Cold Atom Simulation of Interacting Relativistic Quantum Field Theories

We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.

Figure 1

(a) The one-dimensional superlattice with tunneling fermionic atoms that simulates Dirac fermions. Each unit cell includes two fermion sites, $a$ and $b$. An alternating distortion of the tunneling couplings $J$ and $J-\delta$ gives rise to the mass term, $\delta$. (b) The energy dispersion relation as a function of momentum, $p$. At half filling and for $\delta =0$ the low energy behavior is linear with respect to $p$, allowing the Dirac operator description.

Figure 2

The regularized mass $M$, in units of $\hslash /(v_{s}l)$, as a function of the tunneling disorder $\delta$ for various interaction strengths $U$. When no interactions are present the mass increases, as expected, linearly as a function of $\delta$. The presence of interactions dramatically changes this behavior even for moderate ratios of $U/J$.

Figure 3

The one-dimensional optical lattice with tunneling fermions and bosons that simulates the Dirac fermion-scalar field model. The bosonic sites are placed in between the fermionic ones with double spacing. In this way the bosonic population on site $i$ controls the fermionic tunneling within the same cell.