Measurement of interacting quantum phases: A band mapping scheme

doi:10.1007/s11467-023-1326-y

Front. Phys.

2023, Vol. 18

Issue (5) : 52307 https://doi.org/10.1007/s11467-023-1326-y

RESEARCH ARTICLE

Measurement of interacting quantum phases: A band mapping scheme

Qi Huang¹(

), Zijie Zhu², Yifei Wang³, Libo Liang¹, Qinpei Zheng¹, Xuzong Chen¹(

)

¹. School of Electronics, Peking University, Beijing 100871, China
². Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
³. Institute for Advanced Study, Tsinghua University, Beijing 100084, China

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Abstract

Band mapping is widely used in various scenarios of cold atom physics to measure the quasi-momentum distribution and band population. However, conventional methods fail in strongly interacting systems. Here we propose and experimentally realize a novel scheme of band mapping that can accurately measure the quasi-momentum of interacting many-body systems. Through an anisotropic control in turning down the three-dimensional optical lattice, we can eliminate the effect of interactions on the band mapping process. Then, based on a precise measurement of the quasi-momentum distribution, we introduce the incoherent fraction as a physical quantity that can quantify the degree of incoherence of quantum many-body states. This method enables precise measurement of processes such as the superfluid to Mott insulator phase transition. Additionally, by analyzing the spatial correlation derived from the quasi-momentum of superfluid-Mott insulator phase transitions, we obtain results consistent with the incoherent fraction. Our scheme broadens the scope of band mapping and provides a method for studying quantum many-body problems.

Keywords ultracold physics Mott insulator superfluid band mapping

Corresponding Author(s): Qi Huang,Xuzong Chen

Issue Date: 25 July 2023

Cite this article:

Qi Huang,Zijie Zhu,Yifei Wang, et al. Measurement of interacting quantum phases: A band mapping scheme[J]. Front. Phys. , 2023, 18(5): 52307.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1326-y
https://academic.hep.com.cn/fop/EN/Y2023/V18/I5/52307

Fig.1 Sketch of experiment setup, time sequence, and images for band mapping. (a) A schematic diagram of the experimental system. (b) The temporal sequence of the lattice potential along the x, y, and z directions. The potential along the x and y directions is ramped down to zero within 2 ms, while the potential along the z direction is abruptly quenched to zero. (c) We obtained band mapping images with our method at three different lattice depths corresponding to the superfluid regime, the critical point of phase transition, and the deep Mott insulator regime.

Fig.2 Quasi-momentum distribution from two methods. (a) Integration graphs of (c) along the

x

axis. (b) Quasi-momentum distribution is calculated from the first Brillouin zone of (a). (c) The integrated column density

n (x, y)

, represented by the optical density (OD) in arbitrary units, is measured from the experiment at

15 E r

. The inset shows the quasi-momentum obtained from the first Brillouin zone of momentum distribution. (d) Integrated graphs of band mapping at different lattice depths. Red points represent quasi-momentum distribution calculated from momentum distribution, while blue points represent the data obtained from the new band mapping method. Experimental data are averaged over several realizations. Error bars denote standard deviation; most error bars are smaller than their marker size if not visible.

Fig.3 Incoherent fraction and correlation. (a) Band mapping images reveal the quasi-momentum distribution at various lattice depths, showing a transition from SF to MI as indicated by the diminishing peak and the increasing plateau. (b) Lattice depth dependence of the incoherent fraction. The inset depicts the method for extracting the incoherent fraction from the quasi-momentum distribution. (c) Correlation versus space distance at different lattice depths. The gray area has errors due to inhomogeneous optical lattice.

Fig.4 Transformation of momentum distribution between different Brillouin zones. (a) The momentum distribution in an optical lattice with a potential depth of

15 E r

. (b) By extrapolating the momentum distribution within the first Brillouin zone, we derived the complete momentum distribution. (c) We integrated (a) and (b) along the x and y directions, shown as blue and orange lines, respectively.

Fig.A1 Comparison of conventional method and improved band mapping at several typical lattice depths.

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