Ramsey interferometry in three-level and five-level systems of 87Rb^{87}Rb Bose-Einstein condensates

Our work here presents the analytical expressions for a typical Ramsey interferometric sequence for a three- and a five-level system. The analytical expressions are derived starting from the first principals of unitary time evolution operators. We focus on the three- and five-level systems because we propose a novel Ramsey interferometer created by a trapped two-state Bose-Einstein Condensate driven by dipole oscillations and gravitational sag. It involves the $^{87}Rb$ atoms in states $\vert F=2, m_F=+2 \rangle$ $(\vert +2 \rangle)$ and $\vert F=2, m_F=+1 \rangle$ $(\vert +1 \rangle)$ of the $5 ^2S_{\frac{1}{2}}$ ground state. Though the interferometer focusses on the two-levels, the experimental readouts involve all the five states in $F = 2$ hyperfine manifold. Therefore, the analytical derivation was first tested for three-levels and then expanded to five-levels. We developed the expressions for five-levels for greater analytical accuracy of the experimental scenario. This work provides a step-by-step outline for the derivation and methodology for the analytical expressions. These analytical formulae denote the population variation during Rabi and Ramsey oscillations for each state as well as the overall average for both the three- and five-level cases. The expressions are derived within the rotating wave approximation (RWA) under the equal Rabi condition. Further, by following the derivation methodology, these analytical expressions can be easily expanded for Ramsey sequences with unequal pulses, and Ramsey sequences with spin echo techniques.Comment: 19 pages, 7 figure

Dynamics of reflection of ultracold atoms from a periodic 1D magnetic lattice potential

We report on an experimental study of the dynamics of the reflection of ultracold atoms from a periodic one-dimensional magnetic lattice potential. The magnetic lattice potential of period 10 \textmu m is generated by applying a uniform bias magnetic field to a microfabricated periodic structure on a silicon wafer coated with a multilayered TbGdFeCo/Cr magneto-optical film. The effective thickness of the magnetic film is about 960 nm. A detailed study of the profile of the reflected atoms as a function of externally induced periodic corrugation in the potential is described. The effect of angle of incidence is investigated in detail. The experimental observations are supported by numerical simulations.Comment: 15 pages, 11 figure

Trapping ultracold atoms at 100 nm from a chip surface in a 0.7-micrometer-period magnetic lattice

We report the trapping of ultracold 87Rb atoms in a 0.7 micron-period 2D triangular magnetic lattice on an atom chip. The magnetic lattice is created by a lithographically patterned magnetic Co/Pd multilayer film plus bias fields. Rubidium atoms in the F=1, mF=-1 low-field seeking state are trapped at estimated distances down to about 100 nm from the chip surface and with calculated mean trapping frequencies as high as 800 kHz. The measured lifetimes of the atoms trapped in the magnetic lattice are in the range 0.4 - 1.7 ms, depending on distance from the chip surface. Model calculations suggest the trap lifetimes are currently limited mainly by losses due to surface-induced thermal evaporation following loading of the atoms from the Z-wire trap into the very tight magnetic lattice traps, rather than by fundamental loss processes such as surface interactions, three-body recombination or spin flips due to Johnson magnetic noise. The trapping of atoms in a 0.7 micrometer-period magnetic lattice represents a significant step towards using magnetic lattices for quantum tunneling experiments and to simulate condensed matter and many-body phenomena in nontrivial lattice geometries.Comment: 11 pages, 7 figure

THE PROBLEM OF RUSSIAN POST-REVOLUTIONARY EMIGRATION IN THE CONTEXT OF THE INTERNATIONAL POSITION OF THE SOVIET STATE IN THE FIRST HALF OF THE 1920S

Aim. To consider the Soviet perception of Russian post-revolutionary emigration in the context of the key foreign policy challenges to the Soviet Country of the first half of the 1920s.Methodology. On the basis of the principles of historism and scientific objectivity, the authors analyzed a number of archival and official Soviet documents, as well as parts of the memoirs and journalistic heritage of the Russia Abroad related to the research.Results. It is concluded that during this period the Bolsheviks considered the post-revolutionary emigration as one of the biggest threats to the security of the young Soviet state.Research implications. The article introduced for the first time into the scientific circulation some archival documents that give a more detailed idea of the formation of the Soviet position regarding the plans of F. Nansen for a large-scale repatriation of Russian emigrants to their homeland in the 1920s.</html

Radiofrequency spectroscopy of a linear array of Bose-Einstein condensates in a magnetic lattice

We report site-resolved radiofrequency spectroscopy measurements of Bose-Einstein condensates of 87Rb atoms in about 100 sites of a one-dimensional 10 micron-period magnetic lattice produced by a grooved magnetic film plus bias fields. Site-to-site variations of the trap bottom, atom temperature, condensate fraction and chemical potential indicate that the magnetic lattice is remarkably uniform, with variations in trap bottoms of only +/- 0.4 mG. At the lowest trap frequencies (radial and axial frequencies 1.5 kHz and 260 Hz, respectively), temperatures down to 0.16 microkelvin are achieved in the magnetic lattice and at the smallest trap depths (50 kHz) condensate fractions up to 80% are observed. With increasing radial trap frequency (up to 20 kHz, or aspect ratio up to about 80) large condensate fractions persist and the highly elongated clouds approach the quasi-1D Bose gas regime. The temperature estimated from analysis of the spectra is found to increase by a factor of about five which may be due to suppression of rethermalising collisions in the quasi-1D Bose gas. Measurements for different holding times in the lattice indicate a decay of the atom number with a half-life of about 0.9 s due to three-body losses and the appearance of a high temperature (about 1.5 microkelvin) component which is attributed to atoms that have acquired energy through collisions with energetic three-body decay products

Magnetic Lattices for Ultracold Atoms

This article reviews the development in our laboratory of magnetic lattices comprising periodic arrays of magnetic microtraps created by patterned magnetic films to trap periodic arrays of ultracold atoms. Recent achievements include the realisation of multiple Bose-Einstein condensates in a 10 $\mu$m-period one-dimensional magnetic lattice; the fabrication of sub-micron-period square and triangular magnetic lattice structures suitable for quantum tunnelling experiments; the trapping of ultracold atoms in a sub-micron-period triangular magnetic lattice; and a proposal to use long-range interacting Rydberg atoms to achieve spin-spin interactions between sites in a large-spacing magnetic lattice

Dynamical properties of S-gap shifts and other shift spaces

We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts and balanced shifts. It turns out that any almost specified shift is both BSM and balanced, and any balanced shift is BSM. However, as we will demonstrate, there are examples of shifts which are BSM but not balanced. We also study the measure theoretic properties of balanced shifts. We show that a shift space admits a Gibbs state if and only if it is balanced. Restricting ourselves to S-gap shifts, we relate certain dynamical properties of an S-gap shift to combinatorial properties from expansions in non-integer bases. This identification allows us to use the machinery from expansions in non-integer bases to give straightforward constructions of S -gap shifts with certain desirable properties. We show that for any q∈(0,1) there is an S-gap shift which has the specification property and entropy q . We also use this identification to address the question, for a given q∈(0,1), how many S-gap shifts exist with entropy q? For certain exceptional values of q there is a unique S-gap shift with this entropy