Dynamics of Ultracold Bosons in Artificial Gauge Fields-Angular Momentum, Fragmentation, and the Variance of Entropy.

Axel U J Lode,Camille Lévêque,Sunayana Dutta

doi:10.3390/e23040392

Abstract

We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge field, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well as the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation—multiple macroscopic eigenvalues of the reduced one-body density matrix—emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems.

Highlights

We investigate the physics of a two-dimensional system of harmonically trapped interacting ultracold bosons quenched with an artificial magnetic field (AMF) from a many-body point of view
Is the most widespread tool to theoretically model many-body systems of ultracold bosonic atoms subject to an AMF. This approach recovers many of the physical phenomena observed, but neglects correlations by its construction using a mean-field ansatz; here, we go beyond mean-field and use the multiconfigurational time-dependent Hartree method for bosons (MCTDH-B) [19,20,21] to approximate the solution of the Schrödinger equation for ultracold atoms subject to an AMF
Our paper is structured as follows—in Section 2 we introduce the Hamiltonian and the MCTDH-X method we use, in Section 3 we discuss the observables that we are using in Section 4 to investigate the dynamics of ultracold atoms in an AMF; Section 5 summarizes our conclusions and provides an outlook

Summary

Introduction

Since the first realization of Bose-Einstein condensates in 1995 [1,2,3], ultracold atoms have become a standard probe for analog quantum simulations—due to the tunability and flexibility of these quantum states of matter, they can be manipulated to behave like other systems, for instance, condensed matter systems which are not as flexible or easy to observe.Popular examples include the realization of the quantum simulation of the superfluid-toMott-insulator transition [4,5], quantized conductance [6,7], the Dicke model [8,9], and magnetism realized via artificial gauge fields for ultracold atoms [10].Such artificial gauge fields can make the neutral ultracold atoms behave as if they were charged particles experiencing a magnetic field and were investigated experimentally and theoretically with an external lattice potential [11,12,13] or without one [14,15,16].In this paper, we investigate the physics of a two-dimensional system of harmonically trapped interacting ultracold bosons quenched with an artificial magnetic field (AMF) from a many-body point of view. Popular examples include the realization of the quantum simulation of the superfluid-toMott-insulator transition [4,5], quantized conductance [6,7], the Dicke model [8,9], and magnetism realized via artificial gauge fields for ultracold atoms [10]. Such artificial gauge fields can make the neutral ultracold atoms behave as if they were charged particles experiencing a magnetic field and were investigated experimentally and theoretically with an external lattice potential [11,12,13] or without one [14,15,16]. To obtain the results presented in this work, we used the MCTDH-X software hosted at http://ultracold.org (accessed on π-day, 14 March 2021), see References [38,50,71,72,73,74]

Methods

Results

Conclusion