We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed. Motto: There are more things in heaven and earth, Horatio, Than are dreamt of in your...

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Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

Advances in atomic physics, such as cooling and trapping of atoms and molecules and developments in frequency metrology, have added orders of magnitude to the precision of atom-based clocks and sensors. Applications extend beyond atomic physics and this article reviews using these new techniques to address important challenges in physics and to look for variations in the fundamental constants, search for interactions beyond the standard model of particle physics, and test the principles of general relativity.

Search for New Physics with Atoms and Molecules

We show that the physical system consisting of trapped ions interacting with lasers may undergo a rich variety of quantum phase transitions. By changing the laser intensities and polarizations the dynamics of the internal states of the ions can be controlled, in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analogue quantum simulator of spin systems with trapped ions, and observe and analyze quantum phase transitions with unprecedented opportunities for the measurement and manipulation of spins.

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Effective quantum spin systems with trapped ions.

1 The Equations of Gas Dynamics 2 Magnetoplasma Dynamics 3 Waves in Magnetoplasmas 4 Magnetoplasma Stability 5 Transport in Magnetoplasmas 6 Extensions of Theory Bibliography Index

Physics of plasmas

Single crystals of a one-component plasma were observed by optical Bragg diffraction. The plasmas contained 105 to 106 single-positive beryllium-9 ions (9Be+) at particle densities of 108to 109 per cubic centimeter. In approximately spherical plasmas, single body-centered cubic (bcc) crystals or, in some cases, two or more bcc crystals having fixed orientations with respect to each other were observed. In some oblate plasmas, a mixture of bcc and face-centered cubic ordering was seen. Knowledge of the properties of one-component plasma crystals is required for models of white dwarfs and neutron stars, which are believed to contain matter in that form.

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Bragg Diffraction from Crystallized Ion Plasmas

Bragg diffraction from crystallized ion plasmas

We report the first measurements and detailed analysis of extreme ultraviolet (EUV) spectra (4–20 nm) of highly-charged tungsten ions W54+ to W63+ obtained with an electron beam ion trap (EBIT). Collisional-radiative modelling is used to identify strong electric-dipole and magnetic-dipole transitions in all ionization stages. These lines can be used for impurity transport studies and temperature diagnostics in fusion reactors, such as ITER. Identifications of prominent lines from several W ions are confirmed by the measurement of isoelectronic EUV spectra of Hf, Ta and Au. We also discuss the importance of charge-exchange recombination for the correct description of ionization balance in the EBIT plasma.

http://iopscience.iop.org/article/10.1088/0953-4075/41/2/021003/pdf

EUV spectra of highly-charged ions W54+–W63+ relevant to ITER diagnostics

Optical frequencies of the D lines of (6,7)Li were measured with a relative accuracy of 5 × 10⁻¹¹ using an optical comb synthesizer. Quantum interference in the laser induced fluorescence for the partially resolved D2 lines was found to produce polarization dependent shifts as large as 1 MHz. Our results resolve large discrepancies among previous experiments and between all experiments and theory. The fine-structure splittings for ⁶Li and ⁷Li are 10052.837(22) MHz and 10053.435(21) MHz. The splitting isotope shift is 0.599(30) MHz, in reasonable agreement with recent theoretical calculations.

Absolute transition frequencies and quantum interference in a frequency comb based measurement of the (6,7)Li D lines.

We observed spectra of highly ionized tungsten in the extreme ultraviolet with an electron beam ion trap (EBIT) and a grazing-incidence spectrometer at the National Institute of Standards and Technology. Stages of ionization were distinguished by varying the energy of the electron beam between 2.1 keV and 4.3 keV and correlating the energies with spectral line emergence. The spectra were calibrated by reference lines of highly ionized iron produced in the EBIT. Identification of the observed lines was aided by collisional-radiative modelling of the EBIT plasma. Good quantitative agreement was obtained between the modelling results and the experimental observations. Our line identifications complement recent results for W40+–W45+ observed in a tokamak plasma by Putterich et al (2005 J. Phys. B: At. Mol. Opt. Phys. 38 3071). For most lines we agree with their assignment of ionization stage. Additionally, we present new identifications for some allowed and forbidden lines of W39+, W44+, W46+ and W47+. The uncertainties of our wavelengths range from 0.002 nm to 0.010 nm.

https://iopscience.iop.org/article/10.1088/0953-4075/40/19/007/pdf

Joseph N. Tan

Papers

Bragg Diffraction from Crystallized Ion Plasmas

Bragg diffraction from crystallized ion plasmas

EUV spectra of highly-charged ions W54+–W63+ relevant to ITER diagnostics

Absolute transition frequencies and quantum interference in a frequency comb based measurement of the (6,7)Li D lines.

Spectra of W39+–W47+ in the 12–20 nm region observed with an EBIT light source