Universal dynamic scaling and Contact dynamics in quenched quantum gases

doi:10.1007/s11467-023-1341-z

Front. Phys.

2024, Vol. 19

Issue (2) : 22201 https://doi.org/10.1007/s11467-023-1341-z

RESEARCH ARTICLE

Universal dynamic scaling and Contact dynamics in quenched quantum gases

Jia-Nan Cui¹, Zhengqiang Zhou¹, Mingyuan Sun^1,²(

)

¹. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
². State Key Lab of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China

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Abstract

Recently universal dynamic scaling is observed in several systems, which exhibit a spatiotemporal self-similar scaling behavior, analogous to the spatial scaling near phase transition. The latter one arises from the emergent continuous scaling symmetry. Motivated by this, we investigate the possible relation between the scaling dynamics and the continuous scaling symmetry in this paper. We derive a theorem that the scaling invariance of the quenched Hamiltonian and the initial density matrix can lead to the universal dynamic scaling. It is further demonstrated both in a two-body system analytically and in a many-body system numerically. For the latter one, we calculate the dynamics of quantum gases quenched from the zero interaction to a finite interaction via the non-equilibrium high-temperature virial expansion. A dynamic scaling of the momentum distribution appears in certain momentum-time windows at unitarity as well as in the weak interacting limit. Remarkably, this universal scaling dynamics persists approximately with smaller scaling exponents even if the scaling symmetry is fairly broken. Our findings may offer a new perspective to interpret the related experiments. We also study the Contact dynamics in the BEC−BCS crossover. Surprisingly, the half-way time displays a maximum near unitarity while some damping oscillations occur on the BEC side due to the dimer state, which can be used to detect possible two-body bound states in experiments.

Keywords dynamic scaling Contact dynamics quantum gases cold atom quench dynamics virial expansion continuous scaling symmetry

Corresponding Author(s): Mingyuan Sun

Just Accepted Date: 28 August 2023 Issue Date: 26 September 2023

Cite this article:

Jia-Nan Cui,Zhengqiang Zhou,Mingyuan Sun. Universal dynamic scaling and Contact dynamics in quenched quantum gases[J]. Front. Phys. , 2024, 19(2): 22201.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1341-z
https://academic.hep.com.cn/fop/EN/Y2024/V19/I2/22201

Fig.1 The momentum distribution

δ n k

at the large momentum region for various times

t / t λ

= 0.02 (black), 0.04 (red), 0.06 (blue), 0.08 (pink), 0.10 (green), 0.12 (navy) in the quench dynamics of quantum gases. Here,

λ = 2 π / (m T)

is the thermal wavelength, while

t λ = 1 / T

t ~ = t / t 0

with

t 0 / t λ = 0.02

. The results in the BEC-BCS crossover are displayed with the scattering length labelled in the first row. In the second row, the corresponding scalings of both the horizontal and vertical axes are taken via Eq. (1), to demonstrate whether there exists a dynamic scaling behavior. The scaling exponents

α

and

β

are shown in the corresponding graphs.

Fig.2 The quench dynamics of the momentum distribution

| δ n k |

at finite momentum region for various times

t / t λ

= 0.1 (black), 0.2 (red), 0.3 (blue), 0.4 (pink), 0.5 (green). The results for the unitarity are plotted with unscaled axes (a) and scaled axes (b), while they are only demonstrated in scaled axes for

λ / a s = ? 100

(c) and

λ / a s = 100

(d). According to the theorem, they are not expected to display any strict dynamic scaling behavior, due to the breakdown of the scale invariance of the initial density matrix. However, an approximate scaling dynamics can still be seen in all three cases with smaller scaling exponents

α

and

β

displayed in the corresponding graphs.

Fig.3 The Contact dynamics after the quench for

λ / a s =

?3 (black), ?1 (red), 0 (blue), 1 (pink), 3 (green). They all start from zero and approach to a steady value at long times. On the BEC side, they exhibit damping oscillations.

Fig.4 The Contact dynamics in the BEC-BCS crossover. (a) The Contact at infinite time (

t → ∞

) in the whole BEC-BCS crossover, obtained from Eq. (14). (b) The half-way time

τ

as a function of the interaction. (c) The relative value at the peak

Δ C p = C p ? C (t → ∞)

for

λ / a s =

3 (black), 4 (red), 5 (blue), which obeys a power-law decay with the same power approximately. (d) The frequencies of oscillations at various interactions on the BEC side, with a linear fitting (red line).

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