Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter

Abstract

The coupling between gauge and matter fields plays an important role in many models of highenergy and condensed matter physics [1][2][3]. In these models, the gauge fields are dynamical quantum degrees of freedom in the sense that they are influenced by the spatial configuration and motion of the matter field. Since the resulting dynamics is hard to compute, it was proposed to implement this fundamental coupling mechanism in quantum simulation platforms with the ultimate goal to emulate lattice gauge theories [4][5][6][7]. So far, synthetic magnetic fields for atoms in optical lattices were intrinsically classical, as these did not feature back-action from the atoms [8,9]. Here, we realize the fundamental ingredient for a density-dependent gauge field by engineering non-trivial Peierls phases that depend on the site occupation of fermions in a Hubbard dimer. Our method relies on breaking timereversal symmetry (TRS) by driving the optical lattice simultaneously at two frequencies. This creates interfering pathways for density-induced tunnelling, each in resonance with the on-site interaction of two fermionic atoms, and controllable in amplitude and phase. We demonstrate a technique to quantify the amplitude of the resulting density-assisted tunnelling matrix element and to directly measure its Peierls phase with respect to the single-particle hopping. The tunnel coupling features two distinct regimes as a function of the two modulation amplitudes, which can be characterised by a Z 2 -invariant. Moreover, we provide a full tomography of the winding structure of the Peierls phase around a Dirac point that appears in the driving parameter space. For future experiments, this structure provides unique tunability of the associated density-dependent gauge field by using modulation parameters with temporal or spatial dependencies.The fundamental manifestation of a gauge field in electromagnetism is the Lorentz force acting on charged particles. In ultracold Bose and Fermi gases, the charge neutrality of the atoms requires to engineer synthetic magnetic fields. This has been achieved for bulk systems by a rotation of the gas or a suitable coupling of momentum states via Raman lasers [10,11]. For a tight-binding model on a lattice, the equivalent of an Aharonov-Bohm phase can be synthesized with Peierls phases resulting from a complex-valued tunnelling matrix element. Such phases can be engineered in a Floquet approach by a suitable driving scheme [12,13], which has been used in cold atom experiments to generate static gauge fields [14][15][16][17]. In contrast to these classical fields, the simulation of dynamical gauge fields requires the implementation of a back-action mechanism that couples the gauge and matter fields. One possibility is to engineer densitydependent gauge fields by making use of interactions [18]. Such a scheme has recently been implemented experimentally by adding a directional mean-field shift in momentum space to a Bose-Einstein condensate [19]. For tight-binding models a back-action mechanism encode...

Dynamical Spin-Orbit Coupling of a Quantum Gas

“…Our experiment realizes key aspects of several (previously unrealized) theoretical proposals for creating exotic quantum many-body states via cavity-induced dynamical gauge fields, including SOC [16][17][18][19][20][21][22][23][24][25][26][27][28] [29]. By doing so, this work opens avenues toward observing exotic phenomena predicted in these works as well as the creation of dynamical gauge fields, complementing recent progress demonstrating density-dependent gauge fields using optical lattices [30,31]. Specifically, one might be able to explore unusual nonlinear dynamics [19], novel cooling effects in cavity optomechanics [32], striped and quantum Hall-like phases [16,17,21], artificial Meissnerlike effects [28,33], exotic magnetism [18,34], and topological superradiant states [35][36][37].…”

ZN gauge theories coupled to topological fermions: QED2 with a quantum mechanical θ angle

“…We refer the reader to existing literature reviewing these schemes, and extensions thereof [37,50], and to the recent experiments [88] realizing a digital QS (and a variational eigensolver of the massive Schwinger model). We note that there has also been recent progress on the analog QS of dynamical gauge fields [89][90][91][92]. In the following, we will focus on analog QS of the topological Schwinger model (4) using a Bose-Fermi mixture of ultra-cold neutral atoms trapped in an optical lattice.…”

Rabi-resonant behavior of periodically driven correlated fermion systems

“…[51]). In turn, some of its nonequilibrium properties have been also recently considered and experimentally realized [20,22]. Due to underlying symmetries (H 2s commutes with total spin and parity, exchanging i = {1, 2}, operators) Hamiltonian (5) can be block diagonalized.…”

“…In this light, the perturbative approaches to correlated fermions based on the Floquet theorem [11][12][13][14][15][16][17][18][19], though restricted to time-periodic drivings, have turned out to be very efficient and powerful tools, capturing well the experimental realizations [20][21][22][23]. Usually, the accurate determination of the energy absorption in an arbitrarily driven correlated fermion system involves heavy numerical simulation [7,24,25].…”