170$ MeV. Two important resonant features are seen in our calculations. In order to understand the origin of these resonances, we have performed relativistic random phase approximation (RPA)calculations of the temperature-dependent spectrum of the $η$ mesons for $T<T_c$. For the RPA calculations, use is made of a simple model in which we introduce temperature- dependent constituent quark masses calculated in a mean-field approximation and a temperature-dependent confining interaction whose form is motivated by recent studies made using lattice simulations of QCD with dynamical quarks. We also introduce temperature-dependent coupling constants in our generalized NJL model. Our motivation in the latter case is the simulation of the approach to a weakly interacting system at high temperatures. We present some evidence that supports our use of temperature-dependent coupling constants for the NJL model. We suggest that our results may be of interest to researchers who use lattice simulations of QCD to obtain temperature dependent spectral functions for various hadronic current correlation functions.
The Nambu--Jona-Lasinio (NJL) model has been extensively studied by many researchers. In previous work we have generalized the NJL model to include a covariant model of confinement. In the present work we consider further modification of the model so as to reproduce the type of Euclidean-space momentum- dependent quark mass values obtained in lattice simulations of QCD. This may be done by introducing a nonlocal interaction, while preserving the chiral symmetry of the Lagrangian. In other work on nonlocal models, by other researchers, the momentum dependence of the quark self-energy is directly related to the regularization scheme. In contrast, in our work, the regularization is independent of the nonlocality we introduce. It is of interest to note that the value of the condensate ratio, $<\bar{s}s>/<\bar{u}d>$, is about 1.7 when evaluated using chiral perturbation theory and is only about 1.1 in standard applications of the NJL model. We find that our nonlocal model can reproduce the larger value of the condensate ratio when reasonable values are used for the strength of the 't Hooft interaction. (In an earlier study of the $η$(547) and $η$'(958) mesons, we found that use of the larger value of the condensate ratio led to a very good fit to the mixing angles and decay constants of these mesons.) We also study the density dependence of both the quark condensate and the momentum-dependent quark mass values. Without the addition of new parameters, we reproduce the density dependence of the condensate given by a well-known model- independent expression valid for small baryon density.
We calculated the SU(2) gluon propagator in Landau gauge on an anisotropic coarse lattice with the improved action. The standard and the improved scheme are used to fix the gauge in this work. Even on the coarse lattice the lattice gluon propagator can be well described by a function of the continuous momentum. The effect of the improved gauge fixing scheme is found not to be apparent. Based on the Marenzoni's model, the mass scale and the anomalous dimension are extracted and can be reasonably extrapolated to the continuum limit with the values $α\sim 0.3$ and $M\sim 600MeV$. We also extract the physical anisotropy $ξ$ from the gluon propagator due to the explicit $ξ$ dependence of the gluon propagator.
The SU(2) gluonic correlation functions, glueball effective masses in the $J^{P}=0^{+}$, $2^{+}$ and $0^{-}$ channels were calculated from the lattice classical gauge configurations which were obtained by smoothing the thermal gauge configurations through the improved cooling method. The instanton-induced attractive force in the $0^{+}$ channel and the repulsive force in the $0^-$ channel are confirmed in the Monte Carlo simulation. There is evidence that the instanton vacuum contribution to the $0^+$ glueball mass is significant.
It is shown that the application of the non-Abelian Stokes theorem to the computation of the operators constructed with Wilson loop will lead to ambiguity, if the gauge field under consideration is a non-trivial one. This point is illustrated by the specific examples of the computation of a non-local operator.