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

For a system at a temperature of absolute zero, all thermal fluctuations are frozen out, while quantum fluctuations prevail. These microscopic quantum fluctuations can induce a macroscopic phase transition in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value. Here we observe such a quantum phase transition in a Bose-Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. As the potential depth of the lattice is increased, a transition is observed from a superfluid to a Mott insulator phase. In the superfluid phase, each atom is spread out over the entire lattice, with long-range phase coherence. But in the insulating phase, exact numbers of atoms are localized at individual lattice sites, with no phase coherence across the lattice; this phase is characterized by a gap in the excitation spectrum. We can induce reversible changes between the two ground states of the system.

Quantum Phase Transition From a Superfluid to a Mott Insulator in a Gas of Ultracold Atoms

The statistical error in any estimation can be reduced by repeating the measurement and averaging the results. The central limit theorem implies that the reduction is proportional to the square root of the number of repetitions. Quantum metrology is the use of quantum techniques such as entanglement to yield higher statistical precision than purely classical approaches. In this Review, we analyse some of the most promising recent developments of this research field and point out some of the new experiments. We then look at one of the major new trends of the field: analyses of the effects of noise and experimental imperfections.

Advances in quantum metrology

This Colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems There is particularly a focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian Several aspects of the slow dynamics in driven systems are discussed and the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions is emphasized Recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis is also reviewed and relaxation in integrable systems is discussed Finally key experiments probing quantum dynamics in cold atom systems are overviewed and put into the context of our current theoretical understanding

Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.

Dynamics of Bose-Einstein condensates in optical lattices

We report manipulation of the atom number statistics associated with Bose-Einstein condensed atoms confined in an array of weakly linked mesoscopic traps We used the interference of atoms released from the traps as a sensitive probe of these statistics By controlling relative strengths of the tunneling rate between traps and atom-atom interactions within each trap, we observed trap states characterized by sub-Poissonian number fluctuations and adiabatic transitions between these number-squeezed states and coherent states of the atom field The quantum states produced in this work may enable substantial gains in sensitivity for atom interference-based instruments as well as fundamental studies of quantum phase transitions

https://science.sciencemag.org/content/sci/291/5512/2386.full.pdf

Squeezed states in a Bose-Einstein condensate

The study of ionized gases in neutral plasma physics spans temperatures ranging from 10 16 K in the magnetosphere of a pulsar to 300 K in the earth’s ionosphere [1]. At lower temperatures, the properties of plasmas are expected to differ significantly. For instance, three-body recombination, which is prevalent in high temperature plasmas, should be suppressed [2]. If the thermal energy of the particles is less than the Coulomb interaction energy, the plasma becomes strongly coupled, and the usual hydrodynamic equations of motion and collective mode dispersion relations are no longer valid [3]. Strongly coupled plasmas are difficult to produce in the laboratory and only a handful of examples exist [4], but such plasmas do occur naturally in astrophysical systems. In this work, we create an ultracold neutral plasma with an electron temperature as low as Te 100 mK, an ion temperature as low as Ti 10 mK, and densities as high as n 2 3 10 9 cm 23 . We obtain this novel plasma by photoionization of laser-cooled xenon atoms. Within the experimentally accessible ranges of temperatures and densities, both components can be simultaneously strongly coupled. A simple model describes the evolution of the plasma in terms of the competition between the kinetic energy of the electrons and the Coulomb attraction between electrons and ions. A numerical calculation accurately reproduces the data. Photoionization and laser cooling have been used before in plasma experiments. Photoionization in a 600 K Cs vapor cell produced a plasma with Te $ 2000 K [5], and a strongly coupled non-neutral plasma was created by laser cooling magnetically trapped Be 1 ions [6]. A plasma is often defined as an ionized gas in which the charged particles exhibit collective effects [7]. The length scale which divides individual particle behavior and collective behavior is the Debye screening length lD. It is the distance over which an electric field is screened by redistribution of electrons in the plasma, and is given by lD p

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Creation of an Ultracold Neutral Plasma

Optical Control of Ultracold Collisions in Metastable Xenon.

We study the nonequilibrium evolution of the phase coherence of a Bose-Einstein condensate in a one-dimensional optical lattice as the lattice array is suddenly quenched from a highly-number-squeezed to a superfluid state. We observe slowly damped phase coherence oscillations in the regime of large filling factor ($\ensuremath{\sim}100$ bosons per site) at a frequency proportional to the generalized Josephson frequency.

Nonequilibrium coherence dynamics of a soft boson lattice

We have measured ultracold ionizing collision rates for three bosonic ${(}^{132}\mathrm{Xe},{}^{134}\mathrm{Xe},$ and ${}^{136}\mathrm{Xe})$ and two fermionic ${(}^{129}\mathrm{Xe}$ and ${}^{131}\mathrm{Xe})$ isotopes of xenon in the $6s[3/2{]}_{2}$ metastable state, for both spin-polarized and unpolarized samples. For unpolarized samples at temperatures above the p-wave centrifugal barrier $(\ensuremath{\sim}39 \ensuremath{\mu}\mathrm{K}),$ we find that collision rates for all isotopes are identical. Quantum-statistical effects forbid s-wave collisions for spin-polarized fermions, giving rise to significant differences between bosonic and fermionic isotopes below the p-wave barrier. We present a technique for measuring collision rates at temperatures below $1 \ensuremath{\mu}\mathrm{K},$ and find that the ratio of polarized to unpolarized collision rates for fermions decreases by a factor of 2 at low temperatures, while the ratio for bosons increases by $50%.$ We find no evidence of an overall reduction in the collision rate for spin-polarized samples, as has been observed in metastable helium. These results are explained using a simple theoretical model of transmission and quantum reflection off long-range interatomic potentials.

Chad Orzel

Papers

Squeezed states in a Bose-Einstein condensate

Creation of an Ultracold Neutral Plasma

Optical Control of Ultracold Collisions in Metastable Xenon.

Nonequilibrium coherence dynamics of a soft boson lattice

Spin polarization and quantum-statistical effects in ultracold ionizing collisions