Curvature vs. Thickness in quantum waveguides

It is known that there is at least one bound state in a curved quantum waveguide provided it is sufficiently thin. In this paper we investigate the critical thickness of two-dimensional waveguides above which the discrete spectrum becomes void. We have found an expression for it in the case of a small bending angle. In the general case, its asymptotic behaviour with respect to the bending angle is shown to be governed by local smoothness properties of the boundary. Uniqueness of the critical thickness is also discussed.Dedicated to the memory of M. Gmitro.One of the authors (P.E.) is grateful for the hospitality extended to him at the University of Toulon and C.N.R.S. Marseille where the most part of this work was done. A partial support by Czechoslovak Grant Agency under Contract No. 14814 is acknowledged.     

量子引力的曲率两点真空相关

以平坦的Minkowski时空为背景，得到了任意坐标系和谐和坐标系中，n维GR引力和高导数引力的引力子自由传播子，求得了四种可能的曲率两点真空相关函数的首项.用微扰计算证明了曲率的两点真空相关函数在GR引力中为零，而在高导数引力中不为零.讨论了高导数引力与GR的引力子传播子、曲率相关函数的关系. 关键词： GR 高导数引力 引力子自由传播子 曲率真空相关函数 平移传播子     

Trapped modes in finite quantum waveguides

The eigenstates of an electron in an infinite quantum waveguide (e.g., a bent strip or a twisted tube) are often trapped or localized in a bounded region that prohibits the electron transmission through the waveguide at the corresponding energies. We revisit this statement for resonators with long but finite branches that we call ??finite waveguides??. Although the Laplace operator in bounded domains has no continuous spectrum and all eigenfunctions have finite L ₂ norm, the trapping of an eigenfunction can be understood as its exponential decay inside the branches. We describe a general variational formalism for detecting trapped modes in such resonators. For finite waveguides with general cylindrical branches, we obtain a sufficient condition which determines the minimal length of branches for getting a trapped eigenmode. Varying the branch lengths may switch certain eigenmodes from non-trapped to trapped or, equivalently, the waveguide state from conducting to insulating. These concepts are illustrated for several typical waveguides (L-shape, bent strip, crossing of two strips, etc.). We conclude that the well-established theory of trapping in infinite waveguides may be incomplete and require further development for applications to finite-size microscopic quantum devices.     

On quantum vs. classical probability

Quantum theory shares with classical probability theory many important properties. I show that this common core regards at least the following six areas, and I provide details on each of these: the logic of propositions, symmetry, probabilities, composition of systems, state preparation and reductionism. The essential distinction between classical and quantum theory, on the other hand, is shown to be joint decidability versus smoothness; for the latter in particular I supply ample explanation and motivation. Finally, I argue that beyond quantum theory there are no other generalisations of classical probability theory that are relevant to physics.     

Rashba electron transport in one-dimensional quantum waveguides

The properties of Rashba wave function in the planar one-dimensional waveguide are studied, and the following results are obtained. Due to the Rashba effect, the plane waves of electron with the energy E divide into two kinds of waves with the wave vectors k 1 =k 0 +k δ and k 2 =k 0 -k δ , where k δ is proportional to the Rashba coefficient, and their spin orientations are +π/2 (spin up) and -π/2 (spin down) with respect to the circuit, respectively. If there is gate or ferromagnetic contact in the circuit, the Rashba wave function becomes standing wave form exp(±ik δ l)sin[k 0 (l-L)], where L is the position coordinate of the gate or contact. Unlike the electron without considering the spin, the phase of the Rashba plane or standing wave function depends on the direction angle θ of the circuit. The travel velocity of the Rashba waves with the wave vector k 1 or k 2 are the same hk0/m * . The boundary conditions of the Rashba wave functions at the intersection of circuits are given from the continuity of wave functions and the conservation of current density. Using the boundary conditions of Rashba wave functions we study the transmission and reflection probabilities of Rashba electron moving in several structures, and find the interference effects of the two Rashba waves with different wave vectors caused by ferromagnetic contact or the gate. Lastly we derive the general theory of multiple branches structure. The theory can be used to design various spin polarized devices.     

Polariton propagation in coupled quantum wire waveguides

The propagation of the excitonic polariton along the directional coupler consisting of adjacent parallel GaAs quantum-wire waveguides is simulated by using a finite element method. It is found that the coupling length is as short as 2.5-4 μm, which is three orders of magnitude shorter than the conventional optical directional coupler made of bulk GaAs. Such short coupling length will make it possible to fabricate extremely small optoelectronic devices such as directional-coupler-type switches.     

Optical solitons in semiconductor quantum dot waveguides

A theory of self-induced transparency for a TM-mode propagating in a planar semiconductor waveguide sandwiched between two dielectric media is developed. A transition layer between the waveguide and one of the connected media is described using a model of a two-dimensional sheet of quantum dots. Explicit analytical expressions for the optical soliton in the presence of single-excitonic and biexcitonic transitions are obtained with realistic parameters which can be reached in current experiments.     

Fano resonances in stubbed quantum waveguides with impurities

We consider T–shaped, two–dimensional quantum waveguides containing attractive or repulsive impurities with a smooth, realistic shape, and study how the resonance behavior of the total conductance depends upon the strength of the defect potential and the geometry of the device. The resonance parameters are determined locating the relevant S–matrix poles in the Riemann energy surface. The total scattering operator is obtained from the S–matrices of the various constituent segments of the device through the –product composition rule. This allows for a numerically stable evaluation of the scattering matrix and of the resonance parameters.     

Interference of quantum states in electronic waveguides with impurities

Effects of interference between propagating and localized states in quasi-one-dimensional electronic waveguides containing finite-size attracting impurities (quantum dots) are investigated. The electron scattering matrix is calculated in the framework of the Feshbach theory [H. Feshbach, Ann. Phys. 5, 357 (1958); Ann. Phys. 19, 287 (1962)], when resonant states in closed channels are taken into account exactly, while non-resonant states are taken into account in perturbation theory. It is shown that finite-size attracting impurities may generate a series of asymmetric Fano resonances in the waveguide transmission. As a result of interference of electron states, the characteristics of resonances may oscillate upon a change in the impurity parameters. The conditions are determined under which the interference of an electron wave leads to a “collapse” and “swing” of Fano resonances.     

Multi-pass classical vs. quantum strategies in lossy phase estimation

The use of classical multiple-pass approach for phase estimation which mimics the behavior of the N00N states, is compared with quantum techniques. It is shown that in the presence of losses its performance is significantly worse than the one of the optimal quantum strategy.     

Quantum computer elements based on coupled quantum waveguides

Possible applications of two weakly coupled quantum waveguides for quantum computation are considered. The approach is based on the resonance phenomena in the system. Two different qubits interpretations are described. Some single-qubit and two-qubits operations are realized in the framework of these interpretations. The text was submitted by the authors in English.     

Vacuum energy: Quantum hydrodynamics vs. quantum gravity

We compare quantum hydrodynamics and quantum gravity. They share many common features. In particular, both have quadratic divergences, and both lead to the problem of the vacuum energy, which, in quantum gravity, transforms to the cosmological constant problem. We show that, in quantum liquids, the vacuum energy density is not determined by the quantum zero-point energy of the phonon modes. The energy density of the vacuum is much smaller and is determined by the classical macroscopic parameters of the liquid, including the radius of the liquid droplet. In the same manner, the cosmological constant is not determined by the zero-point energy of quantum fields. It is much smaller and is determined by the classical macroscopic parameters of the Universe dynamics: the Hubble radius, the Newton constant, and the energy density of matter. The same may hold for the Higgs mass problem: the quadratically divergent quantum correction to the Higgs potential mass term is also cancelled by the microscopic (trans-Planckian) degrees of freedom due to the thermodynamic stability of the whole quantum vacuum.     

Thermal effects vs. gain in femtosecond laser written waveguides in neodymium doped fused silica

The influence of thermal effects in gain measurements of fs laser-written waveguides in actively doped glass is reported for the first time. We show that these effects strongly contribute to the signal enhancement (up to 50% observed). Thus, a new measurement scheme to distinguish between thermal induced signal increase and real amplification is proposed. PACS 42.82.-m; 42.82.Et; 42.65.Re     

Retardation effects in quantum dot systems coupled via one-dimensional waveguides

We investigate the retardation effect on the radiative decay and entanglement of two quantum dots. The retardation effect is found to be very weak if the dots are coupled to free-space vacuum reservoir. To enhance the effect, we propose to embed the dots inside a one-dimensional waveguide. It is found that populations and entanglement can saturate to non-vanishing values with appropriate conditions. Furthermore, entanglement sudden-rise and sudden-fall are also observed due to this non-Markovian retardation.     

Existence of bound states in quantum waveguides under weak conditions

The existence of bound states in a plane quantum waveguide is proved under weak conditions: Within a bounded set a more general shape than a curved parallel strip is admitted and the curvature of the reference curve need not be differentiable. Furthermore, no upper bound for the width of the strip is required.     

Quantum information processing through quantum dots in slow-light photonic crystal waveguides

We propose a scheme to realize controlled phase-flip gate between two single photons through a single quantum dot (QD) in a slow-light photonic crystal (PhC) waveguide. Enhanced Purcell factor and large β-factor lead to high gate fidelity over broadband frequencies compared to cavity-assisted system. The excellent physical integration of this PhC waveguide system provides tremendous potential for large-scale quantum information processing. Then we generalize to a multi-atom controlled phase-flip gate based on waveguide system in Sagnac interferometer. Through the Sagnac interferometer, the single photon adds the phase-flip operation on the atomic state without changing the photonic state. The controlled phase-flip gate on the atoms can be successfully constructed with high fidelity in one step, even without detecting the photon.     

Atomic spectroscopy and quantum optics in hollow‐core waveguides

Atomic spectroscopy is a well‐established, integral part of the physicist's toolbox with an extremely broad range of applications ranging from astronomy to single atom quantum optics. While highly desirable, miniaturization of atomic spectroscopy techniques on the chip scale was hampered by the apparent incompatibility of conventional solid‐state integrated optics and gaseous media. Here, the state of the art of atomic spectroscopy in hollow‐core optical waveguides is reviewed The two main approaches to confining light in low index atomic vapors are described: hollow‐core photonic crystal fiber (HC‐PCF) and planar antiresonant reflecting optical waveguides (ARROWs). Waveguide design, fabrication, and characterization are reviewed along with the current performance as compact atomic spectroscopy devices. The article specifically focuses on the realization of quantum interference effects in alkali atoms which may enable radically new optical devices based on low‐level nonlinear interactions on the single photon level for frequency standards and quantum communication systems.     

Macroscopic instructions vs microscopic operations in quantum circuits

In many experiments on microscopic quantum systems, it is implicitly assumed that when a macroscopic procedure or “instruction” is repeated many times – perhaps in different contexts – each application results in the same microscopic quantum operation. But in practice, the microscopic effect of a single macroscopic instruction can easily depend on its context. If undetected, this can lead to unexpected behavior and unreliable results. Here, we design and analyze several tests to detect context-dependence. They are based on invariants of matrix products, and while they can be as data intensive as quantum process tomography, they do not require tomographic reconstruction, and are insensitive to imperfect knowledge about the experiments. We also construct a measure of how unitary (reversible) an operation is, and show how to estimate the volume of physical states accessible by a quantum operation.