We study the evolution from few- to many-body physics of fermionic systems in one spatial dimension with attractive pairwise interactions. We determine the detailed form of the momentum distribution, the structure of the one-body density matrix, and the pairing properties encoded in the two-body density matrix. From the low- and high-momentum scaling behavior of the single-particle momentum distribution we estimate the speed of sound and Tan's contact, respectively. Both quantities are found to be in agreement with previous calculations. Based on our calculations of the one-body density matrices, we also present results for the particle-partition entanglement entropy, for which we find a logarithmic dependence on the total particle number.We study the evolution from few- to many-body physics of fermionic systems in one spatial dimension with attractive pairwise interactions. We determine the detailed form of the momentum distribution, the structure of the one-body density matrix, and the pairing properties encoded in the two-body density matrix. From the low- and high-momentum scaling behavior of the single-particle momentum distribution we estimate the speed of sound and Tan's contact, respectively. Both quantities are found to be in agreement with previous calculations. Based on our calculations of the one-body density matrices, we also present results for the particle-partition entanglement entropy, for which we find a logarithmic dependence on the total particle number.

arXiv:1706.00031Physical Review ASep 27, 201733 citations

Relaxations in few-body systems

Yasushi Kondo

Bulletin of the American Physical SocietyMar 15, 20170 citations

Emergence of Many-Body Physics in Two-Dimensional Few-Fermion Systems

Luca Bayha

This thesis reports on experiments investigating the emergence of many-body physics in mesoscopic two-dimensional (2D) few-fermion systems. \nThe starting point are low-entropy samples of ultracold 6Li atoms in a quasi-2D geometry. When scanning the depth of the trapping potential, we observe an enhanced stability of closed-shell configurations of the 2D harmonic oscillator. This enables us to deterministically initialize closed-shell configurations of 2, 6 and 12 atoms in the ground state. \nBy modulating the interaction strength we probe the excitation spectrum arising from the interplay of the finite single-particle gap in closed-shell configurations with the tunable attractive interactions. The full atom-counting statistics reveal pair excitations with a non-monotonous interaction dependence. These modes can be identified as the few-body precursors of a Higgs mode associated with a normal to superfluid phase transition in the thermodynamic limit. \nAdditionally, we can access the momentum distribution with single-particle resolution. This is demonstrated by measuring the momentum distribution of up to six non-interacting fermions in the ground state of the 2D trap. We observe strong density correlations that arise from fermionic quantum statistics. In the future, extending the imaging scheme to interacting systems will allow us to observe the emergence of fermionic many-body paring directly in momentum space.This thesis reports on experiments investigating the emergence of many-body physics in mesoscopic two-dimensional (2D) few-fermion systems. \nThe starting point are low-entropy samples of ultracold 6Li atoms in a quasi-2D geometry. When scanning the depth of the trapping potential, we observe an enhanced stability of closed-shell configurations of the 2D harmonic oscillator. This enables us to deterministically initialize closed-shell configurations of 2, 6 and 12 atoms in the ground state. \nBy modulating the interaction strength we probe the excitation spectrum arising from the interplay of the finite single-particle gap in closed-shell configurations with the tunable attractive interactions. The full atom-counting statistics reveal pair excitations with a non-monotonous interaction dependence. These modes can be identified as the few-body precursors of a Higgs mode associated with a normal to superfluid phase transition in the thermodynamic limit. \nAdditionally, we can access the momentum distribution with single-particle resolution. This is demonstrated by measuring the momentum distribution of up to six non-interacting fermions in the ground state of the 2D trap. We observe strong density correlations that arise from fermionic quantum statistics. In the future, extending the imaging scheme to interacting systems will allow us to observe the emergence of fermionic many-body paring directly in momentum space.

Jan 1, 20200 citations

Probing universal few-body dynamics

Seth T. Rittenhouse

Bulletin of the American Physical SocietyJun 16, 20110 citations

Bounds on eigenstate thermalization

Shoki Sugimoto, Ryusuke Hamazaki, Masahito Ueda

The eigenstate thermalization hypothesis (ETH), which asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble, plays a pivotal role in understanding thermalization of isolated quantum systems. Yet, no evidence has been obtained as to whether the ETH holds for all few-body operators in a chaotic system; such few-body operators include key quantities in statistical mechanics, such as the total magnetization, the momentum distributions, and their low-order thermal and quantum fluctuations. Here, we formulate a conjecture that for a generic nonintegrable system the ETH holds simultaneously for all $m$ -body operators with $m < α_{\ast} N$ in the thermodynamic limit for some nonzero constant $α_{\ast} > 0$ . We first show the existence of such nontrivial constants for idealized (pseudo) random-matrix descriptions of many-body eigenstates. We then verify the conjecture for generic spin, Bose, and Fermi systems with local and few-body interactions by large-scale numerical calculations. Our results imply that generic systems satisfy the ETH simultaneously for all few-body operators, including their thermal and quantum fluctuations.The eigenstate thermalization hypothesis (ETH), which asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble, plays a pivotal role in understanding thermalization of isolated quantum systems. Yet, no evidence has been obtained as to whether the ETH holds for all few-body operators in a chaotic system; such few-body operators include key quantities in statistical mechanics, such as the total magnetization, the momentum distributions, and their low-order thermal and quantum fluctuations. Here, we formulate a conjecture that for a generic nonintegrable system the ETH holds simultaneously for all $m$-body operators with $m < α_{\ast} N$ in the thermodynamic limit for some nonzero constant $α_{\ast} > 0$. We first show the existence of such nontrivial constants for idealized (pseudo) random-matrix descriptions of many-body eigenstates. We then verify the conjecture for generic spin, Bose, and Fermi systems with local and few-body interactions by large-scale numerical calculations. Our results imply that generic systems satisfy the ETH simultaneously for all few-body operators, including their thermal and quantum fluctuations.

arXiv:2303.10069Mar 17, 20231 citation

m

-body operators with

m < α_{\ast} N

in the thermodynamic limit for some nonzero constant

α_{\ast} > 0

. We first show the existence of such nontrivial constants for idealized (pseudo) random-matrix descriptions of many-body eigenstates. We then verify the conjecture for generic spin, Bose, and Fermi systems with local and few-body interactions by large-scale numerical calculations. Our results imply that generic systems satisfy the ETH simultaneously for all few-body operators, including their thermal and quantum fluctuations.