Spin Correlation Effects in Fermion Matter

Recent calculations with an effective isospin-dependent contact interaction show the possibility of the crossover from superfluidity of neutron Cooper pairs in the ${^{1}\mathrm{S}}_{0}$ pairing channel to Bose-Einstein condensation (BEC) of di-neutron bound states in dilute nuclear matter. The density and spin correlation functions are calculated for a di-neutron condensate in asymmetric nuclear matter with the aim of finding the possible features of the BCS-BEC crossover. It is shown that the zero-momentum transfer spin correlation function satisfies the sum rule at zero temperature. In symmetric nuclear matter, the density correlation function changes sign at low momentum transfer across the BCS-BEC transition, and this feature can be considered as a signature of the crossover. At finite isospin asymmetry, this criterion gives too large a value for the critical asymmetry ${\ensuremath{\alpha}}_{c}^{d}~0.9$, at which the BEC state is quenched. Therefore, it can be trusted for the description of the density-driven BCS-BEC crossover of neutron pairs only at small isospin asymmetry. This result generalizes the conclusion of the study in Phys. Rev. Lett. 95, 090402 (2005), where the change of sign of the density correlation function at low momentum transfer in two-component quantum fermionic atomic gas with the balanced populations of fermions of different species was considered as an unambiguous signature of the BCS-BEC transition.Recent calculations with an effective isospin-dependent contact interaction show the possibility of the crossover from superfluidity of neutron Cooper pairs in the ${^{1}\mathrm{S}}_{0}$ pairing channel to Bose-Einstein condensation (BEC) of di-neutron bound states in dilute nuclear matter. The density and spin correlation functions are calculated for a di-neutron condensate in asymmetric nuclear matter with the aim of finding the possible features of the BCS-BEC crossover. It is shown that the zero-momentum transfer spin correlation function satisfies the sum rule at zero temperature. In symmetric nuclear matter, the density correlation function changes sign at low momentum transfer across the BCS-BEC transition, and this feature can be considered as a signature of the crossover. At finite isospin asymmetry, this criterion gives too large a value for the critical asymmetry ${\ensuremath{\alpha}}_{c}^{d}~0.9$, at which the BEC state is quenched. Therefore, it can be trusted for the description of the density-driven BCS-BEC crossover of neutron pairs only at small isospin asymmetry. This result generalizes the conclusion of the study in Phys. Rev. Lett. 95, 090402 (2005), where the change of sign of the density correlation function at low momentum transfer in two-component quantum fermionic atomic gas with the balanced populations of fermions of different species was considered as an unambiguous signature of the BCS-BEC transition.

arXiv:0803.3362Physical Review CJul 9, 200815 citations

Experimental Demonstration of Fermion Spin Correlations

Robert A. Close

Bulletin of the American Physical SocietyOct 19, 20120 citations

Nonlocal quench spectroscopy of fermionic excitations in quantum spin chains

Saverio Bocini, Filippo Caleca, Fabio Mezzacapo +1 more

The elementary excitations of quantum spin systems have generally the nature of weakly interacting bosonic quasiparticles, generated by local operators acting on the ground state. Nonetheless in one spatial dimension the nature of the quasiparticles can change radically, since many relevant one-dimensional $S=1/2$ Hamiltonians can be exactly mapped onto models of spinless fermions with local hopping and interactions. Due to the nonlocal nature of the spin-to-fermion mapping, observing directly the fermionic quasiparticle excitations is impossible using local probes, which are at the basis of all the forms of spectroscopy (such as neutron scattering) traditionally available in condensed-matter physics. Here, we show theoretically that quench spectroscopy for synthetic quantum matter---which probes the excitation spectrum of a system by monitoring the nonequilibrium dynamics of its correlation functions---can reconstruct accurately the dispersion relation of fermionic quasiparticles in spin chains. This possibility relies on the ability of quantum simulation experiments to measure nonlocal spin-spin correlation functions, corresponding to elementary fermionic correlation functions. Our analysis is based on exact results for the quench dynamics of quantum spin chains, and it opens the path to probe arbitrary quasiparticle excitations in synthetic quantum matter.The elementary excitations of quantum spin systems have generally the nature of weakly interacting bosonic quasiparticles, generated by local operators acting on the ground state. Nonetheless in one spatial dimension the nature of the quasiparticles can change radically, since many relevant one-dimensional $S=1/2$ Hamiltonians can be exactly mapped onto models of spinless fermions with local hopping and interactions. Due to the nonlocal nature of the spin-to-fermion mapping, observing directly the fermionic quasiparticle excitations is impossible using local probes, which are at the basis of all the forms of spectroscopy (such as neutron scattering) traditionally available in condensed-matter physics. Here, we show theoretically that quench spectroscopy for synthetic quantum matter---which probes the excitation spectrum of a system by monitoring the nonequilibrium dynamics of its correlation functions---can reconstruct accurately the dispersion relation of fermionic quasiparticles in spin chains. This possibility relies on the ability of quantum simulation experiments to measure nonlocal spin-spin correlation functions, corresponding to elementary fermionic correlation functions. Our analysis is based on exact results for the quench dynamics of quantum spin chains, and it opens the path to probe arbitrary quasiparticle excitations in synthetic quantum matter.

Physical review. B./Physical review. BMar 25, 20254 citations

Local three-spin correlations in the free-fermion and

R. J. Baxter, T. C. CHOYt

Jan 1, 20160 citations

Digital programming of spin correlations in a fermionic lattice quantum simulator

Yann Kiefer, Lars Fischer, Zijie Zhu +2 more

Analog quantum simulation provides a highly controlled platform to study diverse quantum many-body phenomena. However, current methods for state initialisation are limited to thermal ensembles or uncorrelated product states. Here we present a hybrid approach that complements analog preparation with a digital quantum-gate protocol. This approach enables the engineering of target states with specific, long-range spin-correlations from the same initial resource state. By applying collisional gates to adiabatically prepared and filtered four-fermion singlet chains, we program diverse spin-correlation patterns, including that of a Heisenberg chain. We measure the spin correlations using a sequence of quantum gates followed by singlet-pair measurements. Our method paves the way to the targeted preparation of strongly correlated states of matter.Analog quantum simulation provides a highly controlled platform to study diverse quantum many-body phenomena. However, current methods for state initialisation are limited to thermal ensembles or uncorrelated product states. Here we present a hybrid approach that complements analog preparation with a digital quantum-gate protocol. This approach enables the engineering of target states with specific, long-range spin-correlations from the same initial resource state. By applying collisional gates to adiabatically prepared and filtered four-fermion singlet chains, we program diverse spin-correlation patterns, including that of a Heisenberg chain. We measure the spin correlations using a sequence of quantum gates followed by singlet-pair measurements. Our method paves the way to the targeted preparation of strongly correlated states of matter.

cond-mat.quant-gasCross-listedarXiv:2606.13772Jun 15, 20260 citations

Recent calculations with an effective isospin-dependent contact interaction show the possibility of the crossover from superfluidity of neutron Cooper pairs in the

{^{1}\mathrm{S}}_{0}

pairing channel to Bose-Einstein condensation (BEC) of di-neutron bound states in dilute nuclear matter. The density and spin correlation functions are calculated for a di-neutron condensate in asymmetric nuclear matter with the aim of finding the possible features of the BCS-BEC crossover. It is shown that the zero-momentum transfer spin correlation function satisfies the sum rule at zero temperature. In symmetric nuclear matter, the density correlation function changes sign at low momentum transfer across the BCS-BEC transition, and this feature can be considered as a signature of the crossover. At finite isospin asymmetry, this criterion gives too large a value for the critical asymmetry ${\ensuremath{\alpha}}_{c}^{d}~0.9$, at which the BEC state is quenched. Therefore, it can be trusted for the description of the density-driven BCS-BEC crossover of neutron pairs only at small isospin asymmetry. This result generalizes the conclusion of the study in Phys. Rev. Lett. 95, 090402 (2005), where the change of sign of the density correlation function at low momentum transfer in two-component quantum fermionic atomic gas with the balanced populations of fermions of different species was considered as an unambiguous signature of the BCS-BEC transition.

S=1/2

Hamiltonians can be exactly mapped onto models of spinless fermions with local hopping and interactions. Due to the nonlocal nature of the spin-to-fermion mapping, observing directly the fermionic quasiparticle excitations is impossible using local probes, which are at the basis of all the forms of spectroscopy (such as neutron scattering) traditionally available in condensed-matter physics. Here, we show theoretically that quench spectroscopy for synthetic quantum matter---which probes the excitation spectrum of a system by monitoring the nonequilibrium dynamics of its correlation functions---can reconstruct accurately the dispersion relation of fermionic quasiparticles in spin chains. This possibility relies on the ability of quantum simulation experiments to measure nonlocal spin-spin correlation functions, corresponding to elementary fermionic correlation functions. Our analysis is based on exact results for the quench dynamics of quantum spin chains, and it opens the path to probe arbitrary quasiparticle excitations in synthetic quantum matter.