Cold Atom, Optical Lattice

We consider the Bose-Hubbard model of attractive Bose gas in an optical lattice potential and in an additional
inhomogeneous double well magnetic trap potential. We calculate the energy spectrum and the on-site number
fluctuation of the system using numerical exact diagonalization procedure. Our results shows very clearly the role played
by the degenerate double well minimum of the trap potential on the nature of instability of the attractive Bose-Hubbard
model and the phase-transition picture of the system.

We investigate the photonic bands of an atomic Bose-Einstein condensate with a triangular vortex lattice. Index contrast between the vortex cores and the bulk of the condensate is achieved through the enhancement of the index via atomic coherence. The frequency-dependent dielectric function is used in the calculations of the bands, resulting in photonic band gap widths of a few megahertz.

We theoretically investigate the wave–particle duality based on a Raman atom interferometer, via the interaction between the atom and Raman laser, which is similar to the optical Mach–Zehnder interferometer. The wave and which-way information are stored in the atomic internal states. For the ϕ − π − π/2 type of atom interferometer, we find that the visibility (V) and predictability (P) still satisfy the duality relation, P 2 +V 2 ≤ 1.

We study the electromagnetically induced-absorption-like (EIA-like) effect for an n-type system in an 87 Rb Bose-Einstein condensate (BEC) using the absorption imaging technique for coupling and driving lasers operating at the D1 and D2 lines of 87 Rb. The coherent effect is probed by measuring the number of atoms remaining after the BEC is exposed to strong driving fields and a weak probe field. The absorption imaging technique accurately reveals the EIA-like effect of the n-type system. This coherent effect in an n-type system is useful for optical storage, tunable optical switching, and so on. Modifying the absorptive or dispersive properties of a medium using coherent driving fields to study coherent phenomena is a hot topic in atomic and optical physics. These phenomena are not only of fundamental interest for understanding light-matter interaction but also applicable in various light-matter-interaction-based devices. The schemes devised for observation of such effects include n-type, ladder-type, Λ-type, V-type, cascade and tripod. In such systems, electromagnetically induced transparency (EIT), [1,2] coherent population trapping, [3] superluminal, [4] and subluminal [5] light propagation, electromagnetically induced absorption (EIA) due to spontaneously generated coherence, [6−9] storage of light, [10,11] coherent nonlinear optics at low light levels [12−14] and lasing without inversion (LWI) [15] have been studied deeply. For this purpose, hot as well as cold atoms are used. However, a BEC is a useful tool for observing various phenomena that are not possible in hot atoms due to the Doppler shift. BECs also allow the absorption imaging technique in addition to transmission or scattering techniques for the probing of such coherent phenomena inside the medium. Such an absorption imaging technique is not suitable for hot atoms as they are moving at high speeds. The absorption imaging studies of the EIT [16] and EIA [17] in a BEC of 87 Rb have already proved that this technique is capable of precisely revealing the coherent properties of the systems under study in ultracold atoms. In this work, we study the EIA-like effect for an n-type system in a 87 Rb BEC as shown in Fig. 1. A similar n-type system studied here is already discussed, [18−20] where the probe light transmission as a function of frequency detuning is measured. Our system, however, is different from the previous systems [18,19] because in our system the driving and coupling lasers share the same lower ground level in the n-type system while in the system of Ref. [18,19] the driving and probe lasers share the same lower level. Also, we measure the number of remaining atoms in the absorption image after the BEC is exposed to strong driving and coupling lasers and weak probe lasers, while they measure the transmission spectrum of the probe laser directly using a photodetector. In principle, this absorption imaging technique is equivalent to the measurement of the transmission of the weak probe beam. In transmission spectroscopy, absorption of the probe reduces the laser transmission while in absorption imaging, the number of atoms reduces in the BEC due to heating caused by the probe laser. As shown in Fig. 1(b), the coupling laser at frequency c , locked between the lower ground state = 1 and the ′ = 1 state of the 1 line and the weak probe laser at frequency p , is optically phase-loop locked to the coupling laser and its frequency may be scanned from the = 2 to ′ = 1 transition , together forming a Λ-type system. We construct the n-type system by adding a driving laser to couple the transition between the | = 1⟩ to | ′ = 2⟩ transition of the 2 line. Since the BEC is prepared in the | = 2, = 2⟩ state, we lock the driving laser to the | = 1⟩ to | ′ = 2⟩ transition of the 2 line represented by d , as opposed to the study in Ref. [18-20] The Λ-type system results in the standard EIT (Fig. 2(a)) but adding the driving laser transforms the EIT into an EIA-like shape (Fig. 2(c)), and it is quite different from the EIA. This n-type configuration resembles the absorption line-shape of EIA just as Autler-Townes splitting in a three-level system resembles the line-shape of EIT although having different origins. [18,21] *

The self-similar energy spectrum of a particle in a periodic potential under a magnetic field, known as the Hofstadter butterfly, is determined by the lattice geometry as well as the external field. Recent realizations of artificial gauge fields and adjustable optical lattices in cold atom experiments necessitate the consideration of these self-similar spectra for the most general two-dimensional lattice. In a previous work, we investigated the evolution of the spectrum for an experimentally realized lattice which was tuned by changing the unit cell structure but keeping the square Bravais lattice fixed. We now consider all possible Bravais lattices in two dimensions and investigate the structure of the Hofstadter butterfly as the lattice is deformed between lattices with different point symmetry groups. We model the optical lattice by a sinusoidal real space potential and obtain the tight binding model for any lattice geometry by calculating the Wannier functions. We introduce the magnetic field via Peierls substitution and numerically calculate the energy spectrum. The transition between the two most symmetric lattices, i.e. the triangular and the square lattice displays the importance of bipartite symmetry featuring deformation as well as closing of some of the major energy gaps. The transition from the square to rectangular and from the triangular to centered rectangular lattices are analyzed in terms of coupling of one-dimensional chains. We calculate the Chern numbers of the major gaps and Chern number transfer between bands during the transitions. We use gap Chern numbers to identify distinct topological regions in the space of Bravais lattices.

by Botao Wang, F Nur Ünal, André Eckardt.
The idea of inserting a local magnetic flux, representing the field of a thin solenoid, plays an important role in various condensed matter models, especially in the understanding of topological systems. One example is the creation and manipulation of quasiparticle or hole excitations in these systems, which are essential for fault-tolerant quantum information processing. Implementing such local fluxes in cold atom experiments promises great potential. Here, we propose an experimental scheme to realize a local flux in a cold atom setting which takes advantage of the recent developments in synthetic gauge fields and quantum microscopes. To demonstrate the feasibility of our method, we consider quantum-Hall-type lattice systems and study the dynamical creation of topological excitations. We analyze the adiabatic charge pumping by tuning the strength of the local flux.

Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum
simulations and manipulations of many quantum phases. However, so far, how to detect these quantum phases
effectively remains an outstanding challenge. Here, we show that the optical Bragg scattering of cold atoms
loaded on optical lattices can be used to detect many quantum phases, which include not only the conventional
superfluid and Mott insulating phases, but also other important phases, such as various kinds of charge density
wave (CDW), valence bond solid (VBS), CDW supersolid (CDW-SS) and Valence bond supersolid (VB-SS).

We  investigate  ground  state  properties  of  the  attractive  Bose-gas  confined  on  square  optical  lattice  and
superimposed  wine-bottle-bottom  or  Mexican  hat  trap  potential.  The  system  is  modeled  by  two-dimensional  Bose-Hubbard model with attractive interactions and inhomogeneous lattice potential. We calculate the energy spectrum, the on-site  number  fluctuation,  local  density  and  local  compressibility  using  numerical  exact  diagonalization  method  for incommensurate  lattice  filling.  The  trap  potential  has  several  degenerate  minimum  sites  distributed  along  a  ring  at  the wine-bottle-bottom. It is shown that beyond a certain value of the attractive interaction strength there is phase coherent
condensate on these degenerate sites with finite value of the on-site number fluctuation and local compressibility giving
rise to localized superfluidity or superfluidity on a ring. For the same value of the interaction strength the non-degenerate sites produces Mott region.