In the last 30 days

• Open/close A computational toolbox for quantum and atomic optics

  Sze M Tan 1999 J. Opt. B: Quantum Semiclass. Opt. 1 424 Tag this article

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  A collection of routines is described which largely automates the process of generating the quantum mechanical equations of motion for problems involving systems with relatively few degrees of freedom. Their use allows the user to adopt a high-level approach to writing simulation programs which concentrates on the physics of the problem, rather than on the details of the solution. Examples are taken from the fields of quantum and atomic optics, but the toolbox is also useful for problems involving quantum information and in teaching quantum mechanics. The toolbox has been implemented using the Matlab programming language, but the ideas may be applied to any other object-oriented language.

• Open/close Mott–Hubbard transition of cold atoms in optical lattices

  Wilhelm Zwerger 2003 J. Opt. B: Quantum Semiclass. Opt. 5 S9 Tag this article

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  We discuss the superfluid (SF) to Mott-insulator transition of cold atoms in optical lattices recently observed by Greiner et al (2002 Nature 415 39). The fundamental properties of both phases and their experimental signatures are discussed carefully, including the limitations of the standard Gutzwiller approximation. It is shown that in a one-dimensional dilute Bose-gas with a strong transverse confinement (Tonks-gas), even an arbitrary weak optical lattice is able to induce a Mott-like state with crystalline order, provided the dimensionless interaction parameter is larger than a critical value of order one. The SF–insulator transition of the Bose–Hubbard model in this case continuously evolves into a transition of the commensurate–incommensurate type with decreasing strength of the external optical lattice.

• Open/close Bloch oscillations and Zener breakdown in an optical lattice

  Martin Holthaus 2000 J. Opt. B: Quantum Semiclass. Opt. 2 589 Tag this article

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  We study the dynamics of ultracold atoms in an optical lattice under constant bias. After recapitulating the ideas underlying Bloch oscillations and Zener's formula for interband transitions, the Bloch-Zener scenario is tested by means of accurate numerical solutions to the time-dependent Schrödinger equation. It is shown how two shortcomings of the traditional Zener formula can be removed: the common weak-binding approximation can be circumvented by combining Kohn's insight into the structure of complex energy bands with the Dykhne-Davis-Pechukas description of transitions in terms of adiabatic excursions on analytically continued eigenvalue surfaces, and a usually neglected Stokes phenomenon comes into play when accounting for the finite width of the Brillouin zone. Treating Bose-Einstein condensates in optical lattices within the standard mean-field approximation at zero temperature, the ideal Bloch-Zener scenario turns out to be remarkably stable against the condensate's nonlinear self-interaction. Yet, under appropriate conditions a Bloch-oscillating Gross-Pitaevskii wavepacket reveals characteristic signatures of that nonlinearity, such as sudden phase jumps, slight shifts of the oscillation frequency or non-classical breathing modes. It is suggested that such experimentally detectable signatures will play an important role in future high-precision experiments aiming at the exploration of many-body dynamics in periodic potentials with condensates in optical lattices.

• Open/close Quantum imaging

  L A Lugiato et al 2002 J. Opt. B: Quantum Semiclass. Opt. 4 S176 Tag this article

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  We provide a brief overview of the newly born field of quantum imaging, and discuss some concepts that lie at the root of this field.

• Open/close Negativity of the Wigner function as an indicator of non-classicality

  Anatole Kenfack and Karol Życzkowski 2004 J. Opt. B: Quantum Semiclass. Opt. 6 396 Tag this article

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  A measure of non-classicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyse this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition of two Gaussian wavepackets.

• Open/close Spatiotemporal optical solitons

  Boris A Malomed et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 R53 Tag this article

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  In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic–cubic or cubic–quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose–Einstein condensates supported by full or low-dimensional optical lattices.

• Open/close Studies on nonlinear coherent states

  S Sivakumar 2000 J. Opt. B: Quantum Semiclass. Opt. 2 R61 Tag this article

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  Nonclassical states of light are of fundamental importance in quantum optics. The properties of these states are due to the quantal nature of the electromagnetic field. In recent years there have been many experimental demonstrations of the realizability of nonclassical states in various physical schemes such as resonance fluorescence, four-wave mixing, centre-of-mass motion of a trapped ion and manipulation of field in a cavity. It is of interest to introduce new classes of nonclassical states and investigate their properties. In this context, generalization of the concept of coherent states (CSs) has played a major role. New concepts such as the nonlinear coherent states (NCSs) and interference in phase space have emerged from such studies. In this tutorial review we are concerned with the construction of new classes of nonclassical states by generalizing the notion of CSs. Our investigations on the photon-added coherent states (PACSs) indicate that these states can be interpreted as NCSs. Also, we introduce a new class of nonclassical states related to the PACSs. Having introduced a realizable example of NCSs, we extend the notion of even and odd CSs to the case of NCSs by introducing even and odd NCSs. With this new definition we interrelate some of the well known states of light. We suggest a scheme to generate a class of even and odd NCSs in the centre-of-mass motion of a trapped, laser-cooled, two-level ion.

• Open/close Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation

  Julien Laurat et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S577 Tag this article

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  A powerful theoretical structure has emerged in recent years on the characterization and quantification of entanglement in continuous-variable systems. After reviewing this framework, we will illustrate it with an original set-up based on a type-II OPO (optical parametric oscillator) with adjustable mode coupling. Experimental results allow a direct verification of many theoretical predictions and provide a sharp insight into the general properties of two-mode Gaussian states and entanglement resource manipulation.

• Open/close An algebraic solution of Lindblad-type master equations

  A B Klimov and J L Romero 2003 J. Opt. B: Quantum Semiclass. Opt. 5 S316 Tag this article

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  We propose an algebraic solution for a wide class of Lindblad-type master equations. Examples of dissipation in free field evolution, field evolution in the Kerr medium, two-photon field dissipation, atomic dissipation and two-mode field dissipation are given.

• Open/close Characterizing the spin state of an atomic ensemble using the magneto-optical resonance method

  B Julsgaard et al 2004 J. Opt. B: Quantum Semiclass. Opt. 6 5 Tag this article

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  Quantum information protocols utilizing atomic ensembles require preparation of a coherent spin state (CSS) of the ensemble as an important starting point. We investigate the magneto-optical resonance method for characterizing a spin state of caesium atoms in a paraffin coated vapour cell. Atoms in a constant magnetic field are subject to an off-resonant laser beam and an RF magnetic field. The spectrum of the Zeeman sub-levels, in particular the weak quadratic Zeeman effect, enables us to measure the spin orientation, the number of atoms, and the transverse spin coherence time. Notably the use of 894 nm pumping light on the D1 line, ensuring the state F = 4, m _F = 4 is a dark state, helps us to achieve spin orientation of better than 98%. Hence we can establish a CSS with high accuracy, which is critical for the analysis of the entangled states of atoms.