Incommensurate Wavelengths Research Articles

Local integrals of motion in quasiperiodic many-body localized systems

Local integrals of motion play a central role in the understanding of many-body localization in many-body quantum systems in one dimension subject to a random external potential, but the question of how these local integrals of motion change in a deterministic quasiperiodic potential is one that has received significantly less attention. Here we develop a powerful new implementation of the continuous unitary transform formalism and use this method to directly compute both the effective Hamiltonian and the local integrals of motion for many-body quantum systems subject to a quasiperiodic potential. We show that the effective interactions between local integrals of motion retain a strong fingerprint of the underlying quasiperiodic potential, exhibiting sharp features at distances associated with the incommensurate wavelength used to generate the potential. Furthermore, the local integrals of motion themselves may be expressed in terms of an operator expansion which allows us to estimate the critical strength of quasiperiodic potential required to lead to a localization/delocalization transition, by means of a finite size scaling analysis.

Asymmetric high energy dual optical parametric amplifier for parametric processes and waveform synthesis.

We report on an asymmetric high energy dual optical parametric amplifier (OPA) which is capable of having either the idlers, signals, or depleted pumps, relatively phase locked at commensurate or incommensurate wavelengths. Idlers and signals can be locked on the order of 200 mrad rms or better, corresponding to a 212 as jitter at λ=2 µm. The high energy arm of the OPA outputs a combined 3.5 mJ of signal and idler, while the low energy arm outputs 1.5 mJ, with the entire system being pumped with a 1 kHz, 18 mJ Ti:Sapphire laser. Both arms are independently tunable from 1080 nm-2600 nm. The combination of relative phase locking, high output power and peak intensity, and large tunability makes our OPA an ideal tool for use in difference frequency generation (DFG) in the strong pump regime, and for high peak field waveform synthesis in the near-infrared. To demonstrate this ability we generate terahertz radiation through two color waveform synthesis in air plasma and show the influence of the relative phase on the generated terahertz intensity. The ability to phase lock multiple incommensurate wavelengths at high energies opens the door to a multitude of possibilities of strong pump DFG and waveform synthesis.

Laser-induced plasma generation of terahertz radiation using three incommensurate wavelengths

We present the generation of THz radiation by focusing ultrafast laser pulses with three incommensurate wavelengths to form a plasma. The three colors include 800 nm and the variable IR signal and idler outputs from an optical parametric amplifier. We observe that stable THz is generated when all three colors are present, with a peak-to-peak field strength of ∼200 kV cm−1 and a relatively broad, smooth spectrum extending out to 6 THz, without any strong dependence on the selection of signal and idler IR wavelengths (in the range from 1300 to 2000 nm). We confirm that three colors are indeed needed, and we present plasma current modeling that corroborates our observations.

Localization of a dipolar Bose–Einstein condensate in a bichromatic optical lattice

By numerical simulation and variational analysis of the Gross–Pitaevskii equation we study the localization, with an exponential tail, of a dipolar Bose–Einstein condensate (DBEC) of 52Cr atoms in a three-dimensional bichromatic optical lattice (OL) generated by two monochromatic OLs of incommensurate wavelengths along three orthogonal directions. For a fixed dipole–dipole interaction, a localized state of a small number of atoms (∼1000) could be obtained when the short-range interaction is not too attractive or not too repulsive. A phase diagram showing the region of stability of a DBEC with a short-range interaction and dipole–dipole interaction is given.

Localization of a Bose-Einstein-condensate vortex in a bichromatic optical lattice

By numerical simulation of the time-dependent Gross-Pitaevskii equation we show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC) vortex can be localized in a three-dimensional bichromatic quasiperiodic optical-lattice (OL) potential generated by the superposition of two standing-wave polarized laser beams with incommensurate wavelengths. We also study the localization of a (nonrotating) BEC in two and three dimensions by bichromatic OL potentials along orthogonal directions. This is a generalization of the localization of a BEC in a one-dimensional bichromatic OL as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We demonstrate the stability of the localized state by considering its time evolution in the form of a stable breathing oscillation in a slightly altered potential for a large period of time. Finally, we consider the localization of a BEC in a random one-dimensional potential in the form of several identical repulsive spikes arbitrarily distributed in space.

An ideal Bose–Einstein condensate: From Anderson localization to precision measurements

The experimental achievement of Bose–Einstein condensation (BEC) in dilute atomic systems has opened up the study of several quantum phenomena, linking together different subfields of physics. In particular, Bose–Einstein condensates in optical potentials represent a great opportunity for engineering simple quantum systems, acting as a quantum simulator of much more complicated physics. Here we describe two different experiments that show the high potentialities offered by combining a tunable interacting BEC of potassium atoms and periodic potentials. In the first experiment we trap the ideal BEC in a quasi-periodic potential obtained superimposing two laser standing waves with incommensurate wavelengths. In this case we observe the Anderson transition from extended to exponentially localized states with coherent matter waves. We clearly demonstrate localization by investigating transport properties, spatial and momentum distributions. Since the interaction in the condensate can be controlled, thanks to a broad Feshbach resonance, this system represents a novel tool to solve fundamental questions on the interplay of disorder and interaction and to explore exotic quantum phases. In a second experiment we instead realize an atomic lattice-based interferometer with very high-spatial resolution. We measure a strong increase of the coherence time of the interferometer with vanishing scattering lengths, and we get evidence of the effect of the weak magnetic dipole–dipole interaction.

Modulated Misfit Structure of the Thermoelectric [Bi0.84CaO2]2[CoO2]1.69 Cobalt Oxide

The structure of the thermoelectric lamellar misfit cobalt oxide [Bi0.84CaO2]2[CoO2]1.69 has been refined using single crystal X-ray diffraction data. Using the four dimensional superspace formalism for aperiodic structures, the superspace group is confirmed P2/m(0delta1/2) (a1 = 4.9069(4), b1 = 4.7135(7), b2 = 2.8256(4), c1 = 14.668(5) A, beta1 = 93.32(1) degrees). The modulated displacements and site occupancies have been refined and are both compatible with the misfit character of the structure, and with a longitudinal modulation of the Bi-O layers of the structure. This modulation is similar to the corresponding one in the related Sr phase [Bi0.87SrO2]2[CoO2]1.82, but now oriented in the orthogonal direction. Because its incommensurate wavelength is locked with the aperiodicity of the misfit structure, it is possible to distinguish between the modulation parameters induced by the accommodation of both subsystems and those related to the longitudinal modulation of the Bi-O layers. In this original structure, two independent aperiodic phenomena coexist in an single crystallographic direction. A particular attention has been paid to the structural configuration of the CoO2 layer, in relation with other similar phases. The thermoelectric properties are probably directly related to the specific distortion of the compressed layer, but the different measured values for the Seebeck coefficient cannot be related to a significant modification of the CoO6 octahedra.

Energy localization and transport in two-dimensional Fermi–Pasta–Ulam lattices

We investigate energy localization and transport in the form of discrete breathers and their movability in two-dimensional Fermi–Pasta–Ulam(FPU) lattices. We study the dynamics of the two-dimensional Fermi–Pasta–Ulam(FPU) lattice, incorporating the complicated effects of geometry, long-range interactions as well as nonlinear dispersion. We obtain several exact discrete breather(DB) solutions, such as the odd-parity and even-parity DBs, compact-like DBs and moving DBs for various geometries of the two-dimensional FPU chain. We show that DBs also exist in the same lattice in presence of next-nearest neighbour interaction. Large-amplitude exact subsonic travelling kink-soliton solutions are obtained in such a periodic chain in presence of long-range nonlinear dispersive interaction in the long-wavelength and weakly nonlinear limit. Such a two-dimensional FPU lattice admits finite amplitude nonlinear sinusoidal wave (NSW) solutions with short commensurate as well as incommensurate wavelengths for different geometries of the chain. The usefulness of these solutions for energy localization and transport in various physical systems are discussed.

Dynamics of a curved Fermi-Pasta-Ulam chain: Effects of geometry, long-range interaction, and nonlinear dispersion

We study the dynamics of the bent Fermi-Pasta-Ulam (FPU) chain, incorporating the complicated effects of geometry, long-range interactions, as well as nonlinear dispersion. Within the rotating wave approximation, we obtain several exact discrete breather (DB) solutions, such as the odd-parity and even-parity discrete breathers, compactlike discrete breathers and moving discrete breathers for various geometries of the chain. In presence of long-range nonlinear dispersive interactions, we show that DBs exist in the discrete curved lattice for next-nearest-neighbor interactions as well. For all neighbors interactions, we treat the problem in the long-wavelength (continuum) and weakly nonlinear limit of the system and obtain exact static breather solutions and large-amplitude, traveling kink-soliton solutions. The curved FPU chain also admits finite amplitude discrete nonlinear sinusoidal wave solutions with short commensurate as well as incommensurate wavelengths. The usefulness of these solutions for energy localization and transport in various physical systems are discussed.

Anomalous pressure-induced transition(s) in ice XI.

The effects of pressure on the structure of ice XI-an ordered form of the phase of ice Ih, which is known to amorphize under pressure-are investigated theoretically using density-functional theory. We find that pressure induces a mechanical instability, which is initiated by the softening of an acoustic phonon occurring at an incommensurate wavelength, followed by the collapse of the entire acoustic band and by the violation of the Born stability criteria. It is argued that phonon collapse may be a quite general feature of pressure-induced amorphization. The implications of our findings for the amorphization of ice Ih are also discussed.

An atomic model for premartensitic tweed in Ni-Al as derived from HREM images

The premartensitic microstructures observed in the quenched Ni1-XAlx (B2) phase have been examined at room temperature by HREM. Depending on the composition the material transforms martensitically to a close-packed 7R (5) stacking at Ms≈200 K (x=0.37) or to the 3R (L10) structure at Ms≈290 K (x=0.36). In CTEM images the premartensitic structure is revealed as the well known two-beam tweed contrast. In HREM phase contrast images a random fine-scale mosaic assembly of micromodulated domains is observed (fig. 1). Fig. 2 shows a single domain in which the intensity modulation can clearly be seen. From images taken under different conditions the following observations (among others) could be made: 1) the micromodulation has an averaged incommensurate wavelength of≈1.3 nm, 2) OD reproduces the <110>* diffuse streaks confirming the static nature and the correlation with the tweed image, 3) each domain exhibits a single modulation, 4) the intensity difference is of the order of 60-85%, 5) some images (e.g., fig. 2) reveal dots elongated perpendicular to the wave-vector, 6) in some cases a small average deviation (≈1%) from the cubic symmetry can be measured. These different characteristics could be explained by assuming, per domain, small transverse shuffle plus shear distortions of the {110}<> type and including a decrease in atom displacement from the center to the edge of each domain. The atomic model and one calculated image are presented in fig. 3.

Smectic–smectic phase transitions in binary liquid-crystalline mixtures of DB5–T8

We have used high-resolution x-ray diffraction and ac calorimetry to study the liquid–crystalline smectic-A-smectic-A phase transitions in binary mixtures of polar mesogenic compounds DB5 [benzoic acid, (4-cyano)-4-[(4-pentylphenoxy) carbonyl] phenyl ester] and T8 [(E)-benzoic acid, 4-octyloxy-4-[2-(4-cyanophenyl) ethenyl] phenyl ester]. A detailed synthesis for each of these compounds is presented. The smectic A1 phase in this system shows two collinear diffuse x-ray maxima at incommensurate wave vectors, indicating a tendency to form the predicted Ai1 phase with two strongly coupled density modulations having incommensurate wavelengths. The Ad peak position, while both temperature and concentration dependent, is remarkably constant along the N–Ad phase boundary. In the vicinity of 16 mol % T8, both the x-ray and heat-capacity results are reproducibly history dependent. The simultaneous observation of sharp A2 and Ad peaks most likely results from phase coexistence, but a condensed incommensurate Ai2 phase cannot be ruled out.

Planar defects and surfaces in crystals undergoing structural phase transitions.

A one-dimensional model assuming any finite range of effective, temperature-dependent harmonic interactions is proposed to describe structural phase transitions driven by a single soft mode. Incommensurate wavelengths of the soft mode are included. Static and dynamic response functions are derived for the model crystal in a closed form and are shown to be analytically expressible if the range of interactions does not exceed four nearest neighbors. The response functions are applied here to the study of distortions caused by planar defects and free surfaces for the model with third-nearest-neighbor interactions, which is the simplest case capable of reproducing a commensurate-incommensurate phase transition. The pretransitional appearance of modulated structures, the relaxed surface structure, and the surface-relaxation instability are quantitatively accounted for as functions of the effective force constants.

Incommensurate Coexistent Density Fluctuations in Liquid-Crystal Phases of Cyano Compounds

X-ray diffraction investigations of both nematic and smectic phases of a number of compounds containing cyano end groups have revealed several of them to have a novel structure. This consists of two coexisting mass density fluctuations (heavily damped for the nematics) with incommensurate wavelengths corresponding, respectively, to some-what less than the molecular length $l$ and to the cyano bilayer spacing ($\ensuremath{\sim}1.4l$).