We discuss the dynamic properties of a trapped Bose-condensed gas under variations confining field and find analytical scaling solutions for evolving coherent state (condensate). further characteristic features depletion this state.

We discuss three-body recombination of ultracold atoms to a weakly bound $s$ level. In this case, characterized by large and positive scattering length $a$ for pair interaction, we find repulsive effective potential collisions, which strongly reduces the probability. zero temperature limit obtain universal relation, independent detailed shape interaction potential, (event) rate constant recombination:...

We find scaling solutions for the evolution of a Bose gas in time-dependent anisotropic traps and reveal phenomenon stochastization condensate. In contrast to collisionless gases, thermal hydrodynamic regime proves be many aspects similar that emphasize clear signatures Bose-Einstein condensation effects loss coherence can found local correlation properties evolving through measurement rates intrinsic or light-induced inelastic collisional processes.

We discuss Bose-Einstein condensation in a trapped atomic gas and analyze how the sign of scattering length ratio \ensuremath{\eta} interaction between particles to level spacing trap influence behavior condensate wave function ${\ensuremath{\psi}}_{0}$. find that for $a<0$ $\ensuremath{\eta}\ensuremath{\ll}1$ it is possible form metastable Bose condensate, with long characteristic lifetime respect contraction transitions excited states. For $\ensuremath{\eta}\ensuremath{\gg}1$ negative...

We show a significant reduction of the number quantum operations and improvement circuit depth for realization Toffoli gate by using qudits. This is done establishing general relation between dimensionality qudits their topology connections scalable multiqudit processor, where higher qudit levels are used substituting ancillas. The suggested model importance algorithms as method error correction codes single-qubit operations.

We consider dipolar excitations propagating via dipole-induced exchange among immobile molecules randomly spaced in a lattice. The character of the propagation is determined by long-range hops (Levy flights). analyze eigenenergy spectra and multifractal structure wave functions. In 1D 2D, all states are localized, although 2D localization length can be extremely large leading to an effective localization-delocalization crossover realistic systems. 3D, eigenstates extended but not always...

We consider weakly interacting bosons in a 1D quasiperiodic potential (Aubry-Azbel-Harper model) the regime where all single-particle states are localized. show that interparticle interaction may lead to many-body delocalization and we obtain finite-temperature phase diagram. Counterintuitively, wide range of parameters requires stronger coupling as temperature increases. This means system can undergo transition from fluid insulator (glass) state under heating.

Abstract Remarkable advancements in the ability to create, manipulate, and measure quantum systems are paving way build next generations of devices based on physics. Quantum technologies Russia list strategically important cross-cutting directions framework National Technology Initiative programs Digital Economy Program. The broad focus includes computing simulation, communications, metrology sensing. This paper reviews existing research science summarizes main goals for few years that form...

We demonstrate many-body localization (MBL) transition in a one-dimensional isotropic XY chain with weak next-nearest-neighbor frustration random magnetic field. perform finite-size exact diagonalization calculations of level-spacing statistics and fractal dimensions to characterize the MBL increasing field amplitude. An equivalent representation model terms spinless fermions explains presence delocalized phase by appearance an effective non-local interaction between fermions. This appears...

Two-atom systems in small traps are of fundamental interest for understanding the role interactions degenerate cold gases and creation quantum gates information processing with single-atom traps. One key quantities is inelastic relaxation (decay) time when one atoms or both a higher hyperfine state. Here we measure this quantity heteronuclear system (87)Rb (85)Rb micro optical trap demonstrate experimentally theoretically presence fast slow processes, depending on choice initial states. This...

We study inelastic two-body relaxation in a spin-polarized ultracold Fermi gas the presence of $p$-wave Feshbach resonance. It is shown that reduced dimensionalities, especially quasi-one-dimensional case, enhancement rate constant on approach to resonance strongly suppressed compared three dimensions. This may open promising paths for obtaining novel many-body states.

We discuss the emergence of $p$-wave superfluidity identical atomic fermions in a two-dimensional optical lattice. The lattice potential manifests itself an interplay between increase density states on Fermi surface and modification fermion-fermion interaction (scattering) amplitude. is enhanced due to effective mass atoms. In deep lattices scattering amplitude strongly reduced compared free space small overlap wave functions sitting neighboring sites, which suppresses superfluidity....

Significance One-dimensional bosons in disorder provide a perfect system for studying generic phenomenon of many-body localization–delocalization transition. After the observation single-particle Anderson localization dilute clouds bosonic atoms, obvious direction research is to describe effects repulsion between bosons. Theoretical studies 1D interacting have long history. In case strong enough and zero temperature, problem was solved by Giamarchi Schulz 1988, and, more recently, limit weak...

We analyze the collisionless motion of atoms in magnetic traps relation to evaporative cooling. For example a long Ioffe quadrupole trap we investigate both regular and stochastic regimes motion. emphasize strong influence regime on process evaporation across an axial potential barrier at energies above enables three-dimensional evaporation, i.e., particles acquiring elastic collisions total enery higher than height ${\mathit{E}}_{0}$ escape from trap. The leads evaporation: only which due...

Abstract Recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids fermionic polar molecules. It becomes realistic to obtain a topological p -wave superfluid microwave-dressed molecules in 2D at temperatures order tens nanokelvins, which is promising topologically protected quantum information processing. Another foreseen phase an interlayer bilayer geometry.

We predict and analyze nontrivial relaxational behavior of magnetically trapped gases near the Bose-condensation temperature ${\mathit{T}}_{\mathit{c}}$. Due to strong compression condensate by inhomogeneous trapping field, particularly at low densities, relaxation rate shows a strong, almost jumplike, increase below As consequence maximum fraction particles is limited few percent. This phenomenon can be called ``relaxation explosion.'' discuss its implication for detectability Bose-Einstein...

We present an analytical and numerical analysis of collisionless motion neutral particles in magnetostatic traps. treat the example idealized Ioffe quadrupole trap, emphasizing that essential features coupling between degrees freedom are general relevance for static In common situations axial radial predominantly occurs a regular way. The is weak, particular, when frequency oscillations ${\mathrm{\ensuremath{\Omega}}}_{\mathit{z}}$ much smaller than...

We study the one-dimensional Hubbard model for two-component fermions with infinitely strong on-site repulsion ($t\ensuremath{-}0$ model) in presence of disorder. Our analytical treatment demonstrates that type disorder drastically changes nature emerging phases. The case spin-independent can be treated as a single-particle problem Anderson localization. On contrary, recent numerical findings show spin-dependent disorder, which realized random magnetic field, leads to many-body...

We consider a one-dimensional two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study effect of an SU(2)-symmetry-breaking near-resonant odd- wave within one components. Starting from microscopic Hamiltonian, we derive effective field theory for spin degrees freedom using bosonization technique. It is shown that at critical value odd-wave there first-order phase transition zero total magnetization to spin-segregated where locally differs zero.

We find that inelastic collisional processes in Bose-Einstein condensates induce local variations of the mean-field interparticle interaction, and are accompanied by creation annihilation elementary excitations. The physical picture is demonstrated for case three-body recombination a trapped condensate. For high trap barrier production high-energy single-particle excitations results strong increase loss rate atoms from

We consider a weakly interacting two-component Fermi gas of dipolar particles (magnetic atoms or polar molecules) in two-dimensional geometry. The dipole-dipole interaction (together with the short-range at Feshbach resonances) for dipoles perpendicular to plane translational motion may provide superfluid transition. scattering amplitude is momentum dependent, which violates Anderson theorem that claims independence transition temperature on presence weak disorder. have shown disorder can...