Constrained Dynamics via the Zeno Effect in Quantum Simulation: Implementing Non-Abelian Lattice Gauge Theories with Cold Atoms

Abstract

We show how engineered classical noise can be used to generate constrained Hamiltonian dynamics in atomic quantum simulators of many-body systems, taking advantage of the continuous Zeno effect. After discussing the general theoretical framework, we focus on applications in the context of lattice gauge theories, where imposing exotic, quasi-local constraints is usually challenging. We demonstrate the effectiveness of the scheme for both Abelian and non-Abelian gauge theories, and discuss how engineering dissipative constraints substitutes complicated, non-local interaction patterns by global coupling to laser fields.PACS numbers: 03.65. Xp,37.10.Jk,11.15.Ha Laboratory experiments with atomic quantumdegenerate gases have established a synergetic link between atomic physics and condensed matter [1][2][3], and hold prospects for a similar connection to high-energy physics [4][5][6][7][8][9][10][11][12]. Loaded into optical lattices, cold atoms realize Hubbard models, which can be designed and controlled via external fields to mimic the dynamics of quantum many-body systems in equilibrium and nonequilibrium situations [3, 13]. While a focus of research during the last decade has been the development of a toolbox for designing specific lattice Hamiltonians [1-3], we address below the problem of implementing desired Hubbard dynamics in the presence of constraints, i.e., we wish to keep the system dynamics within a certain subspace of the total Hilbert space. A familiar way of imposing such constraints is to add an energy penalty to the Hamiltonian [14]. Below, we describe an alternative scenario that is based on driving the system with engineered classical noise, exploiting the Zeno effect [15][16][17][18][19][20]. As we will see, 'adding noise' provides a general tool to implement -in an experimentally efficient and accessible way -highly nontrivial constraints in quantum many-body systems.The present work is motivated by the ongoing quest to build a quantum simulator for Abelian and non-Abelian lattice gauge theories (LGTs) with cold atoms in optical lattices [5][6][7][8][9][10][11][12].LGTs play a prominent role in both particle and condensed matter physics: in the standard model, the interaction between constituents of matter are mediated by gauge bosons [21][22][23][24], and in frustrated magnetism, quantum spin liquids are suitably described in the language of gauge theories [14,25,26]. The key feature of a LGT is the presence of local (gauge) symmetries. The generators G a x of these local gauge transformations, with x denoting lattice sites and a a color index, commute with the lattice Hamiltonian, [H 0 , G a x ] = 0 for all x, a, and thus provide local conservation laws. They can be interpreted in analogy to Gauss's law from electrodynamics, as they constrain the dynamics of the system to a physical LGTs consist of fermions ψx living on sites, coupled to gauge fields Ux,x+1 living on links. The dynamics can be constrained to the physical subspace by coupling independent noise sources linearly to each gener...

Formulation of lattice gauge theories for quantum simulations

“…In particular, we focus on characterizing the matter degrees of freedom in terms of fermionic operators which define a Fock space on each lattice vertex and describe multi-component fermions like the ones customarily used in cold atom experiments, for example in the context of lanthanide atoms like ytterbium [34] or erbium [35] presenting several nuclear hyperfine states which can be addressed separately. This method has already been used in several proposals for quantum simulations of lattice gauge theories [15,18,21], applying approaches such as the prepotential formalism [36,37] and the link model [38][39][40][41], in which the gauge degrees of freedom are composed out of bosons or fermions, respectively. In both these approaches, the link is divided into "left" and "right" parts, with two families of such fundamental ingredients.…”

“…Furthermore, the fast developments in the control of the interactions among atoms in an optical lattice (as well as other systems, such as trapped ions and superconducting circuits) envision the possibility of obtaining, in the near future, quantum simulations of both Abelian and non-Abelian lattice gauge theories [11][12][13][14][15][16][17][18][19][20][21][22]. This is of particular interest, for example, for solving problems involving fermions with finite chemical potential (for example, as expected in exotic phases of QCD, such as quark-gluon plasma and color superconductivity [23,24]).…”

Dissipative universal Lindbladian simulation

“…For example one can dissipatively achieve quantum state preparation [17,18], quantum simulation [19], holonomic quantum computation [20] and even universal computation [21]. Simulation of highly non-trivial properties of matter as topological order [22] and non-abelian synthetic gauge fields [23] can also be accomplished by dissipative means. Finally, all forms of QIP that encode information in the ground state of a time-dependent Hamiltonian, e.g., open system adiabatic quantum computation and quantum annealing, also benefit from dissipation and relaxation to negate thermally driven errors [24][25][26].…”

“…[16][17][18][19][20][21][22][23]. In this paper we have shown how a suitable coherent coupling between a quantum system S and an environment comprising multiple qubits subject to strong Markovian dissipation, can be used to simulate universal Lindbladian dynamics over S. More precisely, by using high-order virtual dissipative processes, one can build an effective Liouvillian generator in arbitrary Lindblad form [31] that governs the dynamics of S exactly in the limit (7), as a function of log 10 (t).…”

Zeno Hall Effect

“…Here controlled dissipation can serve as a resource for quantum coherence and entanglement [7,8], with versatile applications to quantumstate preparation [9][10][11], quantum computation [12] and quantum simulation [13,14].…”