Quantum simulation of the Abelian-Higgs lattice gauge theory with ultracold atoms

Abstract

We present a quantum simulation scheme for the Abelian-Higgs lattice gauge theory using ultracold bosonic atoms in optical lattices. The model contains both gauge and Higgs scalar fields, and exhibits interesting phases related to confinement and the Higgs mechanism. The model can be simulated by an atomic Hamiltonian, by first mapping the local gauge symmetry to an internal symmetry of the atomic system, the conservation of hyperfine angular momentum in atomic collisions. By including auxiliary bosons in the simulation, we show how the Abelian-Higgs Hamiltonian emerges effectively. We analyze the accuracy of our method in terms of different experimental parameters, as well as the effect of the finite number of bosons on the quantum simulator. Finally, we propose possible experiments for studying the ground state of the system in different regimes of the theory, and measuring interesting high energy physics phenomena in real time. allows us to obtain information about systems that cannot be accessed experimentally, by investigating others for which state preparation and measurements are much easier tasks.Among the relevant platforms that can serve as quantum simulators, both analog and digital, many atomic and optical systems stand out due to their remarkable experimental controllability. Some examples include ultracold atoms [5][6][7][8][9], trapped ions [10][11][12][13][14], photonic systems [15] and Rydberg atoms [16]. Ultracold atoms in optical lattices, in particular, present the possibility of recreating many different interactions-such as nearestneighbor, long-range forces, on-site interactions, etc-allowing for the simulation of both condensed matter and high energy physics models. Solid-state systems, such as quantum dots [17][18][19] or superconducting circuits [20,21], also show prominent results that make them interesting candidates to perform quantum simulations.Using these ideas, many condensed matter Hamiltonians have been considered for quantum simulations, some of them even realized experimentally. Some examples include spin systems [14,[22][23][24], such as the Ising or Heisenberg models; the Bose-Hubbard model [5,25]; the Tonks-Girardeau gas [26], or copper-oxide superconductors [18]. External gauge potentials can be simulated as well, allowing for the study of the fractional quantum Hall effect [27] and other topological phenomena [28-31]. Quantum simulations of high energy physics models, although more demanding than their condensed matter counterparts, are also possible. Some examples include the simulation of the Dirac [32-34] and Majorana equations [35], the Casimir force [36], the Schwinger mechanism [37] or the oscillations of neutrinos [38, 39]. Simulations of quantum field theories [40, 41], gravitational theories [42] and black holes [43, 44] have been proposed in recent years, some of them realized experimentally as well [45].Within high energy physics, gauge theories are particularly relevant, since they lie in the core of the Standard Model of particle physics [46][47][48][49]; dyn...

Review on novel methods for lattice gauge theories

“…The same authors presented in [394] another simulation scheme for SU (2), which avoided the need for decomposing the links by using the invariant truncation scheme introduced in [363]. More recently González-Cuadra et al [411] showed how six bosonic species would be enough to simulate the Abelian-Higgs model (i.e. a scalar field with U (1) gauge symmetry) based on the same angular momentum conserving scheme.…”

Digital quantum simulation of lattice gauge theories in three spatial dimensions

“…By inspection of (40) we see that for an upper bound on the digitization error of the standard Trotter formula, the commutators among all different parts of the Hamiltonian in (43) have to be evaluated, as well as their norms Since the derivations are very lengthy we will refer the interested reader to the appendix. We provide here the final result: where d is the number of spatial dimensions, d U the dimension of the representation of the group element operator U and  links the number of links in the lattice.…”

“…There are also differences in the proposed simulation scheme: the first one is the analogue approach, where not only the degrees of freedom of the simulated system are mapped to those of the simulating one: by appropriately tailoring the interactions of the simulator, its Hamiltonian is exactly or approximately mapped to the desired one (which can be adiabatically changed). Quantum simulations of this type have been proposed, mostly using ultracold atoms [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], as well as trapped ions [45,46] and superconducting qubits [47,48]. Another approach-the digital one-is based on an idea of Feynman [49], to use a quantum computer (i.e.…”

Quantum phase transitions and the degree of nonidentity in the system with two different species of vector bosons

“…With the help of projectors (16)- (19) and identities (20), we rewrite the block matrix h in terms of spin and pseudospin operators as follows…”

“…Experimental research of ultracold atoms in optical lattices have dramatically expanded the possibilities of a tunable simulation in quantum many-body physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Moreover, ultracold atoms open the path to the parameter range that is hardly possible or even impossible to achieve in the natural condensed matter systems [15][16][17][18][19][20][21].…”