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Theory of quantum gases
Lev P. Pitaevskii,
Ultracold gases are the archetype of a wider class of systems known as quantum fluids. They are dilute and clean; they can be confined in different 3D, 2D and 1D geometries; the interaction between particles can be tuned from very weak to very strong. This is why the theory of these gases is so rich. It is also interdisciplinary, many key concepts being used in different contexts as well, such as solid state physics, superconductors, superfluid helium, neutron stars, but also in systems of photons and more exotic particles.
The theoretical activity in Trento ranges from the description of dilute Bose gases using Gross-Pitaevskii theory to the implementation of more advanced many-body approaches for strongly correlated systems and interacting Fermi gases. Both equilibrium and dynamic properties are investigated at zero and at finite temperatures. Particular attention is devoted to superfluid and quantum coherence effects, quantum mixtures, long range interactions, magnetic properties, low dimensionality and optical lattices.
GP simulations of quantized vortices in a rotating condensate
Superfluidity, like superconductivity, is a spectacular manifestation of quantum mechanics in macroscopic systems. It was first observed in liquid Helium in the late 30's and soon became the object of important experimental investigations and theoretical studies, attracting the attention of leading scientists worldwide.
Ultracold atoms provide an extremely rich environment for studying superfluid phenomena, which are observed below a critical temperature in both Bose and Fermi gases. The peculiar hydrodynamic nature of the collective oscillations, the propagation of first and second sound, the quantization of vorticity, the reduction of the moment of inertia, the existence of permanent currents, the absence of viscosity, are all key aspects of superfluidity. The Trento team has given important contributions to the understanding of these phenomena, developing theoretical approaches, interpreting experimental observations, and stimulating new experiments to test the theoretical predictions.
First and second sound
in a trapped Fermi gas
Matter waves, coherence and disorder
Condensate flowing past an obstacle
Bose-Einstein condensates, and superfluids in general, are characterized by a complex order parameter having a well-defined phase. The appearance of this phase has important consequences. It gives rise to Josephson effects in the presence of weak links or in a double-well geometry. It causes interference patterns in the expansion of BECs, or when a BEC is released from an optical lattice. It produces peculiar effects when the gas is moving in a disordered potential or in the presence of obstacles or impurities. Ultracold atomic gases have been shown to be an extremely versatile tool to investigate all of these effects. Thanks to their extreme controllability, they allow for the characterization of the interplay between phase coherence and decoherence processes, with many implications in the fields of quantum information and quantum computation, among others. Several research lines have been devoted to these topics in Trento.
Strongly interacting Fermi gases
Interacting Fermi gases exhibit a rich variety of many-body states, ranging from a superfluid phase of Cooper pairs to the formation of bosonic molecules. A continuous transition between those regimes, known as BCS-BEC crossover, can be realized experimentally by using an external magnetic field to tune the value of the scattering length across a Feshbach resonance. Exactly on resonance, one finds the unitary Fermi gas, characterized by an infinitely large scattering length leading to a universal behaviour of the thermodynamic functions.
A large number of interesting issues concerning strongly correlated Fermi gases are still open. Among them, the consequences of superfluidity on the dynamics, the properties of solitons and vortices, and the effects of spin polarization are currently the object of deep investigations using different many-body approaches.
The Trento team has published a review paper on this subject: Theory
of ultracold atomic Fermi gases, S.Giorgini, L.Pitaevskii and S.Stringari,
Reviews of Modern Physics 80, 1215 (2008).
A dark solitons developes
a snake instability in
a unitarity Fermi gas
Lowest excitation bands
of a spin-orbit coupled BEC
Quantum mixtures and spinor gases
Mixtures of cold gases exhibit many interesting features, related to their ground states and excitations, that are absent in single-component gases. One can realize Bose-Bose, Fermi-Fermi or Fermi-Bose mixtures, controlling the relative population from the case of a single impurity in a bath, to spinor gases or exotic and subtle phases.
The impurity problem with fermions is relevant for developing a Landau-Fermi liquid theory for strongly interacting gases. For bosons, the behavior of impurities is directly related to the concepts of superfluidity and quantum dissipation. External fields can be used to convert the different species of a mixture into each other. This gives rise to a wealth of new phenomena, including the internal Josephson effect, SU(2) symmetry-breaking phases, and spin-orbit coupling.
Spin-orbit coupled gases
Artificial gauge fields and spin-orbit-coupled configurations have been recently obtained in the laboratory using laser control techniques. This opens new frontiers of research of high interdisciplinary interest, concerning novel quantum phases, unique magnetic properties, anisotropic dynamics, rotonic excitations and supersolid effects. The Trento group has started an intense activity in these new directions.
Low dimensional physics
Atoms can be optically confined in low-dimensional configurations. Indeed, cold gases are ideal systems for the observation of many-body phenomena where quantum and thermal fluctuations, or frustration, play a prominent role.
One-dimensional configurations lead to the realization of exactly solvable models, Luttinger liquids, Tonks-Girardeau gas and spin-charge separation. In 2D it is possible to investigate subtle effects such as the vortex-antivortex proliferation in the Berezinskii-Kosterlitz-Thouless phase transition. Moreover, the presence of the transverse confinement allows for new effects beyond the textbook models.
One of the main goals of using optical lattices is the implementation of Hubbard-like models. This opens a challenging direction of using cold gases as a quantum simulator of known solid-state Hamiltonians and going beyond.
Anisotropy and long range characterize dipolar forces and distinguish them from the usual short-range interatomic potentials. Dipolar forces can have either a magnetic (for atoms with large magnetic moment) or an electric nature (for polar molecules). Dipolar gases are under investigation in Trento, where the emergence of new quantum phases, the effects of dipolar drag and the physics of polarons are currently being studied. Special attention is given to the derivation of the Hubbard models adequate for the description of dipoles in optical lattices.
article has been written on The physics of dipolar bosonic quantum
gases, T.Layaye, C.Menotti, L.Santos, M.Lewenstein and T.Pfau,
Rep. Prog. Phys. 72, 126401 (2009).
Monte Carlo simulations
The aim of quantum Monte Carlo (QMC) methods is to provide an exact solution to the many-body problem using the microscopic Hamiltonian as the only input. Such "ab initio" numerical techniques are particularly well-suited when correlations are strong, in which case mean-field and perturbative approaches are bound to fail. These strong correlations may be induced by interactions, reduced dimensionality, or external fields.
In contrast to Bose systems, where exact results are available for both ground-state and thermodynamic properties, simulations of Fermi systems are plagued by a "sign problem" due to the anti-symmetry of the wave function. Approximate schemes have to be used yielding, quantitatively reliable results in most of the cases.
QMC methods have been applied by the Trento group to many different systems, including Bose and Fermi gases in low dimensions, bosons with disorder, and strongly coupled Fermi systems.
Density profiles of a Bose gas in a random potential produced by optical speckles.