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ULTRACOLD ATOMS Engaged in gauge Two independent cold-atom experiments have demonstrated the building blocks for the simulation of dynamical gauge felds — an advance that holds promise for our understanding of computationally intractable problems in high- . Cheng Chin

nteractions between light and Matter explain how we see things in daily life. Gauge field IBut how atoms in a material transfer their presence to light is non-trivial: the eiϕ0 same carbon atoms that make diamond shiny can make graphite appear pitch black. The reason involves the fundamental eiϕ1 coupling between and atoms, which addresses by treating photons as gauge fields. In practice, however, this formulation quickly becomes computationally intractable as both the matter and photons are many- body quantum fields, and their coupling generally leads to complex correlations and entanglement. Writing in Nature Physics, Frederik Görg and colleagues1 and Christian 2 Schweizer and colleagues have now Fig. 1 | Experimental scheme to generate a dynamical lattice gauge field. Atoms in two spin states — pushed us closer to realizing experimental one (red) representing the matter field and the other (black) representing the gauge field — are loaded simulations of these systems. into optical lattices. Open circles are empty sites. The lattice reported in the experiments

Researchers working with cold atoms (shown in the yellow region) is characterized by different Peierls phases ϕ0 and ϕ1 of the tunnelling of have long attempted to mimic the physics the matter field depending on the site occupancies of the gauge field. of gauge fields, which generalize the concept of electromagnetic fields and carry forces between fundamental particles3. An important milestone was achieved in 2009 The ability to manipulate different vector Secondly, the gauge requires a with an apparatus in which neutral atoms potentials without changing the physics is fine control of the form and the strength feel forces identical to those experienced a property of the theory that is known as of their coupling. Finally, experiments by charged particles in electric and ‘gauge symmetry’. frequently suffer from fast atom loss and magnetic fields4. Despite these advances, The term dynamical gauge fields heating because of the inelastic the task of constructing a quantum system highlights the key difference between scattering, calling for new approaches to whose can be interpreted as a the experiments reported here and improve the stability of the set-ups. coupled matter–gauge field5 remained earlier ones. Previously realized artificial Substantial progress was made recently elusive, as did the ability to use cold atoms electromagnetic fields were either static or by harnessing the Floquet engineering to simulate the physics of dynamical had their dynamics completely constrained technique6. In a Floquet scheme, modulation gauge fields. by external controls. Such static or slaved at frequency ω can couple two quantum So what is a dynamical gauge field? The gauge fields cannot support gauge , states with energy difference ħω, where term gauge field refers to an important analogues of photons in . ħ is the reduced Planck constant, and but technical property of the theory Thus, the experiments reported here one can superimpose multiple frequency of elementary particles: as the force represent a notable improvement of the state components to the modulation waveform to carriers, the gauge fields always interact of the art, where two key ingredients — couple more states. Within this framework, a with particles through their geometrical gauge–matter coupling and gauge symmetry constant proportional to the . For example, electromagnetism — are incorporated simultaneously. atomic density was introduced to a Bose– can be formulated in terms of the vector The synthesis of dynamical gauge Einstein condensate through simultaneous and potentials (the gauge fields), fields in ultracold experiments requires modulations of the lattice potential and but forces all arise from their derivatives: overcoming several challenges. Firstly, new atomic interactions7. electric and magnetic fields. There are an degrees of freedom need to be introduced The experiments conducted by Görg and infinite number of vector potentials that to the cold atoms to allow them to represent colleagues and Schweizer and colleagues give rise to the same electric and magnetic the matter and gauge fields separately, as have brought the synthesis of gauge fields fields, a feature described as ‘gauge freedom’. well as making one depend on the other. to the next level. The ultimate goal is to

Nature Physics | www.nature.com/naturephysics news & views simulate lattice gauge (Fig. 1). synthesized indeed depended on the site progression towards larger systems and more Researchers realized that in a setting based occupancy. exotic gauge symmetries. One can imagine on two atoms in a double-well potential, the Schweizer and colleagues simulated a future where cold-atom experiments 9 presence of an atom in one lattice site — left a Z2 with bosonic play a role in helping to understand lattice or right — affects the quantum-mechanical particlesI in their version of the double-well models, and in phase of the second atom as it tunnels experiment. Here, Z2 symmetry refers to the enabling ab initio calculations of physical between the two sites. This quantum phase, gauge symmetry whereI the product of the quantities of fundamental interest. ❐ called the Peierls phase, is analogous to and its surrounding electric fields is the Aharanov–Bohm phase that a charged a constant of motion2. To control the Peierls Cheng Chin particle acquires in moving through a phases, a clever trick was implemented: James Franck institute, institute, , and is also what characterizes by offsetting the two wells precisely by and Department of Physics, University of Chicago, the lattice gauge field8. A density-dependent the atomic energy, tunnelling Chicago, IL, USA. gauge field thus requires the Peierls phases processes for different occupancies can be e-mail: [email protected] to be different for different atomic lattice induced by the same frequency component site occupancy. in the modulation2. The density dependence Published: xx xx xxxx Görg and colleagues controlled the and the gauge symmetry of the field were https://doi.org/10.1038/s41567-019-0664-8 tunnelling of fermionic particles between confirmed from the dynamics of the coupled References two sites by modulating the lattice at matter–gauge system. 1. Görg, F. et al. Nat. Phys. https://doi.org/10.1038/s41567-019- the frequency that matched the energy The experiments carried out by 0615-4 (2019). difference between the states before and Görg and colleagues and Schweizer and 2. Schweizer, C. et al. Nat. Phys. https://doi.org/10.1038/s41567-019- 0649-7 (2019). after the tunnelling. To imprint different colleagues, while so far limited in sample 3. Cheng, T.-P. & Li, L. F. Gauge Teory of Peierls phases for different occupancies, size, demonstrated the power of Floquet Physics (Oxford University Press, 1991). the researchers employed a two-frequency engineering in the bottom-up construction 4. Lin, Y.-J., Compton, R. L., Jimenez-Garcia, K., Proto, J. V. & Spielman, I. B. Nature 462, 628–632 (2009). modulation with the frequencies specifically of the lattice gauge models with cold atoms 5. Wiese, U. J. Annalen der Physik 525, 777–796 (2013). tuned to assist different tunnelling processes. in optical lattices. Future experiments will 6. Eckardt, A. Rev. Mod. Phys. 89, 011004 (2017). Measurements from Ramsey interferometry continue to add features that are important 7. Clark, L. W. et al. Phys. Rev. Lett. 121, 030402 (2018). 8. Jiménez-García, K. et al. Phys. Rev. Lett. 108, 225303 (2012). confirmed that the Peierls phases, or for the simulation of models of particle and 9. Barbiero, L. et al. Preprint at https://arxiv.org/abs/1810.02777 equivalently the gauge fields, that were high-energy physics. We expect a steady (2018).

Nature Physics | www.nature.com/naturephysics