Optical lattices, atoms

Many systems are being studied to manipulate quantum information. Some make use of individual atoms cold trapped ions, neutral atoms in optical lattices, atoms in crystals. Other involve particle spins or photons in cavity QED or nonlinear optical setups as well as more exotic ones where geometric combinations of elementary excitations are defined as qubits, such as in topological quantum computing [8]. However, none of these systems has yet emerged as a definitive way to build a quantum information processor. A reason for this is that there is an essential dichotomy we need... 

Summary. Coherent optical phonons are the lattice atoms vibrating in phase with each other over a macroscopic spatial region. With sub-10 fs laser pulses, one can impulsively excite the coherent phonons of a frequency up to 50THz, and detect them optically as a periodic modulation of electric susceptibility. The generation and relaxation processes depend critically on the coupling of the phonon mode to photoexcited electrons. Real-time observation of coherent phonons can thus offer crucial insight into the dynamic nature of the coupling, especially in extremely nonequilibrium conditions under intense photoexcitation. 

AM of the coupling arises, for example, for radiative-decay modulation due to atomic motion through a high-Q cavity or a photonic crystal [68,69], or for atomic tunneling in optical lattices with time-varying lattice acceleration [59,70], Let the coupling be turned on and off periodically, for the time and tq -, respectively,... 

Since the Hamiltonian for atoms in accelerated optical lattices is similar to the Legett Hamiltonian for current-biased Josephson junctions [37], the present theory has been extended to describe effects of current modulations on the rate of macroscopic quanmm tunneling in Josephson junctions in Ref. [11]. 

Figure 7.19 Schematic of the Rydberg induced many-body interaction among ultracold Rb atoms in an optical lattice. Reproduced from Ref. [51] with permission from Springer.

POSITION AND MOMENTUM ENTANGLEMENT OF DIPOLE-DIPOLE INTERACTING ATOMS IN OPTICAL LATTICES... 

Abstract We consider a possible realization of the position- and momentum-correlated atomic pairs that are confined to adjacent sites of two mutually shifted optical lattices and are entangled via laser-induced dipole-dipole interactions. The Einstein-Podolsky-Rosen (EPR) "paradox" [Einstein 1935] with translational variables is then modified by lattice-diffraction effects. We study a possible mechanism of creating such diatom entangled states by varying the effective mass of the atoms. 

Figure 2 Proposed scheme of two kinds of mutually shifted overlapping optical lattices used to create the translational EPR state. The lattices are displaced from each other in the y direction by l. They are sparsely occupied by two different kinds of atoms. Each kind of atoms interacts with a different lattice. The oval regions depict the energy minima (potential wells) of the lattices.

Our aim here is to demonstrate the feasibility of preparing a momentum- and position-entangled state of atom pairs in optical lattices, which would be a vari-... 

Let us focus on the subensemble of tube-pairs in which each tube is occupied by exactly one atom. In the ID optical lattice, the single-atom Hamiltonian in x representation is... 

Figure 10. Simulation of the EPR state preparation in an optical lattice with 25 sites, at three consecutive times. First row shows the joint probability distribution in x representation, the second one in p representation, (ol) and (a2) initially (t = 0), the atoms are cooled down to the external harmonic potential ground state, whereas the LIDDI is off. (61) and (62) at t = 1.4 x 10-4 s LIDDI and the repulsive linear potential (with the slope 0.04 Erec per lattice site) are on, whereas the harmonic potential is off. The diatoms are moving through the lattice very slowly in comparison to the single atoms, (cl) and (c2) at t = 2.16 x 10 4 s single atoms are ejected out of the lattice and discarded and the diatoms are separated out.

One may envision extensions of the present approach to matter teleportation [Opatrny 2001] and quantum computation based on continuous variables [Braunstein 1998 (a) Lloyd 1998 Lloyd 1999], Such extensions may involve the coupling of entangled atomic ensembles in optical lattices by photons carrying quantum information. 

Here the authors consider the possibility of inferring such statistical characteristics from the spectral features of probe photons or particles that are scattered by the density fluctuations of trapped atoms, notably in optical lattices, in two hitherto unexplored scenarios, (a) The probe is weakly (perturbatively) scattered by the local atomic density corresponding to the random occupancy of different lattice sites, (b) The probe is multiply scattered by an arbitrary (possibly unknown a priori) multi-atom distribution in the lattice. The highlight of the analysis, which is based on this random matrix approach, is the prediction of a semicircular spectral lineshape of the probe scattering in the large-fluctuation limit of trapped atomic ensembles. Thus far, the only known case of quasi-semicircular lineshapes in optical scattering has been predicted [Akulin 1993] and experimentally verified [Ngo 1994] in dielectric microspheres with randomly distributed internal scatterers. 

The paper by Katz et al. also focuses on BECs and presents new experimental and theoretical results on excitation evolution and decay in a BEC. As the field of Bose-Einstein condensation is rapidly maturing, new regimes of interest are now coming under scrutiny. These include trapping in various optical lattice potentials - leading to squeezed atomic states and the Mott in-... 

We consider the possibility of inferring such statistical characteristics from the spectral features of probe particles scattered by the density fluctuations (DF) of trapped atoms, notably in optical lattices (OL), in two hitherto unex-... 

Here a = kp m cp, with kp the Boltzmann constant, m the mass of the atoms and cp their specific heat, T denotes the temperature, 3 l = kpT and To is the optical lattice potential. The influence of evaporation becomes the dominant effect for T 25 // K. Around T 300 /iK these fluctuations become comparable in size to the square of the optical lattice potential ((IF2) Vq 100(neV)2) and atoms then largely escape from the lattice. 

Figure 1. Density of states g(t) of a probe scattered by bosonic atoms in a ID optical lattice. Solid, dotted and dashed curves stand for A(t) and the thick curve stands for A(e) (dispersion), see text. All curves are numerically computed from G(t) and correspond to average random couplings (IT2) = 0.4, 2 and 10 respectively. The hopping frequency J = 1, and for all curves f deg(t) = 1. Inset (a) a probe weakly scattered by a randomly occupied lattice. Inset (b) a probe multiply scattered by a regular atomic distribution.

Figure 2. DDF vs. temperature for bosonic and fermionic Li atoms in an optical lattice. Thin solid line fluctuations due to evaporation (12) (scaling factor 7.8), thin dashed line statistical fluctuations (13). Thick solid (dashed) line total fluctuations (W2) for bosonic (fermionic) Li atoms. Parameters Vo = 5 neV, (ns) = 0.1, d = 0.1 pm, cv Li) 3.6 x 106 J.kg-1.K-1, AF Li) = 6.10 10 m and u)v (Li) 2.106 s-1 [Kastberg 1995]. Inset solid (dashed) line static structure factor vs. n forphonons (nearly-free fermions) in a lattice at finite T.

In order to treat this system theoretically, the Bloch states of the strong optical lattice must be considered. In this picture we develop a model to explain the collisional decay of the oscillations as a two-particle collision of Bloch-states (and no longer free atoms). There are various quantum paths for this collision (since every lattice momentum has several relevant branches), leading to a destructive interference of the central s-wave collisional sphere, and a splitting in the resulting collisional shell, related to the observed spectral splitting. The matrix elements for this process lead to a suppression of the outward driven shell and enhance the centrally driven collisional shell, which is no longer... 

Here the time-dependent "acceleration" is a(t) = h t)/C, Uo = Ej, m = C and 2kl = 27r/T>o. We shall assume abrupt (step-like) changes of the tilt, causing the acceleration to periodically alternate between a I h(< I). within time intervals of length n, and d (e = 0), within time intervals of length ro — T. This time dependence is realizable in a JJ by rapid (< 0.1 ns) up-down ramping of the bias current. For atomic Bose condensates trapped in optical lattices [Smerzi 1997 Anderson 1998 (a)] we can turn the coupling and tilt between adjacent wells up and down by fast (< 10 ps) modulation of the laser intensity. 

ABSTRACT Radiative forces on atoms can be used both to cool the atoms to temperatures on the order of microkelvlns and to trap them in a periodic array of microscopic potential wells formed by the interference of multiple laser beams, i.e., an optical lattice. The quantum motion of such lattice-trapped atoms can be studied by spectroscopic techniques. Atoms trapped in this way may be further manipulated so as to be cooled by adiabatic expansion, localized by sudden compression or driven into mechanical oscillations. 

OPTICAL LATTICES Considering Fig. 1, and the fact that the thermal energy of the atoms cooled by the Sisjrphus process is about a tenth of the energy depth of the pictured potential wells, one sees that the atoms will become trapped in the potential wells. This is still true when one uses level schemes that are more complicated than J = 1/2 in the ground state. In spite of the atoms being trapped the temperature is linearly dependent on the depth of the well, just as predicted by the simple theory in which atoms are cooled as they move at a quasi-constant velocity across many wells. 

Because atoms are trapped in a periodic array of potentiail wells (formed by the interference of the beams used for laser cooling) such a situation is referred to as an optical lattice. We do not use the term "crystal" because in a crystal the atoms are self-organized due to the interactions between the atoms. In an optical lattice, the organization is imposed by the external light field and does not depend on Interactions between atoms. In fact, in most optical lattices, only a small fraction of the lattice sites are occupied by atoms and the effect of atom-atom interactions is negligible. 

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