Multiple bremsstrahlung in gauge theories at high energies: (III). Finite mass effects in collinear photon bremsstrahlung

We present a method for calculating the various spin amplitudes for QED processes in which an arbitrary number of photons is radiated in directions nearly parallel to the fermion directions. This is accomplished by introducing explicit polarization vectors for the photons and by working in the high energy limit, where finite mass effects are treated in leading order.     

Compact QED tree-level amplitudes from dressed BCFW recursion relations

We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and N²MHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial.     

Grassmann phase space methods for fermions. I. Mode theory

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggest the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum–atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics.     

Natural multiparticle entanglement in a Fermi gas

We investigate multipartite entanglement in a noninteracting fermion gas, as a function of fermion separation, starting from the many particle fermion density matrix. We prove that all multiparticle entanglement can be built only out of two-fermion entanglement. Although from the Pauli exclusion principle we would always expect entanglement to decrease with fermion distance, we surprisingly find the opposite effect for certain fermion configurations. The von Neumann entropy is found to be proportional to the volume for a large number of particles even when they are arbitrarily close to each other. We will illustrate our results using different configurations of two, three, and four fermions at zero temperature although all our results can be applied to any temperature and any number of particles.     

Direct imaging of spatially modulated superfluid phases in atomic fermion systems

It is proposed that the spatially modulated superfluid phase, or the Fulde-Ferrell-Larkin-Ovchinnikov state could be observed in resonant fermion atomic condensates which are realized recently. We examine optimal experimental setups to achieve it by solving the Bogoliubov-de Gennes equation for both idealized one-dimensional and realistic three-dimensional cases. The spontaneous modulation of this superfluid is shown to be directly imaged as the density profiles either by optical absorption or by Stern-Gerlach experiments.     

Bloch oscillations of path-entangled photons

We show that when photons in N-particle path-entangled |N,0)+|0,N) or N00N states undergo Bloch oscillations, they exhibit a periodic transition between spatially bunched and antibunched states. The period of the bunching-antibunching oscillation is N times faster than the period of the oscillation of the photon density, manifesting the unique coherence properties of N00N states. The transition occurs even when the photons are well separated in space.     

Magnetization and dynamically induced finite densities in three-dimensional Chern-Simons QED

In (2 + 1)-dimensional QED with a Chem-Simons term, we show that spontaneous magnetization occurs in the context of finite density vacua, which are the lowest Landau levels fully or half occupied by fermions. Charge condensation is shown to appear so as to complement the fermion anti-fermion condensate, which breaks the flavor U(2N) symmetry and causes fermion mass generation. The solutions to the Schwinger-Dyson gap equation show that the fermion self-energy contributes to the induction of a finite fermion density and/or fermion mass. The magnetization can be supported by charge condensation for theories with the Chem-Simons coefficient κ = Ne²2gp, and κ = Ne²/4π, under the Gauss law constraint. For κ = Ne²/4π, both the magnetic field and the fermion mass are simultaneously generated in the half-filled ground state, which breaks the U(2N) symmetry as well as the Lorentz symmetry.     

Photon Decays in the Radiation-Dominated Universe: Scalar Electrodynamics

The effect of the creation of an arbitrary number of massive pairs by a photon in the spatially flat model of the radiation-dominated Universe is considered. The process added-up probability is calculated within the framework of scalar quantum electrodynamics conformally related to the metric of a curved spacetime. The rate of photon decay in the radiation-dominated universe as well as the mean number of the created particles have been found. Comparison of the rate of the pair creation in the photon decays with the rate of the pair creation in the photon-photon collisions which take place in the Minkowski spacetime has been carried out. The estimates having been made show the number density of the particles created in the processes of the photon decays in the radiation-dominated Universe to be by a factor of 10³⁰ higher than the number density of the particles created from the vacuum of the free scalar field by the gravitational background.     

Relaxation of fermionic excitations in a strongly attractive Fermi gas in an optical lattice

We theoretically study the relaxation of high energy single particle excitations into molecules in a system of attractive fermions in an optical lattice, both in the superfluid and the normal phase. In a system characterized by an interaction scale U and a tunneling rate t, we show that the relaxation rate scales as ～Ctexp[-αU(2)/t(2)ln(U/t)] in the large U/t limit. We obtain explicit expressions for the temperature and density dependent exponent α, both in the low temperature superfluid phase and the high temperature phase with pairing but no coherence between the molecules. We find that the relaxation rate decreases both with temperature and deviation of the fermion density from half filling. We show that quasiparticle and phase degrees of freedom are effectively decoupled within experimental time scales allowing for observation of ordered states even at high total energy of the system.     

The Fermi-sea-like limit of the composite fermion wave function

The experimentally observed filling factors of the fractional quantum Hall effect can be described in terms of the composite fermion wave function of the Jastrow-Slater form [0pt] fully projected into the lowest Landau level. The Slater determinant of the above composite fermion wave function represents the filled Landau levels of composite fermions evaluated at the corresponding reduced magnetic field. For a system of fermions studied in the thermodynamic limit, we prove that in the even-denominator-filled state limit (when the number of filled Landau levels of composite fermions becomes infinite), the above composite fermion wave function exactly transforms into the Rezayi-Read Fermi-sea-like wave function [0pt] constructed by attaching 2m flux quanta to the Slater determinant of two-dimensional free fermions at the density corresponding to that filling. We study the composite fermion wave function and its evolution into the Fermi-sea-like wave function for a range of filling factors very close to the even-denominator-filled state. Received 19 March 1999     

温度对光学微腔光子激子系统玻色凝聚的影响

建立了光学微腔中光子激子系统的物理模型,确定了光学微腔宽度为常数和可变这两种情况下玻色凝聚时化学势的变化范围和粒子数密度随温度和位置的变化规律.以半导体GaAs光学微腔为例,探讨了温度对玻色凝聚的影响.研究表明:系统出现玻色凝聚时激子化学势的变化范围与材料介电函数、微腔宽度有关,而光子和激子的粒子数密度及总粒子数还与温度有关.玻色凝聚温度理论值与实验值接近.刚出现玻色凝聚时,光子和激子的粒子数密度几乎相等,且局限在r=0的附近;随着温度的降低,光子和激子的粒子数密度都增加,且存在的范围也不断扩大;不论光学微腔宽度是否可变,光子和激子的粒子数密度以及总粒子数都随温度的降低而增大,光子数总是多于激子数.     

Fermion bound states in geometrically deformed backgrounds

This work deals with the behavior of fermions in the background of kinklike structures in the twodimensional spacetime. The kinklike structures appear from bosonic scalar field models that engender distinct profiles and interact with the fermion fields via the standard Yukawa coupling. We first consider two models that engender parity symmetry, one leading to the exclusion of fermion bound states, and the other to the inclusion of bound states, when the parameter that controls the bosonic structure varies from zero to unity. We then investigate a third model where the kinklike solution explicitly breaks parity symmetry, leading to fermion bound states that are spatially asymmetric.     

Consequences of gravity-induced couplings in theories with many particle species

In theories with many copies of the Standard Model virtual black hole exchange may produce effective higher-dimensional operators that can be treated below the cutoff scale as fundamental vertices of interspecies non-gravitational interaction. We consider the vertex that couples fermions of one species through magnetic moment to photons of other species, and study the quantum corrections it generates. In particular, we find kinetic mixing between photons of different species produced via fermion loops. Diagonalization of gauge kinetic terms then renders the fermions millicharged under other species' electromagnetism. We explore some phenomenological consequences of such effects by considering possible observable signatures in collider experiments and constraining the interaction strength. The derived bounds are in agreement with non-democratic nature of micro black hole coupling.     

On the difference in creation of particles with spin 0 and12in isotropic cosmologies

The density of boson and fermion pairs, created near the singularity in isotropic homogeneous cosmological models is calculated. The rate of creation of fermions is found to be considerably higher than that of bosons.     

Classical Behavior of the Dirac Bispinor

It is usually supposed that the Dirac and radiation equations predict that the phase of a fermion will rotate through half the angle through which the fermion is rotated, which means, via the measured dynamical and geometrical phase factors, that the fermion must have a half-integral spin. We demonstrate that this is not the case and that the identical relativistic quantum mechanics can also be derived with the phase of the fermion rotating through the same angle as does the fermion itself. Under spatial rotation and Lorentz transformation the bispinor transforms as a four-vector like the potential and Dirac current. Previous attempts to provide this form of transformational behavior have foundered because a satisfactory current could not be derived.⁽¹⁴⁾     

From single- to multiple-pPhoton decoherence in an atom interferometer

We measure the decoherence of a spatially separated atomic superposition due to spontaneous photon scattering. We observe a qualitative change in decoherence versus separation as the number of scattered photons increases, and verify quantitatively the decoherence rate constant in the many-photon limit. Our results illustrate an evolution of decoherence consistent with general models developed for a broad class of decoherence phenomena.     

Quantum entanglement of a large number of photons

A bipartite multiphoton entangled state is created through stimulated parametric down-conversion of strong laser pulses in a nonlinear crystal. It is shown how detectors that do not resolve the photon number can be used to analyze such multiphoton states. Entanglement of up to 12 photons is detected using both the positivity of the partially-transposed density matrix and a newly derived criteria. Furthermore, evidence is provided for entanglement of up to 100 photons. The multiparticle quantum state is such that even in the case of an overall photon collection and detection efficiency as low as a few percent, entanglement remains and can be detected.     

Stability of superflow for ultracold fermions in optical lattices

We investigate the stability of superflow of paired fermions in an optical lattice. We show that there are two distinct dynamical instabilities which limit the superflow in this system. One dynamical instability occurs when the superfluid stiffness becomes negative; this evolves, with increasing pairing interaction, from the fermion pair breaking instability to the well-known dynamical instability of lattice bosons. The second, more interesting, dynamical instability is marked by the emergence of a transient atom density wave. Both dynamical instabilities can be experimentally accessed by tuning the pairing interaction and the fermion density.     

On the Number of Photons in a Classical Electromagnetic Field

Relations determining the number of photons in an electromagnetic field are considered from the point of view of a classical electromagnetic field. A relativistically invariant expression is obtained for the number of emitted photons in terms of charges and currents producing the electromagnetic field. Examples are considered for calculating the numbers of photons in the electromagnetic field for the case of the electric dipole radiation field, as well as the field of a finite and spatially restricted electromagnetic pulse.     

Derivation of the transverse force on a moving vortex in a superfluid

We describe an exact derivation of the total nondissipative transverse force acting on a quantized vortex moving in a uniform background. The derivation is valid for neutral boson or fermion superfluids, provided the order parameter is a complex scalar quantity. The force is determined by the one-particle density matrix far away from the vortex core, and is found to be the Magnus force proportional to the superfluid density.