真空场注入三态叠加MFSS光场广义电场的等幂偶次Y压缩

对真空场注入三态叠加MFSS(多模泛函叠加态)光场|ψ_0~(3)〉q广义电场分量的等幂次偶次振幅压缩特性进行了详细研究,分析了光场经典强度、经典振幅和经典相位的任意空间分布特征、以及真空场注入对该光场的广义电场分量的等幂偶次Y压缩效应其压缩幅度和压缩量的影响。结果发现:导致态|ψ_0~(3)〉q的广义电场分量存在等幂偶次2m次方Y压缩效应的根本原因在于模间的量子干涉效应、态间的量子干涉效应以及模间和态间的量子纠缠效应;真空场注入可使该光场广义电场分量的2m次方Y压缩效应增强、压缩幅度增大、压缩程度加深。     

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass μ≠0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy–momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g_μ,νρ with ρ>0, thus providing a concrete quantum field theoretic model of the cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p0.     

Symmetry Breaking for Matter Coupled to Linearized Supergravity from the Perspective of the Current Supermultiplet

We consider a generic supersymmetric matter theory coupled to linearized supergravity, and analyze scenarios for spontaneous symmetry breaking in terms of vacuum expectation values of components of the current supermultiplet. When the vacuum expectation of the energy momentum tensor is zero, but the scalar current or pseudoscalar current gets an expectation, evaluation of the gravitino self energy using the supersymmetry current algebra shows that there is an induced gravitino mass term. The structure of this term generalizes the supergravity action with cosmological constant to theories with CP violation. When the vacuum expectation of the energy momentum tensor is nonzero, supersymmetry is broken; requiring cancellation of the cosmological constant gives the corresponding generalized gravitino mass formula.     

Analysis of a teleportation scheme involving cavity field states in a linear superposition of Fock states

We analyse a teleportation scheme of cavity field states. The experimental sketch discussed makes use of cavity quantum electrodynamics involving the interaction of Rydberg atoms with superconducting (micromaser) cavities as well as with classical microwave (Ramsey) cavities. In our scheme the Ramsey cavities and the atoms play the role of auxiliary systems used to teleport a field state, which is formed by a linear superposition of vacuum |∅〉 and the one-photon state |1〉, from a micromaser cavity to another.     

Calculation of baryon masses in quantum chromodynamics

The polarization operator of quark currents with baryon quantum numbers is considered in quantum chromodynamics. The non-zero mean vacuum values of the field operator products are taken into account. The sum rules are obtained assuming that in the virtuality region ～1 GeV, among the mean vacuum values violating the chiral invariance, the most important is $\text{〈0|}\text{ψ}\text{ψ|0〉}$. Saturating these sum rules by the lowest baryonic states one is able to calculate the masses of the isobar Δ and nucleon N, M_Δ = 1.4 GeV, M_N = 1 GeV, up to 15% through the known value $\text{〈0|}\text{ψ}\text{ψ|0〉}$. The mass splitting in the baryonic decuplet $\text{M}{}_{\mathrm{\Sigma 1}}\text{?M}{}_{\mathrm{\Delta }}\text{= 125}\text{MeV}$ is calculated in first order in the current strange quark mass m_s = 150 MeV. Certain results for other baryonic resonances have also been obtained.     

Higgs characterisation at NLO in QCD: CP properties of the top-quark Yukawa interaction

We evaluate the Wightman function, the mean field squared and the vacuum expectation value of the energy–momentum tensor for a scalar field with the Robin boundary condition on a spherical shell in the background of a constant negative curvature space. For the coefficient in the boundary condition there is a critical value above which the scalar vacuum becomes unstable. In both the interior and the exterior regions, the vacuum expectation values are decomposed into the boundary-free and sphere-induced contributions. For the latter, rapidly convergent integral representations are provided. In the region inside the sphere, the eigenvalues are expressed in terms of the zeros of the combination of the associated Legendre function and its derivative and the decomposition is achieved by making use of the Abel–Plana type summation formula for the series over these zeros. The sphere-induced contribution to the vacuum expectation value of the field squared is negative for the Dirichlet boundary condition and positive for the Neumann one. At distances from the sphere larger than the curvature scale of the background space the suppression of the vacuum fluctuations in the gravitational field corresponding to the negative curvature space is stronger compared with the case of the Minkowskian bulk. In particular, the decay of the vacuum expectation values with the distance is exponential for both massive and massless fields. The corresponding results are generalized for spaces with spherical bubbles and for cosmological models with negative curvature spaces.     

Stability of Quantum Systems at Three Scales: Passivity, Quantum Weak Energy Inequalities and the Microlocal Spectrum Condition

Quantum weak energy inequalities have recently been extensively discussed as a condition on the dynamical stability of quantum field states, particularly on curved spacetimes. We formulate the notion of a quantum weak energy inequality for general dynamical systems on static background spacetimes and establish a connection between quantum weak energy inequalities and thermodynamics. Namely, for such a dynamical system, we show that the existence of a class of states satisfying a quantum weak inequality implies that passive states (e.g., mixtures of ground- and thermal equilibrium states) exist for the time-evolution of the system and, therefore, that the second law of thermodynamics holds. As a model system, we consider the free scalar quantum field on a static spacetime. Although the Weyl algebra does not satisfy our general assumptions, our abstract results do apply to a related algebra which we construct, following a general method which we carefully describe, in Hilbert-space representations induced by quasifree Hadamard states. We discuss the problem of reconstructing states on the Weyl algebra from states on the new algebra and give conditions under which this may be accomplished. Previous results for linear quantum fields show that, on one hand, quantum weak energy inequalities follow from the Hadamard condition (or microlocal spectrum condition) imposed on the states, and on the other hand, that the existence of passive states implies that there is a class of states fulfilling the microlocal spectrum condition. Thus, the results of this paper indicate that these three conditions of dynamical stability are essentially equivalent. This observation is significant because the three conditions become effective at different length scales: The microlocal spectrum condition constrains the short-distance behaviour of quantum states (microscopic stability), quantum weak energy inequalities impose conditions at finite distance (mesoscopic stability), and the existence of passive states is a statement on the global thermodynamic stability of the system (macroscopic stability).Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany. verch@mis.mpg.de     

Quantized fields propagating in plane-wave spacetimes

This paper contains an account of the interaction of a quantized massive scalar field with the classicalc number gravitational field of a plane sandwich wave of arbitrary profile and polarization. It is shown that the time varying gravitational field of the wave produces no particles and the Feynman propagator for the problem is calculated exactly. This is used to show that any reasonable regularization of the vacuum expectation value of the energy momentum tensor of the field must vanish. This means that a gravitational wave far from its source will propagate without hindrance by quantum effects.     

Unconventional Geometric Phase-Shift Gates Based on Superconducting Quantum Interference Devices Coupled to a Single-Mode Cavity

We present a scheme to realize geometric phase-shift gate for two superconducting quantum interference device （SQUID） qubits coupled to a single-mode microwave field. The geometric phase-shift gate operation is performed in two lower flux states, and the excited state [2〉 would not participate in the procedure. The SQUIDs undergo no transitions during the gate operation. Thus, the docoherence due to energy spontaneous emission based on the levels of SQUIDs are suppressed. The gate is insensitive to the cavity decay throughout the operation since the cavity mode is displaced along a circle in the phase space, acquiring a phase conditional upon the two lower flux states of the SQUID qubits, and the cavity mode is still in the original vacuum state. Based on the SQUID qubits interacting with the cavity mode, our proposed approach may open promising prospects for quantum iogic in SQUID-system.     

Quantum field theory in curved spacetime,the operator product expansion,and dark energy

To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated in a local and covariant manner in terms of locally measurable field observables. Since a generic curved spacetime does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a “vacuum state” and “particles”. We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients—and, thus, the quantum field theory. By contrast, ground/vacuum states—in spacetimes, such as Minkowski spacetime, where they may be defined—cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory. Fourth Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Complete entanglement transfer between light and qubits

Using the two-mode two-photon Jaynes-Cummings model, entanglement transfer between atoms and field is studied. It is found that when the field is in state constructed from the two-mode photon number states |00〉,|11〉 or the two-mode squeezed vacuum states, full entanglement exchange can be attained no matter the atoms are initially in pure or mixed states. These investigations show that CV entangled states can act as perfectly as the entangled number states in entangling initially separable atoms. The two-mode two-photon atom-field interaction also provides a simple way for the quantum teleportation of atomic or field states.     

Surface vacuum energy and stresses for a brane in de Sitter spacetime

Vacuum expectation values of the surface energy–momentum tensor is investigated for a massless scalar field obeying mixed boundary condition on a brane in de Sitter bulk. To generate the corresponding vacuum surface densities we use the conformal relation between de Sitter and Rindler spacetimes.     

Vacuum fluctuations and topological Casimir effect in Friedmann–Robertson–Walker cosmologies with compact dimensions

We investigate the Wightman function, the vacuum expectation values of the field squared and the energy–momentum tensor for a massless scalar field with general curvature coupling parameter in spatially flat Friedmann–Robertson–Walker universes with an arbitrary number of toroidally compactified dimensions. The topological parts in the expectation values are explicitly extracted and in this way the renormalization is reduced to that for the model with trivial topology. In the limit when the comoving lengths of the compact dimensions are very short compared to the Hubble length, the topological parts coincide with those for a conformal coupling and they are related to the corresponding quantities in the flat spacetime by standard conformal transformation. This limit corresponds to the adiabatic approximation. In the opposite limit of large comoving lengths of the compact dimensions, in dependence of the curvature coupling parameter, two regimes are realized with monotonic or oscillatory behavior of the vacuum expectation values. In the monotonic regime and for non-conformally and non-minimally coupled fields the vacuum stresses are isotropic and the equation of state for the topological parts in the energy density and pressures is of barotropic type. For conformal and minimal couplings the leading terms in the corresponding asymptotic expansions vanish and the vacuum stresses, in general, are anisotropic, though the equation of state remains of barotropic type. In the oscillatory regime, the amplitude of the oscillations for the topological part in the expectation value of the field squared can be either decreasing or increasing with time, whereas for the energy–momentum tensor the oscillations are damping. The limits of validity of the adiabatic approximation are discussed.     

三态叠加多模泛函叠加态光场的高次压缩--广义磁场分量等幂次振幅压缩效应研究

构造了由多模真空态|{0j}>q与两个空间强度分布特征不同的多模复共轭泛函相干态|{f(a)f*(x,y,z)}>q和|{f(b)f*(x, y,z)}>q的线性叠加组成的三态叠加多模泛函叠加态光场|ψ(3)f>q,利用多模压缩态理论,研究了态|ψ(3)f>q中广义磁场分量的等幂次高次振幅(Y)压缩特性.结果表明:在一定的条件下,态|ψ(3)f>q的广义磁场分量可呈现出周期性变化的等幂次高次Y压缩效应; 光场经典强度和经典振幅的任意非对称空间分布特征和光场经典初始相位的任意空间分布特征等对其压缩程度将产生直接的影响.     

Probabilistically perfect quantum cloning and unambiguous state discrimination

We consider the N → M probabilistically perfect quantum cloning machine that perfectly produces M faithful copies from N identical input states, where the input states are selected, with prior probabilities η₁and η₂ = 1 − η₁, from a given set of the two linearly independent states |ψ₁〉^⊗ N = (cosθ|0〉 + sinθ|1〉)^⊗ N and |ψ₂〉^⊗ N = (sinθ|0〉 + cosθ|1〉)^⊗ N (θ∈(0,π/2)). We derive the optimal distribution of the success probabilities. When M approaches infinite, the probabilistically perfect quantum cloning can be regarded as a kind of the unambiguous state discrimination, and theoretically provides the upper bound of the unambiguous state discrimination. By using the optimal distribution of the success probabilities of the optimal asymmetric 1 → M probabilistically perfect quantum cloning, we can derive the maximum average success probability of the unambiguous discrimination of two nonorthogonal quantum states |ψ₁〉and|ψ₂〉. As an example, we give the explicit transformation of the optimal symmetric 1 → M probabilistically perfect quantum cloning to copy the two input states |ψ₁〉 and |ψ₂〉.     

Can wormholes exist?

Renormalized vacuum expectation values of electromagnetic stress-energy tensor are calculated in the background spherically-symmetrical metric of the wormhole topology. The covariant geodesic point separation method of regularization is used. Violation of the weak energy condition at the throat of the wormhole takes place for a geometry sufficiently close to that of an infinitely long wormhole of constant radius irrespective of the detailed from of metric. This is an argument in favour of the possibility of the existence of a self-consistent wormhole in empty space maintained by vacuum field fluctuations in the wormhole's background.     

一种新型的两态叠加MSCS光场的广义非线性等阶N次方H压缩

本文利用新近建立的多模压缩态理论,详细研究了一种新型的两态叠加多模薛定谔猫态(即MSCS)光场|ψ⁽²⁾〉_q的广义非线性等阶N次方H压缩效应.结果发现:1态|ψ⁽²⁾〉_q是一种典型的非经典光场;当压缩阶数N与腔模总数q这两者之积为偶数,即qN=2p,并且p为奇数亦即p=2m’+1(m’=0,1,2,3,…,…)时,如果各模的初始相位和∑_j=1^qψ_j态间的初始相位差(θ_pq^(I)-θ_nq^(R))、各多模相干态光场的总的平均光子数∑_j=1^qR_j²等满足一定的量子化条件(或者当∑_j=1^qR_j²在总的平均光子数∑_j=1^qR_j²的一系列压缩区内连续取值时),态|ψ(2)〉q总可呈现出周期性变化的、任意阶的广义非线性等阶N次方H压缩效应.2态|ψ⁽²⁾〉_q的第一及第二两个正交分量,其压缩结果(亦即压缩程度和压缩深度)完全相同,但压缩条件不同;两者的等阶N次方H压缩效应呈现出周期性的互补关系.3与文献16相比,本文所研究的态|ψ⁽²⁾〉_q的等阶N次方H压缩效应是比其等阶N次方Y压缩效应更高阶的广义非线性等阶高阶压缩效应.     

Vacuum quantum effect for curved boundaries in static Robertson–Walker space–time

The energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved boundaries in k=−1 static Robertson–Walker space–time is investigated. We assume that the scalar field satisfies the Dirichlet boundary condition on the boundaries. k=−1 Robertson–Walker space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy–momentum tensor for conformally invariant field in Robertson–Walker space from the corresponding Rindler counterpart by the conformal transformation.     

Low-energy relation for the trace of the energy–momentum tensor in QCD and the gluon condensate in a magnetic field

The nonperturbative QCD vacuum in a magnetic field has been studied. A low-energy relation for the trace of the energy–momentum tensor in the magnetic field has been obtained. It has been shown that the derivatives of the quark and gluon contributions to the trace of the energy–momentum tensor with respect to the magnetic field coincide with each other. The magnetic field dependence of the gluon condensate has been calculated in the limits of strong and weak fields.     

一种新型的两态叠加多模叠加态光场的广义非线性等阶N次方Y压缩

本文根据量子力学中的线性叠加原理,构造了由多模(即q模)相干态的相反态|{-Z_j}〉_q及多模虚相干态的相反态|{-iZ_j}〉_q这两者的线性叠加所组成的一种新型的两态叠加多模叠加态光场|ψ_msc⁽²⁾〉_q.利用新近建立的多模辐射场的广义非线性等阶高阶压缩理论,研究了态|ψ_msc⁽²⁾〉_q的广义非线性等阶N次方Y压缩特性.结果发现,1)当压缩阶数N=2P且P=2m(m=1,2,3,…,…)时,态|ψ_msc⁽²⁾〉_q恒处于N-Y最小测不准态;2)当N=2P且P=2m’+1(m’=0,1,2,…,…)时,如果各模的初始相位φ_j、态间的初始相位差与各单模相干态光场的平均光子数之和∑_j=1^qR_j²即[(θ_pq^(R)-θ_nq^(I))-∑_j=1^qR_j²]满足一定的量子化条件,态|ψ_msc⁽²⁾〉_q可呈现周期性变化的、任意阶的等阶N次方Y压缩效应;3)当N为奇数时,态|ψ_msc⁽²⁾〉_q在一定条件下恒处于N-Y测不准态;4)态|ψ_msc⁽²⁾〉_q与文献21中的态|ψ⁽²⁾〉_q出现部分压缩简并现象,从而更进一步表明压缩简并现象的存在是有某种客观内在联系的.