One electron atoms in both a squeezed vacuum and a magnetic field via path integral methods

In the present paper we study the dynamics of one-electron atoms in the presence of both a linearly polarized squeezed vacuum and a magnetic field along the polarization vector of the photonic field. We adopt the dipole approximation and approach the problem via path integral methods. After integrating over the light variables for certain initial and final squeezed vacuum states we treat the path integral over the spatial variables via Monte-Carlo methods. As an application we calculate the survival probability of the ground state of a one-electron atom for various values of the magnetic field. Received 30 November 2000 and Received in final form 15 February 2001     

3D dissipative motion of atoms in a strongly coupled driven cavity

We develop quantum models for the combined external and internal motion of atoms in a strongly coupled driven cavity mode including the transverse degrees of freedom. Using a simplified Gaussian mode function we determine the parameter regimes and prospects of 3D cooling and confinement of one or two atoms in the cavity field. Analysing the field dynamics for slow atoms traversing the cavity, we show that the spectrum of the transmitted and spontaneously scattered light contains ample information on the motional dynamics of the atom and can be nicely used to investigate the cooling properties of the system. Including several atoms in the dynamics we show how motional correlations build up by the common interaction with the cavity field. This can be looked upon as collisions at far distance and can be monitored via the transmitted field dynamics. Received 5 March 1999 and Received in final form 4 May 1999     

Nonclassical properties and algebraic characteristics of negative binomial states in quantized radiation fields

We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Perelomov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they are excited geometric states. As intermediate states, they interpolate between the number states and geometric states. We also point out that they can be recognized as the nonlinear coherent states. Their nonclassical properties, such as sub-Poissonian distribution and squeezing effect are discussed. The quasiprobability distributions in phase space, namely the Q and Wigner functions, are studied in detail. We also propose two methods of generation of the negative binomial states. d 32.80.Pj Optical cooling of atoms; trapping Received 8 May 1999 and Received in final form 8 November 1999     

Controllable Photonic Band Gap and Defect Mode in a 1D CO2-Laser Optical Lattice

We propose a new method to form a novel controfiable photonic crystal with cold atoms and study the photonic band gap （PBG） of an infinite 1D CO2-laser optical lattice of SSRb atoms under the condition of quantum coherence. A significant gap generated near the resonant frequency of the atom is founded and its dependence on physical parameters is also discussed. Using the eigenquation of defect mode, we calculate the defect mode when a defect is introduced into such a lattice. Our study shows that the proposed new method can be used to optically probe optical lattice in situ and to design some novel and controllable photonic crystals.     

From 2D hyperbolic forests to 3D Euclidean entangled thickets

A method is developed to construct and analyse a wide class of graphs embedded in Euclidean 3D space, including multiply-connected and entangled examples. The graphs are derived via embeddings of infinite families of trees (forests) in the hyperbolic plane, and subsequent folding into triply periodic minimal surfaces, including the P, D, gyroid and H surfaces. Some of these graphs are natural generalisations of bicontinuous topologies to bi-, tri-, quadra- and octa-continuous forms. Interwoven layer graphs and periodic sets of finite clusters also emerge from the algorithm. Many of the graphs are chiral. The generated graphs are compared with some organo-metallic molecular crystals with multiple frameworks and molecular mesophases found in copolymer melts. Received 10 December 1999     

Exact results on decoherence and entanglement in a system of N driven atoms and a dissipative cavity mode

We solve the dynamics of an open quantum system where N strongly driven two-level atoms are equally coupled on resonance to a dissipative cavity mode. Analytical results are derived on decoherence, entanglement, purity, atomic correlations and cavity field mean photon number. We predict decoherencefree subspaces for the whole system and the N-qubit subsystem, the monitoring of quantum coherence and purity decay by atomic populations measurements, the conditional generation of atomic multi-partite entangled states and of cavity cat-like states. We show that the dynamics of atoms prepared in states invariant under permutation of any two components remains restricted within the subspace spanned by the completely symmetric Dicke states. We discuss examples and applications in the cases N = 3, 4. An erratum to this article can be found at     

Collision-assisted Zeeman cooling of neutral atoms

We propose a new method to cool gaseous samples of neutral atoms. The gas is confined in a non dissipative optical trap in the presence of an homogeneous magnetic field. The method accumulates atoms in the m _F =0 Zeeman sub-level. Cooling occurs via collisions that produce atoms in states. Thanks to the second order Zeeman effect kinetic energy is transformed into internal energy and recycling of atoms is ensured by optical pumping. This method may allow quantum degeneracy to be reached by purely optical means. Received 10 May 2000     

Si-based two-dimensional photonic crystals coupled to one-dimensional Bragg mirrors

Planar two-dimensional photonic crystals can be combined with a one-dimensional Bragg mirror to control the quality factor and out-of-plane coupling of optical Bloch modes. We have investigated the optical properties of such structures fabricated on silicon. The photonic crystals are fabricated in the upper Si layer deposited on top of quarter-wave thick SiO₂-polycrystalline Si layers. The optical properties are probed by the room-temperature photoluminescence of Ge/Si self-assembled islands as an internal source. We show that an enhancement of the quality factor can be obtained by controlling the thickness of the silicon upper layer in which the two-dimensional photonic crystal is etched and by controlling the air filling factor of the photonic crystal. Quality factors of 2200 around 1100 nm are obtained by this method for defect-free photonic crystals with a square lattice pattern. The experimental results are supported by three-dimensional finite-difference time-domain (FDTD) calculations of the radiated modes for the investigated structures.     

Fabrication of Two-Dimensional Photonic Crystals with Triangular Rods by Single-Exposure Holographic Lithography

We demonstrate a single-exposure holographic fabrication of two-dimensional photonic crystal with round- cornered triangular ＇atoms＇ arranged in a triangular lattice. Simulation results show that double absolute photonic band gaps exist in this structure. Our experimental results show that holographic lithography can be used to fabricate photonic crystals not only with various lattice structures but also with various kinds of structures of the atoms, to obtain absolute band gaps or a particular band gap structure. Furthermore, the single-exposure holographic method not only makes the fabrication process simple and convenient but also makes the structures of the atoms more perfect.     

Efficient microwave-induced optical frequency conversion

Frequency conversion process is studied in a medium of atoms with a configuration of levels, where transition between two lower states is driven by a microwave field. In this system, conversion efficiency can be very high by virtue of the effect of electromagnetically induced transparency (EIT). Depending on intensity of the microwave field, two regimes of EIT are realized: “dark-state” EIT for the weak field, and Autler-Townes-type EIT for the strong one. We study both cases via analytical and numerical solution and find optimum conditions for the conversion. Received 13 December 1999 and Received in final form 6 March 2000     

The theory of cylindrical photonic wires

The energy modes for a photonic nanowire have been studied and calculated. We model our photonic crystals after Noda et al. (1999) [18] where logs of semiconductor material are stacked to produce photonic band gaps in both the near and far infrared regions. A nominal dispersion relation was adopted in order to achieve qualitatively useful results. Photonic wires were modeled in two schemes, each with two specific geometries. In the first scheme, a pillar of one photonic crystal is embedded in a larger photonic crystal to produce a wire. This pillar was modeled as having either a square or a circular cross-section. The photonic crystals considered consisted of varying proportions of Ga_xAl_1−xAs, so that the wire could be adjusted. The second scheme investigated was a dielectric material for the central pillar, rather than a photonic crystal. Again, circular and square cross sections were considered. It was found that many more modes fit into the near infrared band gap than the far infrared band gap, and that a circular cross-section permits fewer modes. Finally, a dielectric pillar allows for a wire which is physically much smaller than a wire with a photonic crystal in the middle. As many photonic devices include such wires, these qualitative results could be useful in their design.     

Testing Bell inequalities in photonic crystals

We show how entangled atomic pairs can be prepared in order to test the Bell inequalities. The scheme is based on the interaction of the atoms with a highly localized field mode within a photonic crystal. The potential of using optically separated transitions and the stability of the entangled state to spontaneous emission could lead to the closure of the communication and the detection loopholes appearing in experiments so far. The robustness of the scheme against detector inefficiencies, the spread in the atomic velocities and the fact that the entangled pairs are not generated simultaneously is also studied. Received 31 July 2001 and Received in final form 30 November 2001     

基于腔QED的多用户间的多原子量子信道的建立

提出基于腔QED技术的多用户间的多原子W态和GHZ态量子信道的建立方案.在量子网络的空闲时段,各个用户和量子交换机共享EPR对.量子交换机通过原子和腔场的相互作用将两个EPR对制备成W态,再与另一个EPR对进行纠缠交换,经过直接测量后为用户建立三原子W态量子信道;同时讨论了四用户间的W态量子信道的建立方案.量子交换机对三个EPR对进行纠缠交换,将三个原子同时与腔场作用,经过直接测量后为用户建立三原子GHZ态量子信道;并将此方法推广到N个用户间的GHZ态量子信道的建立. 关键词： 腔QED 量子信道 量子交换机 纠缠交换     

Nonlinear photonic crystals as a source of entangled photons

Nonlinear photonic crystals can be used to provide phase matching for frequency conversion in optically isotropic materials. The phase-matching mechanism proposed here is a combination of form birefringence and phase velocity dispersion in a periodic structure. Since the phase matching relies on the geometry of the photonic crystal, it becomes possible to use highly nonlinear materials. This is illustrated considering a one-dimensional periodic Al0.4Ga0.6As/air structure for the generation of 1.5 microm light. We show that phase-matching conditions used in schemes to create entangled photon pairs can be achieved in photonic crystals.     

New approaches for the fabrication of photonic structures of nonlinear optical materials

We revisited two different strategies to fabricate 1D photonic crystals of nonlinear optical dielectric materials based on ultrafast laser ablation of the surface of an RbTiOPO₄ crystal, and selective etching of ferroelectric domains of the surface of a periodically poled LiNbO₄ crystal. We evaluated their behaviour as Bragg diffraction gratings. We also presented the recent advances we developed in a new procedure of fabrication of 2D and 3D photonic crystals of KTiOPO₄ (KTP) grown on the surface of a KTP substrate by liquid phase epitaxial means within the pores of a silicon macroporous template. Optical, structural, morphological, and compositional characterization for the photonic crystals produced through this technique are presented.     

Improvement of absolute band gaps in 2D photonic crystals by anisotropy in dielectricity

Two-dimensional (2D) photonic band gaps (PBG) structure fabricated from anisotropic dielectric is studied by solving Maxwell's equations with use of plane-wave expansion method. Numerical simulations show that absolute photonic band gaps can be substantially improved in two dimensional square and triangular lattices of cylinders by introducing anisotropy in material dielectricity. Owing to different refractive indices for electromagnetic waves with E- and H-polarization, the quasi-independent adjustment of band gaps for the E- and H-polarization modes can be implemented by uniaxial crystals with their extraordinary axis parallel to the cylinders. Large absolute band gaps can be created for uniaxial cylinders in air with a positive anisotropy. In the case of air holes in background uniaxial dielectric with even a weak negative anisotropy, the absolute band gap can be increased 2-3 times. Large absolute band gap can also be obtained in other complex configurations of uniaxial and biaxial materials and this enables a full exploitation of potential utilization for anisotropic materials available in nature. Such a mechanism of band gap adjustment should open up a new scope for designing band gaps in 2D PBG structures. Received 26 January 1999     

Distributed Entangled State Production by Using Quantum Repeater Protocol

We consider entangled state production utilizing a full optomechanical arrangement, based on which we create entanglement between two far three-level V-type atoms using a quantum repeater protocol. At first, we consider eight identical atoms (1,2,? ,8), while adjacent pairs (i,i +?1) with i =?1,3,5,7 have been prepared in entangled states and the atoms 1, 8 are the two target atoms. The three-level atoms (1,2,3,4) and (5,6,7,8) distinctly become entangled with the system including optical and mechanical modes by performing the interaction in optomechanical cavities between atoms (2,3) and (6,7), respectively. Then, by operating appropriate measurements, instead of Bell state measurement which is a hard task in practical works, the entangled states of atoms (1,4) and (5,8) are achieved. Next, via interacting atoms (4,5) of the pairs (1,4) and (5,8) and operating proper measurement, the entangled state of target atoms (1,8) is obtained. In the continuation, entropy and success probability of the produced entangled state are then evaluated. It is observed that the time period of entropy is increased by increasing the mechanical frequency (ω_M) and by decreasing optomechanical coupling strength to the field modes (G). Also, in most cases, the maximum of success probability is increased by decreasing G and via decreasing ω_M.

     

Omni-directional reflection bands in one-dimensional plasma dielectric photonic crystals

In this paper the omni-directional reflection bands in one-dimensional plasma photonic crystal (PPC) have been studied theoretically. We present the study of plasma photonic crystal, having alternate regions of plasma?dielectric (Al₂O₃ or ZnS). Reflectances from this periodic multilayered structure in TE- and TM-modes are calculated for different angles of incidence in microwave region for omni-directional reflection bands. The reflectance is obtained by solving a Maxwell's equation using a translational matrix method. In addition to this, we have also studied the effect of variation of plasma width as well as plasma density on the reflection properties of plasma dielectric photonic crystal in TE- and TM-modes. The study of reflectance bands of such plasma photonic crystals shows that it can be used as omni-directional reflector.     

Nonlinear three-wave interaction in photonic crystals

We present a multi-scale analysis of nonlinear three-wave-interaction processes in photonic crystals. Based on photonic Bloch functions as carrier waves, we derive the effective nonlinear coupled wave equations that govern pulse propagation in these systems and obtain the corresponding effective photonic crystal parameters directly from photonic band-structure computations. As an illustration, we show how hitherto inaccessible radiation-conversion processes such as wave-front reversal of optical pulses can be realized. Furthermore, we describe a novel regime of nonlinear three-wave interaction in photonic crystals associated with the nearly degenerate case and show how these results may be utilized to study experimentally certain problems from plasma physics and hydrodynamics in the context of nonlinear photonic crystals.