We investigate the coherence and correlations of many-body states appearing in topological pumping in a one-dimensional Bose gas. By analyzing the system at zero and infinite interaction strengths, we reveal a rescaling of momentum distributions accompanied by a self-similar behavior in first- and second-order correlation functions. In excited states of non-interacting bosons, the momentum distribution shows a comb-like structure similar to that of non-interacting fermions but at a higher density. This is mirrored by Friedel oscillations in the one-body density matrix. At the same time, the density-density correlations still exhibit the bosonic enhancement. Our work illustrates how topological pumping induces a nontrivial mapping between bosonic and fermionic correlations.We investigate the coherence and correlations of many-body states appearing in topological pumping in a one-dimensional Bose gas. By analyzing the system at zero and infinite interaction strengths, we reveal a rescaling of momentum distributions accompanied by a self-similar behavior in first- and second-order correlation functions. In excited states of non-interacting bosons, the momentum distribution shows a comb-like structure similar to that of non-interacting fermions but at a higher density. This is mirrored by Friedel oscillations in the one-body density matrix. At the same time, the density-density correlations still exhibit the bosonic enhancement. Our work illustrates how topological pumping induces a nontrivial mapping between bosonic and fermionic correlations.

arXiv:2504.19569Apr 28, 20251 citation

How to distinguish fermionized bosons from noninteracting fermions through one-body and two-body density

Sangita Bera, Rhombik Roy, Barnali Chakrabarti

Fermionization is what happens when repulsive interacting bosons in one spatial dimension feel infinite interaction. Due to their strong repulsion the bosons try to minimize their spatial overlap like the fermions. Fermionized bosons and noninteracting fermions resemble each other and we trace these similarities of strongly correlated one-dimensional bosonic systems and fermionic system by exploring their ground state properties using the one- and two-body density matrix in coordinate space. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. Using the one- and two-body density in momentum space, fermionized bosons can be distinguished from noninteracting fermions.Fermionization is what happens when repulsive interacting bosons in one spatial dimension feel infinite interaction. Due to their strong repulsion the bosons try to minimize their spatial overlap like the fermions. Fermionized bosons and noninteracting fermions resemble each other and we trace these similarities of strongly correlated one-dimensional bosonic systems and fermionic system by exploring their ground state properties using the one- and two-body density matrix in coordinate space. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. Using the one- and two-body density in momentum space, fermionized bosons can be distinguished from noninteracting fermions.

AIP conference proceedingsJan 1, 20195 citations

Fermionization of a strongly interacting Bose-Fermi mixture in a one-dimensional harmonic trap

Bess Fang, Patrizia Vignolo, Christian Miniatura +1 more

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient $C$ is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient $C$ is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.

arXiv:0809.4419Physical Review AFeb 26, 200920 citations

Quantum-information-theoretical measures to distinguish fermionized bosons from noninteracting fermions

Barnali Chakrabarti, Arnaldo Gammal, N. D. Chavda +1 more

We study the dynamical fermionization of strongly interacting one-dimensional bosons in Tonks-Girardeau limit by solving the time-dependent many-boson Schr\"odinger equation numerically exactly. We establish that the one-body momentum distribution approaches the ideal Fermi gas distribution at the time of dynamical fermionization. The analysis is further complemented by the measures on the two-body level. The dynamical fermionization in the two-body level should be inferred as the presence of a distinct correlation hole along the diagonal of two-body correlation. Investigation of two-body momentum distribution for the strongly interacting bosons clearly exhibits a pattern along the diagonal which is not extinguished at the time of fermionization. Two-body local and nonlocal correlation also clearly distinguish the fermionized bosons from noninteracting fermions. The magnitude of distinguishablity between the two systems is further discussed employing suitable measures of information theory, i.e., the well-known Kullback-Leibler relative entropy and the Jensen-Shannon divergence entropy. We also observe very rich structure in the higher-body density for strongly correlated bosons, whereas noninteracting fermions do not possess any higher-order correlation beyond two-body.We study the dynamical fermionization of strongly interacting one-dimensional bosons in Tonks-Girardeau limit by solving the time-dependent many-boson Schr\"odinger equation numerically exactly. We establish that the one-body momentum distribution approaches the ideal Fermi gas distribution at the time of dynamical fermionization. The analysis is further complemented by the measures on the two-body level. The dynamical fermionization in the two-body level should be inferred as the presence of a distinct correlation hole along the diagonal of two-body correlation. Investigation of two-body momentum distribution for the strongly interacting bosons clearly exhibits a pattern along the diagonal which is not extinguished at the time of fermionization. Two-body local and nonlocal correlation also clearly distinguish the fermionized bosons from noninteracting fermions. The magnitude of distinguishablity between the two systems is further discussed employing suitable measures of information theory, i.e., the well-known Kullback-Leibler relative entropy and the Jensen-Shannon divergence entropy. We also observe very rich structure in the higher-body density for strongly correlated bosons, whereas noninteracting fermions do not possess any higher-order correlation beyond two-body.

Physical Review AJun 4, 20247 citations

Fermionization in an Expanding 1D Gas of Hard-Core Bosons

Marcos Rigol, Alejandro Muramatsu

We show by means of an exact numerical approach that the momentum distribution of a free expanding gas of hard-core bosons on a one-dimensional lattice approaches that of noninteracting fermions, acquiring a Fermi edge. Yet there is a power-law decay of the one-particle density matrix ${\ensuremath{\rho}}_{x}\ensuremath{\sim}1/\sqrt{x}$, as usual for hard-core bosons in the ground state, which accounts for a large occupation of the lowest natural orbitals for all expansion times. The fermionization of the momentum distribution function, which is not observed in equilibrium, is analyzed in detail.We show by means of an exact numerical approach that the momentum distribution of a free expanding gas of hard-core bosons on a one-dimensional lattice approaches that of noninteracting fermions, acquiring a Fermi edge. Yet there is a power-law decay of the one-particle density matrix ${\ensuremath{\rho}}_{x}\ensuremath{\sim}1/\sqrt{x}$, as usual for hard-core bosons in the ground state, which accounts for a large occupation of the lowest natural orbitals for all expansion times. The fermionization of the momentum distribution function, which is not observed in equilibrium, is analyzed in detail.

arXiv:cond-mat/0410683Physical Review LettersJun 22, 2005141 citations

Topological density correlations in a Fermi gas

Pok Man Tam, C. L. Kane

A Fermi gas of noninteracting electrons, or ultracold fermionic atoms, has a quantum ground state defined by a region of occupancy in momentum space known as the Fermi sea. The Euler characteristic ${\ensuremath{\chi}}_{F}$ of the Fermi sea serves to topologically classify these gapless fermionic states. The topology of a $D$ -dimensional Fermi sea is physically encoded in the $D+1$ point equal time density correlation function. In this work, we first present a simple proof of this fact by showing that the evaluation of the correlation function can be formulated in terms of a triangulation of the Fermi sea with a collection of points, links, and triangles and their higher dimensional analogs. We then make use of the topological $D+1$ point density correlation to reveal universal structures of the more general $M$ point density correlation functions in a $D$ -dimensional Fermi gas. Two experimental methods are proposed for observing these correlations in $D=2$ . In cold atomic gases imaged by quantum gas microscopy, our analysis supports the feasibility of measuring the third-order density correlation, from which ${\ensuremath{\chi}}_{F}$ can be reliably extracted in systems with as few as around 100 atoms. For solid-state electron gases, we propose measuring correlations in the speckle pattern of intensity fluctuations in nonlinear x-ray scattering experiments.A Fermi gas of noninteracting electrons, or ultracold fermionic atoms, has a quantum ground state defined by a region of occupancy in momentum space known as the Fermi sea. The Euler characteristic ${\ensuremath{\chi}}_{F}$ of the Fermi sea serves to topologically classify these gapless fermionic states. The topology of a $D$-dimensional Fermi sea is physically encoded in the $D+1$ point equal time density correlation function. In this work, we first present a simple proof of this fact by showing that the evaluation of the correlation function can be formulated in terms of a triangulation of the Fermi sea with a collection of points, links, and triangles and their higher dimensional analogs. We then make use of the topological $D+1$ point density correlation to reveal universal structures of the more general $M$ point density correlation functions in a $D$-dimensional Fermi gas. Two experimental methods are proposed for observing these correlations in $D=2$. In cold atomic gases imaged by quantum gas microscopy, our analysis supports the feasibility of measuring the third-order density correlation, from which ${\ensuremath{\chi}}_{F}$ can be reliably extracted in systems with as few as around 100 atoms. For solid-state electron gases, we propose measuring correlations in the speckle pattern of intensity fluctuations in nonlinear x-ray scattering experiments.

arXiv:2310.03737Physical review. B./Physical review. BJan 11, 202413 citations

C

is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.

D

-dimensional Fermi sea is physically encoded in the

D+1

point equal time density correlation function. In this work, we first present a simple proof of this fact by showing that the evaluation of the correlation function can be formulated in terms of a triangulation of the Fermi sea with a collection of points, links, and triangles and their higher dimensional analogs. We then make use of the topological

D+1

point density correlation to reveal universal structures of the more general

M

point density correlation functions in a

D

-dimensional Fermi gas. Two experimental methods are proposed for observing these correlations in

D=2

. In cold atomic gases imaged by quantum gas microscopy, our analysis supports the feasibility of measuring the third-order density correlation, from which ${\ensuremath{\chi}}_{F}$ can be reliably extracted in systems with as few as around 100 atoms. For solid-state electron gases, we propose measuring correlations in the speckle pattern of intensity fluctuations in nonlinear x-ray scattering experiments.