In the last 30 days

• Open/close Experimental tests of quantum nonlinear dynamics in atom optics

  Winfried K Hensinger et al 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R83 Tag this article

  Article References Full text PDF (6.44 MB)

  Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose–Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 ^° out of phase with the initial state.

• Open/close Editorial

  Wolfgang Lange and Jean-Michel Gerard 2004 J. Opt. B: Quantum Semiclass. Opt. 6 117 Tag this article

  Article References Full text PDF (30 KB)

  A single two-level emitter coupled to a single mode of an electromagnetic resonator constitutes the most fundamental instance of light--matter interaction. Realizations of this type of system are investigated in the field of cavity quantum electrodynamics (cavity QED). Particularly important are schemes in which the coupling is strong enough to exceed the spontaneous emission rate as well as cavity damping. In this case, the coherent exchange of excitation between source and photon is the dominating process, providing the unique possibility to deterministically control the quantum evolution of the system.

  Great progress has recently been accomplished, technologically as well as conceptually, and the focus section in this issue of Journal of Optics B: Quantum and Semiclassical Optics features five articles highlighting important recent developments in the field.

  Strong coupling between single atoms and the electromagnetic cavity field have been achieved in two distinct regimes, the optical and the microwave region. The latter is represented by the micromaser, a high-Q microwave cavity pumped by a beam of highly excited Rydberg atoms. It has proved to be an almost ideal system for the generation of non-classical field states. A constraint in these experiments is the fact that the field inside the cavity can only be examined indirectly, by analysing the occupation of atoms leaving the cavity. While only two atomic states were previously identified for this purpose, V A Reshetov shows in his article (pages 119--126) that more information on the field may be extracted by taking advantage of the Zeeman substructure of the atomic levels.

  In the optical domain of cavity QED, by contrast, the state of the resonator field may be probed directly by measuring the light leaking from the cavity using photodetectors. In order to minimize damping, high-quality cavities must be employed. In most optical experiments these are Fabry--Perot resonators with ultra-high reflectivity mirrors, with losses as low as a few parts per million being state of the art. At the same time, the coupling of atoms and photons is enhanced by reducing the length of the cavity, so that strong coupling conditions are reached.

  A very attractive application of this type of cavity QED setup is the possibility of exerting control over the quantum dynamics of the system. An impressive example is the implementation of quantum feedback, reported in the paper by W P Smith and L A Orozco (pages 127--134). Using information gained from detecting a single photon escaping from the cavity, active feedback is applied to halt the dynamical evolution of the system. This is the first time active feedback has been used to modify the quantum evolution of a system at the single-photon level. The authors discuss how detunings between the subsystems affect the quantum feedback, an issue particularly relevant for ensembles of atoms with a spread in detuning. Perfect quantum feedback in this case requires the use of additional parameters to control the system.

  The majority of optical cavity QED experiments performed so far have used as a medium atoms traversing the cavity on random trajectories, such as, for example, thermal atomic beams. In this case, the observation of quantum effects is degraded in two ways. The Doppler effect and the finite transit time lead to line broadening, while the spatial structure of the cavity mode results in atoms in different locations experiencing different coupling with the photonic field. J E Reiner et al (pages 135--142) investigate the impact of these effects on quantum fluctuations in their cavity QED system. In order to overcome line broadening, they have developed a continuous cold atomic beam, extracted from a magneto-optical trap.

  An even better control of broadening effects and fluctuating coupling strength is provided by trapping the atoms inside the cavity and cooling them to temperatures at which their position spread is smaller than the optical wavelength. Much recent activity has been devoted to developing such an ultimate cavity QED system. A Vukics et al (pages 143--153) present a theoretical proposal for dynamically trapping and cooling atoms inside a cavity. By driving the atoms with a standing wave injected from the side of the cavity and by weakly exciting the cavity field itself, they predict three-dimensional trapping of the atom for periods around 1 second, an extremely long time on the typical scale of cavity QED dynamics. The essential component of their scheme is the interference between the two driving fields, determining the temperature of the particle and the stable trapping positions.

  In the quest for better confinement of radiation, lately, an appealing alternative to the Fabry--Perot cavity has been investigated -- the optical microsphere resonator. A sphere with a diameter of a few tens of microns, it supports so-called whispering gallery modes near its circumference, for which quality factors up to 10 ¹⁰ have been measured. In order to exploit the correspondingly low field damping rates for cavity QED, a method must be found to couple atomic or solid state emitters to these modes. S Göotzinger et al (pages 154--158) report the coupling of single nanocrystals on the surface of a microsphere through the evanescent field of the mode. Selective excitation of a single nano-emitter was accomplished with a scanning confocal microscope. The system is a promising candidate for cavity QED with single-quantum emitters.

  The ability to fully control the quantum dynamics of atoms and light is beginning to spawn early applications. The most notable example is quantum information processing. This requires the coherent manipulation of single-quantum systems, which is ideally provided by cavity QED interaction in the strong-coupling limit. The development of practical devices will be among the principal future tasks for research in the field. This will include physical systems, which have not been covered in this issue, such as semiconductors, quantum dots as emitters, or photonic crystals as resonator structures. Cavity QED is therefore guaranteed to remain a vigorous field in the years to come.

• 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

  Article References Full text PDF (262 KB)

  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 Quantum imaging

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

  Article References Full text PDF (593 KB)

  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 Operator ordering in quantum optics theory and the development of Dirac's symbolic method

  Hong-yi Fan 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R147 Tag this article

  Article References Full text PDF (262 KB)

  We present a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering (or symmetric ordering)) by fashioning Dirac's symbolic method and representation theory. We propose the technique of integration within an ordered product (IWOP) of operators to realize our goal. The IWOP makes Dirac's representation theory and the symbolic method more transparent and consequently more easily understood. The beauty of Dirac's symbolic method is further revealed. Various applications of the IWOP technique, such as in developing the entangled state representation theory, nonlinear coherent state theory, Wigner function theory, etc, are presented.

• 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

  Article References Full text PDF (200 KB)

  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 Optical angular-momentum flux

  Stephen M Barnett 2002 J. Opt. B: Quantum Semiclass. Opt. 4 S7 Tag this article

  Article References Full text PDF (129 KB)

  We introduce the angular-momentum flux as the natural description of the angular momentum carried by light. We present four main results: (i) angular-momentum flux is the flow of angular momentum across a surface and, in conjunction with the more familiar angular-momentum density, expresses the conservation of angular momentum. (ii) The angular-momentum flux for a light beam about its axis (or propagation direction) can be separated into spin and orbital parts. This separation is gauge invariant and does not rely on the paraxial approximation. (iii) Angular-momentum flux can describe the propagation of angular momentum in other geometries, but the identification of spin and orbital parts is then more problematic. We calculate the flux for a component of angular momentum that is perpendicular to the axis of a light beam and for the field associated with an electric dipole. (iv) The theory can be extended to quantum electrodynamics.

• Open/close Spatiotemporal optical solitons

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

  Article References Full text PDF (923 KB)

  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 Remarks on entanglement swapping

  Daegene Song 2004 J. Opt. B: Quantum Semiclass. Opt. 6 L5 Tag this article

  Article References Full text PDF (112 KB) View as HTML

  In two partially entangled states, entanglement swapping by Bell measurement will yield the weaker entanglement of the two. This scheme is optimal because the average entanglement cannot increase under local operation and classical communication. However, for more than two states, this scheme does not always yield the weakest link. We consider projective measurements other than Bell-type measurement and show, numerically, that while Bell measurement may not be unique, it is indeed optimal among these projective measurements. We also discuss the non-uniqueness of Bell measurements.

• Open/close Observation of electromagnetically induced transparency within an electron spin resonance transition

  Changjiang Wei and Neil B Manson 1999 J. Opt. B: Quantum Semiclass. Opt. 1 464 Tag this article

  Article References Full text PDF (890 KB)

  A sharp transparency feature is induced in an allowed electron spin resonance (ESR) transition by driving a nominally spin-forbidden transition. The width of the feature is narrower than the homogeneous linewidth of the ESR transition and is interpreted as being associated with electromagnetically induced transparency (EIT). Measurements are made for the nitrogen-vacancy centre in diamond and the signals are detected using a coherent optical technique.