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Physical Review A

Symmetry oscillation sensitivity to SU(2)-symmetry breaking in quantum mixtures

S. Musolino, Mathias Albert, Patrizia Vignolo, Anna Minguzzi

Published Oct 20, 2025• 0 citations
Publisher

Abstract

The authors study the time modulation of the momentum distributions of one-dimensional Bose-Bose mixtures with strong repulsive interactions, described via SU(2)-symmetry-breaking Hamiltonians. They show that the phenomenon of symmetry oscillations is not restricted to a specific model or fine-tuned parameters, but instead constitutes a robust and universal dynamical feature of multicomponent strongly interacting one-dimensional quantum mixtures.

DOI
10.1103/bl58-878c

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The authors study the time modulation of the momentum distributions of one-dimensional Bose-Bose mixtures with strong repulsive interactions, described via SU(2)-symmetry-breaking Hamiltonians. They show that the phenomenon of symmetry oscillations is not restricted to a specific model or fine-tuned parameters, but instead constitutes a robust and universal dynamical feature of multicomponent strongly interacting one-dimensional quantum mixtures.
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Multicomponent quantum mixtures in one dimension can be characterized by their symmetry under particle exchange. For a strongly interacting Bose-Bose mixture, we show that the time evolution of the momentum distribution from an initially symmetry-mixed state is quasiconstant for a SU(2) symmetry conserving Hamiltonian, while it displays large oscillations in time for the symmetry-breaking case where inter- and intraspecies interactions are different. Using the property that the momentum distribution operator at strong interactions commutes with the class-sum operator, the latter acting as a symmetry witness, we show that the momentum distribution oscillations correspond to symmetry oscillations, with a mechanism analogous to neutrino flavor oscillations.
Understanding the effect of correlations in interacting many-body systems is one of the main challenges in quantum mechanics. While the general problem can only be addressed by approximate methods and numerical simulations, in some limiting cases, it is amenable to exact solutions. I will present a family of exact solutions for strongly interacting 1D quantum gases in arbitrary external potential, valid for bosons, multicomponent fermions and mixtures, and in particular our new exact solution for the case of symmetric-breaking mixtures.The solutions allow one to obtain experimental observables such as the density profiles and momentum distribution at all momentum scales, beyond the Luttinger liquid approach, as well as to describe finite-temperature conditions, spin, and magnetization effects. I will present some uses of these solutions to obtain the exact quantum dynamics, both for the small oscillation regime and for the strongly out-of-equilibrium spin dynamics, where I will propose a protocol to observe symmetry oscillations in binary bosonic mixtures.
The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of a system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of quantum chaos in a minimal system describing one-dimensional harmonically trapped Bose-Bose mixtures by tuning the particle-particle interactions. Using an improved exact diagonalization scheme, we examine the transition from integrability to chaos when the inter-component interaction changes from weak to strong. Our study is based on the analysis of the level spacing distribution and the distribution of the matrix elements of observables in terms of the eigenstate thermalization hypothesis and their dynamics. We show that one can obtain strong signatures of chaos by increasing the inter-component interaction strength and breaking the symmetry of intra-component interactions.
We consider multi-component quantum mixtures (bosonic, fermionic, or mixed) with strongly repulsive contact interactions in a one-dimensional harmonic trap. In the limit of infinitely strong repulsion and zero temperature, using the class-sum method, we study the symmetries of the spatial wave function of the mixture. We find that the ground state of the system has the most symmetric spatial wave function allowed by the type of mixture. This provides an example of the generalized Lieb–Mattis theorem. Furthermore, we show that the symmetry properties of the mixture are embedded in the large-momentum tails of the momentum distribution, which we evaluate both at infinite repulsion by an exact solution and at finite interactions using a numerical DMRG approach. This implies that an experimental measurement of the Tan’s contact would allow to unambiguously determine the symmetry of any kind of multi-component mixture.
We study the ground states of one-dimensional Bose-Bose mixtures under harmonic confinement. As we vary the interspecies coupling strength up to the limit of infinite repulsion, we observe a generalized, composite-fermionization crossover. The initially coexisting phases demix as a whole for weak intraspecies interactions, whereas the atoms localize individually for strong intraspecies repulsion. By symmetry, the two components end up with strongly overlapping profiles, albeit sensitive to symmetry-breaking perturbations. Different pathways emerge if the two components have different atom numbers, different intraspecies interactions, or different masses and/or trap frequencies.