There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

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

Experiments with ultracold quantum gases provide a platform for creating many-body systems that can be well controlled and whose parameters can be tuned over a wide range. These properties put these systems in an ideal position for simulating problems that are out of reach for classical computers. This review surveys key advances in this field and discusses the possibilities offered by this approach to quantum simulation.

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Quantum simulations with ultracold quantum gases

The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the $s$-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.

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Theory of ultracold atomic Fermi gases

We established superfluidity in a two-state mixture of ultracold fermionic atoms with imbalanced state populations. This study relates to the long-standing debate about the nature of the superfluid state in Fermi systems. Indicators for superfluidity were condensates of fermion pairs and vortices in rotating clouds. For strong interactions, near a Feshbach resonance, superfluidity was observed for a broad range of population imbalances. We mapped out the superfluid regime as a function of interaction strength and population imbalance and characterized the quantum phase transition to the normal state, known as the Pauli limit of superfluidity.

Fermionic Superfluidity with Imbalanced Spin Populations

We have observed Fermi polarons, dressed spin-down impurities in a spin-up Fermi sea of ultracold atoms. The polaron manifests itself as a narrow peak in the impurities' rf spectrum that emerges from a broad incoherent background. We determine the polaron energy and the quasiparticle residue for various interaction strengths around a Feshbach resonance. At a critical interaction, we observe the transition from polaronic to molecular binding. Here, the imbalanced Fermi liquid undergoes a phase transition into a Bose liquid, coexisting with a Fermi sea.

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Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms

We have observed phase separation between the superfluid and the normal component in a strongly interacting Fermi gas with imbalanced spin populations. The in situ distribution of the density difference between two trapped spin components is obtained using phase-contrast imaging and 3D image reconstruction. A shell structure is clearly identified where the superfluid region of equal densities is surrounded by a normal gas of unequal densities. The phase transition induces a dramatic change in the density profiles as excess fermions are expelled from the superfluid.

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Observation of phase separation in a strongly interacting imbalanced fermi gas

A major controversy has surrounded the stability of superfluidity in spin-polarized Fermi gas systems with resonant interactions when the 'up' and 'down' spin components are imbalanced. This problem is explored for a Fermi gas of 6Li atoms, using tomographic techniques to map out the superfluid phases as the temperature and density imbalance are varied. Evidence is found for various types of phase transitions, enabling quantitative tests of theoretical calculations on the stability of resonant superfluidity. The pairing of fermions lies at the heart of superconductivity and superfluidity. The stability of these pairs determines the robustness of the superfluid state, and the quest for superconductors with high critical temperature equates to a search for systems with strong pairing mechanisms. Ultracold atomic Fermi gases present a highly controllable model system for studying strongly interacting fermions1. Tunable interactions (through Feshbach collisional resonances) and the control of population or mass imbalance among the spin components provide unique opportunities to investigate the stability of pairing2,3,4—and possibly to search for exotic forms of superfluidity5,6. A major controversy has surrounded the stability of superfluidity against an imbalance between the two spin components when the fermions interact resonantly (that is, at unitarity). Here we present the phase diagram of a spin-polarized Fermi gas of 6Li atoms at unitarity, experimentally mapping out the superfluid phases versus temperature and density imbalance. Using tomographic techniques, we reveal spatial discontinuities in the spin polarization; this is the signature of a first-order superfluid-to-normal phase transition, and disappears at a tricritical point where the nature of the phase transition changes from first-order to second-order. At zero temperature, there is a quantum phase transition from a fully paired superfluid to a partially polarized normal gas. These observations and the implementation of an in situ ideal gas thermometer provide quantitative tests of theoretical calculations on the stability of resonant superfluidity.

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Phase diagram of a two-component Fermi gas with resonant interactions

Spin-polarized gaseous Bose-Einstein condensates were confined by a combination of gravitational and magnetic forces. The partially condensed atomic vapors were adiabatically decompressed by weakening the gravito-magnetic trap to a mean frequency of 1hertz, then evaporatively reduced in size to 2500 atoms. This lowered the peak condensate density to 5 × 1010 atoms per cubic centimeter and cooled the entire cloud in all three dimensions to a kinetic temperature of 450 ± 80 picokelvin. Such spin-polarized, dilute, and ultracold gases are important for spectroscopy, metrology, and atom optics.

https://science.sciencemag.org/content/sci/301/5639/1513.full.pdf

Andre Schirotzek

Papers

Fermionic Superfluidity with Imbalanced Spin Populations

Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms

Observation of phase separation in a strongly interacting imbalanced fermi gas

Phase diagram of a two-component Fermi gas with resonant interactions

Cooling Bose-Einstein Condensates Below 500 Picokelvin