Strongly interacting trapped one-dimensional quantum gases: an exact solution

Abstract

Quantum correlations can be used as a resource for quantum computing, eg for quantum state manipulation, and for quantum sensing, eg for creating non-classical states which allow to achieve the quantum advantage regime. This review collects the predictions coming from a family of exact solutions which allows to describe the many-body wavefunction of strongly correlated quantum fluids confined by a tight waveguide and subjected to any form of longitudinal confinement. It directly describes the experiments with trapped ultracold atoms where the strongly correlated regime in one dimension has been achieved. The exact solution applies to bosons, fermions and mixtures. It allows to obtain experimental observables such as the density profiles and momentum distribution at all momentum scales, beyond the Luttinger liquid approach. It also predicts the exact quantum dynamics at all the times, including the small oscillations regime yielding the collective modes of the system and the large quench regime where the system parameters are changed considerably. The solution can be extended to describe finite-temperature conditions, spin and magnetization effects. The review illustrates the idea of the solution, presents the key theoretical achievements and the main experiments on strongly correlated one-dimensional quantum gases.

22 pages, 19 figures

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Cited by in corpus (22)

• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Persistent currents in ultracold gases
• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Exact solution for $SU(2)$-symmetry breaking bosonic mixtures at strong interactions
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• Classical and quantum metrology of the Lieb-Liniger model
• High-momentum oscillating tails of strongly interacting 1D gases in a box
• Comparison of renormalized interactions using one-dimensional few-body systems as a testbed
• Symmetry oscillations in strongly interacting one-dimensional mixtures
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states
• Fate of the "vacuum point'' and of grey solitons in dispersive quantum shock waves in a one-dimensional Bose gas
• Dynamical probing of high-order spin coherence in one-dimensional mixtures
• Exact spectral function and nonequilibrium dynamics of the strongly interacting Hubbard model
• Analytical solution of a free-fermion chain with time-dependent ramps
• Effective two- and three-body interactions between dressed impurities in a tilted double-well potential
• Effective theory for strongly attractive one-dimensional fermions
• The Lieb excitations and topological flat mode of spectral function of Tonks-Girardeau gas in Kronig-Penney potential
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Necklace Ansatz for strongly repulsive spin mixtures on a ring
• Composite Bosons Superposition Ansatz Approach to One-Dimensional Trapped Few-Fermion Systems
• Symmetry oscillations sensitivity to SU(2)-symmetry breaking in quantum mixtures