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 in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.

https://arxiv.org/pdf/cond-mat/9806038.pdf

Theory of Bose-Einstein condensation in trapped gases

1. Introduction 2. Theoretical foundations 3. Propagation and focusing of optical fields 4. Spatial resolution and position accuracy 5. Nanoscale optical microscopy 6. Near-field optical probes 7. Probe-sample distance control 8. Light emission and optical interaction in nanoscale environments 9. Quantum emitters 10. Dipole emission near planar interfaces 11. Photonic crystals and resonators 12. Surface plasmons 13. Forces in confined fields 14. Fluctuation-induced phenomena 15. Theoretical methods in nano-optics Appendices Index.

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Principles of nano-optics

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.

Feshbach resonances in ultracold gases

The author shows that a system of charged harmonic oscillators interacting with one transverse electromagnetic field mode does not undergo the super-radiant phase transition. The proof does not make use of the multipole expansion and takes retardation into account.

http://iopscience.iop.org/0305-4470/12/11/024/pdf/0305-4470_12_11_024.pdf

Thermodynamics of oscillators interacting with radiation

We extend our model for two-color above threshold ionization to include an infinite number of continua, which are labeled by their angular momenta. Results are presented for the photoelectron spectra and the angular photoelectron distributions.

Photoelectron angular distributions and energy spectra of atomic hydrogen in above threshold ionization

We present results for the statistics of scattered photons using a quantum electrodynamic description of spontaneous emission from a continuum state to a bound state. The continuum has a resonant structure, the so-called Fano profile1, which accounts for the mixing of a multielectron discrete state with the continuum.

Photoemission Spectra for Laser-Induced Autoionization in Strong Fields: Phase Fluctuations and Radiative Damping

We analyze the ground state of the two-component gas of trapped ultracold fermionic atoms. We neglect the forces between atoms in the same hyperfine state (the same component). For the case when the forces between distinguishable atoms (i.e., atoms in different hyperfine states) are repulsive (positive mutual scattering length), we find the existence of critical interaction strength above which one atomic fraction expels the other from the center of the trap. When atoms from different components attract each other (negative mutual scattering length) the ground state of the system dramatically changes its structure for strong enough attraction-the Cooper pairs built of atoms in different hyperfine states appear.

Ground state of two-component degenerate fermionic gases (9 pages)

A model of strong bound-free coupling by a stochastic train of delta-function impulses is solved analytically. The model can be used to describe transitions caused by strong isolated collisions. The decay of bound-state population and photoelectron spectra is discussed, and the limits of the applicability of Fermi’s Golden Rule are evaluated. It turns out that the results depend nontrivially on the statistics of the driving signal.

Kazimierz Rzazewski

Papers

Thermodynamics of oscillators interacting with radiation

Photoelectron angular distributions and energy spectra of atomic hydrogen in above threshold ionization

Photoemission Spectra for Laser-Induced Autoionization in Strong Fields: Phase Fluctuations and Radiative Damping

Ground state of two-component degenerate fermionic gases (9 pages)

Collisionally induced configuration mixing: soluble model with continuous spectrum