This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition optical lattices, strongly interacting gases one two dimensions, or lowest-Landau-level physics quasi-two-dimensional fast rotation. Strong correlations fermionic are discussed lattices near-Feshbach resonances BCS-BEC crossover.

This paper presents the results of a functional-integral approach to dynamics two-state system coupled dissipative environment. It is primarily an extended account obtained over last four years by authors; while they try provide some background for orientation, it emphatically not intended as comprehensive review literature on subject. Its contents include (1) exact and general prescription reduction, under appropriate circumstances, problem tunneling between two wells in presence...

A quantum theory of cooling a mechanical oscillator by radiation pressure-induced dynamical back-action is developed, which analogous to sideband trapped ions. We find that final occupancies well below unity can be attained when the oscillation frequency larger than cavity linewidth. It shown average occupancy retrieved directly from optical output spectrum.

We study the statics and dynamics of a quantum Brownian particle moving in periodic potential coupled to dissipative environment way which reduces Langevin equation with linear friction classical limit. At zero temperature there is transition from an extended localized ground state as dimensionless \ensuremath{\alpha} raised through one. The scaling equations are derived by applying perturbative renormalization group system's partition function. studied using Feynman's influence-functional...

We present a self-consistent theory for the thermodynamics of BCS-BEC crossover in normal and superfluid phase which is both conserving gapless. It based on variational many-body formalism developed by Luttinger Ward DeDominicis Martin. Truncating exact functional entropy to that obtained within ladder approximation, resulting integral equations anomalous Green functions are solved numerically arbitrary coupling. The critical temperature, equation state, determined as function dimensionless...

We discuss the superfluid (SF) to Mott-insulator transition of cold atoms in optical lattices recently observed by Greiner et al (2002 Nature 415 39). The fundamental properties both phases and their experimental signatures are discussed carefully, including limitations standard Gutzwiller approximation. It is shown that a one-dimensional dilute Bose-gas with strong transverse confinement (Tonks-gas), even an arbitrary weak lattice able induce Mott-like state crystalline order, provided...

We realize and study a strongly interacting two-component atomic Fermi gas confined to two dimensions in an optical lattice. Using radio-frequency spectroscopy we measure the interaction energy of gas. observe confinement-induced Feshbach resonance find existence molecules very good agreement with theoretical predictions.

We study the dynamics of an atomic quantum dot, i.e., a single atom in tight optical trap which is coupled to superfluid reservoir via laser transitions. Quantum interference between collisional interactions and induced coupling results tunable dot-bath coupling, allowing essentially complete decoupling from environment. dots embedded 1D Luttinger liquid cold bosonic atoms realize spin-boson model with Ohmic exhibits dissipative phase transition allows us directly measure parameters.

Abstract Starting from a model of free Fermions in two dimensions with an arbitrary strong effective interaction, we derive Ginzburg‐Landau theory describing the crossover BCS‐superconductivity to Bose‐condensation. We find smooth standard BCS‐limit Gross‐Pitaevski type equation for order parameter Bose superfluid. The mean field transition temperature exhibits maximum at coupling strength, where behaviour crosses over BCS like corresponding values 2 Δ 0 /T c ≈ 5 which are characteristic...

A single down-spin fermion with an attractive zero-range interaction a Fermi sea of up-spin fermions forms polaronic quasiparticle. The associated quasiparticle weight vanishes beyond critical strength the interaction, where many-body bound state is formed. From variational wave function in molecular limit, we determine value for polaron-to-molecule transition. agrees well diagrammatic Monte Carlo results Prokof'ev and Svistunov consistent recent rf-spectroscopy measurements by Schirotzek et...

We present a calculation of the spectral functions and associated rf response ultracold fermionic atoms near Feshbach resonance. The single-particle spectra are peaked at energies that can be modeled by modified BCS dispersion. However, even very low temperatures their width is comparable to energy except for small region around dispersion minimum. structure excitation spectrum unitary gas infinite scattering length agrees with recent momentum-resolved critical temperature. A detailed...

We observe transport of electrons through a metallic island on the tip nanomechanical pendulum. The resulting tunneling current shows distinct features corresponding to discrete mechanical eigenfrequencies report measurements covering temperature range from 300 down 4.2 K. explain I-V curve, which unexpectedly differs previous theoretical predictions, with model calculations based master equation approach.

We discuss an integrable model of interacting fermions in one dimension that allows a complete description the crossover from BCS- to Bose-like superfluid. This bridges Gaudin-Yang attractive spin $1/2$ Lieb-Liniger repulsive bosons. Using geometric resonance one-dimensional scattering length, inverse coupling constant varies $\ensuremath{-}\ensuremath{\infty}$ $+\ensuremath{\infty}$ while system evolves BCS-like state through Tonks-Girardeau gas weakly Bose dimers. study ground energy,...

We investigate the physical properties of quasi-1D quantum gases fermionic atoms confined in harmonic traps. Using fact that for a homogeneous gas low-energy are exactly described by Luttinger model, we analyze nature and manifestations spin-charge separation, where case "spin" "charge" refer to two internal atomic states mass density, respectively. discuss necessary conditions experimental limitations confronting possible implementations.

An atomic gas subject to a commensurate periodic potential generated by an optical lattice undergoes superfluid-Mott insulator transition. Confining strongly interacting one dimension generates instability where arbitrary weak is sufficient pin the atoms into Mott state; here, we derive corresponding phase diagram. The pinned state may be detected via its finite excitation gap and Bragg peaks in static structure factor.

We analyze the quantum regime of dynamical backaction cooling a mechanical resonator assisted by driven harmonic oscillator (cavity). Our treatment applies to both optomechanical and electromechanical realizations includes effect thermal noise in oscillator. In perturbative case, we derive corresponding motional master equation using Nakajima–Zwanzig formalism calculate output spectrum for case. Then strong coupling limit small cavity linewidth. Finally, consider steady state covariance...

Using the adaptive time-dependent density-matrix renormalization group method for 1D Hubbard model, splitting of local perturbations into separate wave packets carrying charge and spin is observed in real-time. We show robustness this separation beyond low-energy Luttinger liquid theory by studying time-evolution single particle excitations density packets. A striking signature spin-charge found cold Fermi gases a harmonic trap at boundary between Mott-insulating phases. give quantitative...

We show that strong pairing correlations in Fermi gases lead to the appearance of a gaplike structure rf spectrum, both balanced superfluid and normal phase above Clogston-Chandrasekhar limit. The average shift unitary gas is proportional ratio velocity scattering length with final state. In strongly imbalanced case, spectrum measures binding energy minority atom sea majority atoms. Our results provide qualitative understanding recent experiments by Schunck et al.

We investigate a quasi-one dimensional system of trapped cold bosonic atoms in an optical lattice by using the density matrix renormalization group to study Bose-Hubbard model at T=0 for experimentally realistic numbers sites. It is shown that properly rescaled one-particle characterizes superfluid versus insulating states just as homogeneous system. For typical parabolic traps we also confirm widely used local approach describing correlations limit weak interaction. Finally, note...

We discuss the effective interactions between two localized perturbations in one-dimensional (1D) quantum liquids. For non-interacting fermions, exhibit Friedel oscillations, giving rise to a RKKY-type interaction familiar from impurity spins metals. In interacting case, at low energies, Luttinger liquid description applies. case of repulsive oscillations system are replaced, long distances, by universal Casimir-type which depends only on sound velocity and decays inversely with separation....