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1. Generalized Bose–Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases

   https://doi.org/10.1088/1751-8121/aca302  

   Yang, Li; Alam, Shah Saad; Pu, Han (November 2022, Journal of Physics A: Mathematical and Theoretical)

   Abstract Quantum many-body systems in one dimension (1D) exhibit some peculiar properties. In this article, we review some of our work on strongly interacting 1D spinor quantum gas. First, we discuss a generalized Bose–Fermi mapping that maps the charge degrees of freedom to a spinless Fermi gas and the spin degrees of freedom to a spin chain model. This also maps the strongly interacting system into a weakly interacting one, which is amenable for perturbative calculations. Next, based on this mapping, we construct an ansatz wavefunction for the strongly interacting system, using which many physical quantities can be conveniently calculated. We showcase the usage of this ansatz wavefunction by considering the collective excitations and quench dynamics of a harmonically trapped system. 

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2. An alternative formalism for modeling spin

   https://doi.org/10.1140/epjc/s10052-022-10652-y  

   Powers, Sam; Stojkovic, Dejan (August 2022, The European Physical Journal C)

   Abstract We present an alternative formalism for modeling spin. The ontological elements of this formalism are base-2 sequences of length n . The machinery necessary to model physics is then developed by considering correlations between base-2 sequences. Upon choosing a reference base-2 sequence, a relational system of numbers can be defined, which we interpret as quantum numbers. Based on the properties of these relational quantum numbers, the selection rules governing interacting spin systems are derived from first principles. A tool for calculating the associated probabilities, which are the squared Clebsch–Gordan coefficients in quantum mechanics, is also presented. The resulting model offers a vivid information theoretic picture of spin and interacting spin systems. Importantly, this model is developed without making any assumptions about the nature of space-time, which presents an interesting opportunity to study emergent space-time models. 

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3. Many-body quantum chaos in stroboscopically-driven cold atoms

   https://doi.org/10.1038/s42005-023-01258-1  

   Dağ, Ceren B; Mistakidis, Simeon I; Chan, Amos; Sadeghpour, H R (December 2023, Communications Physics)

   Abstract In quantum chaotic systems, the spectral form factor (SFF), defined as the Fourier transform of two-level spectral correlation function, is known to follow random matrix theory (RMT), namely a ‘ramp’ followed by a ‘plateau’ in late times. Recently, a generic early-time deviation from RMT, so-called the ‘bump’, was shown to exist in random quantum circuits as toy models for many-body quantum systems. We demonstrate the existence of ‘bump-ramp-plateau’ behavior in the SFF for a number of paradigmatic and stroboscopically-driven 1D cold-atom models: spinless and spin-1/2 Bose-Hubbard models, and nonintegrable spin-1 condensate with contact or dipolar interactions. We find that the scaling of the many-body Thouless timet_Th—the onset of RMT—, and the bump amplitude are more sensitive to variations in atom number than the lattice size regardless of the hyperfine structure, the symmetry classes, or the choice of driving protocol. Moreover,t_Thscaling and the increase of the bump amplitude in atom number are significantly slower in spinor gases than interacting bosons in 1D optical lattices, demonstrating the role of locality. We obtain universal scaling functions of SFF which suggest power-law behavior for the bump regime in quantum chaotic cold-atom systems, and propose an interference measurement protocol. 

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4. Nonlinear multistate tunneling dynamics in a spinor Bose-Einstein condensate

   https://doi.org/10.1103/PhysRevA.108.053307  

   Hardesty-Shaw, Z. N.; Guan, Q.; Austin-Harris, J. O.; Blume, D.; Lewis-Swan, R. J.; Liu, Y. (November 2023, Physical Review A)

   Thomas Pattard; Jan Michael Rost; Franco Dalfovo (Ed.)

   We present an experimental realization of dynamic self-trapping and nonexponential tunneling in a multistate system consisting of ultracold sodium spinor gases confined in moving optical lattices. Taking advantage of the fact that the tunneling process between different momentum states in the sodium spinor system is resolvable over a broader dynamic energy scale than previously observed in rubidium scalar gases, we demonstrate that the tunneling dynamics in the multistate system strongly depends on an interaction induced nonlinearity and is influenced by the spin degree of freedom under certain conditions. We develop a rigorous multistate tunneling model to describe the observed dynamics. Combined with our recent observation of spatially manipulated spin dynamics, these results open up prospects for alternative multistate ramps and state transfer protocols. 

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5. Hydrodynamic nonlinear response of interacting integrable systems

   https://doi.org/10.1073/pnas.2106945118  

   Fava, Michele; Biswas, Sounak; Gopalakrishnan, Sarang; Vasseur, Romain; Parameswaran, S. A. (September 2021, Proceedings of the National Academy of Sciences)

   We develop a formalism for computing the nonlinear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb–Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems. 

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