Analog quantum simulation of(1+1)-dimensional lattice QED with trapped ions

Abstract

The prospect of quantum simulating lattice gauge theories opens exciting possibilities for understanding fundamental forms of matter. Here, we show that trapped ions represent a promising platform in this context when simultaneously exploiting internal pseudo-spins and external phonon vibrations. We illustrate our ideas with two complementary proposals for simulating lattice-regularized quantum electrodynamics (QED) in (1 + 1) space-time dimensions. The first scheme replaces the gauge fields by local vibrations with a high occupation number. By numerical finite-size scaling, we demonstrate that this model recovers Wilson's lattice gauge theory in a controlled way. Its implementation can be scaled up to tens of ions in an array of micro-traps. The second scheme represents the gauge fields by spins 1/2, and thus simulates a quantum link model. As we show, this allows the fermionic matter to be replaced by bosonic degrees of freedom, permitting smallscale implementations in a linear Paul trap. Both schemes work on energy scales significantly larger than typical decoherence rates in experiments, thus enabling the investigation of phenomena such as string breaking, Coleman's quantum phase transition, and false-vacuum decay. The underlying ideas of the proposed analog simulation schemes may also be adapted to other platforms, such as superconducting qubits.

Meissner-like Effect for a Synthetic Gauge Field in Multimode Cavity QED

“…Most intriguingly, the tunability of the parameters controlling the effective matter-light coupling potentially allow one to simulate the behaviour of matter with alternate values of the fine structure constant α. This could provide a continuum gauge field theory simulator complementary to the proposals for simulating lattice gauge field theories using ultracold atoms [55][56][57][58][59][60][61][62][63][64][65], trapped ions [66][67][68][69], or superconducting circuits [70,71]. Other opportunities arising from our work are to explore the differences between Bose-condensed, thermal, and fermionic atoms in the geometry considered above: The Meissner effect depends on the phase stiffness of superfluid atoms, so should vanish at higher temperatures.…”

Quantum dynamics of trapped ions in a dynamic field gradient using dressed states

“…The equivalence of static and dynamic MAGIC shown above allows for applying results obtained using static MAGIC, such as [26,33,34], to dynamic MAGIC. One consequence is that the scheme proposed heredynamic MAGIC combined with dressed states-does not require to null the dynamic magnetic field at the ion position.…”

U(1) Wilson lattice gauge theories in digital quantum simulators

“…However, non-equilibrium properties, as relevant for a variety of high-energy physics phenomena including particle-antiparticle production at high-intensity laser facilities [11,12], are not accessible, due to the fundamental sign (or complex action) problem affecting numerical simulations in real time [13]. In the last few years, several proposals for quantum simulations of real-time dynamics of lattice gauge theories have been put forward [14][15][16], based on a variety of platforms ranging from cold atoms in optical lattices [17][18][19][20][21][22][23], to superconducting circuits [24,25] and trapped ions [26,27]. The main difficulties in implementing gauge theories in quantum simulators stem from the fact that complex many-body interactions have to be realized, while at the same time local (gauge) symmetries have to be imposed on the system dynamics [14][15][16].…”