Enhancing the Thermal Stability of Majorana Fermions with Redundancy Using Dipoles in Optical Lattices

Pairing between spinless fermions can generate Majorana fermion excitations that exhibit intriguing properties arising from nonlocal correlations. But, simple models indicate that nonlocal correlation between Majorana fermions becomes unstable at nonzero temperatures. We address this issue by showing that anisotropic interactions between dipolar fermions in optical lattices can be used to significantly enhance thermal stability. We construct a model of oriented dipolar fermions in a square optical lattice. We find that domains established by strong interactions exhibit enhanced correlation between Majorana fermions over large distances and long times even at finite temperatures, suitable for stable redundancy encoding of quantum information. Our approach can be generalized to a variety of configurations and other systems, such as quantum wire arrays.

Figure 1

Schematic of dipolar fermions (spheres) in a 2D optical lattice. Dipolar moments $\overrightarrow{p}$ (arrows on each sphere) align along an applied field, at an angle $\theta$ with the $x$ axis.

Figure 2

The thermal expectation value of SOs from QMC calculations as a function of an applied global field for several system sizes for $V_y=4.8t$ and $\mu =0$. The top (bottom) panel shows data for a characteristic low (high) temperature. The insets show schematic examples of a MF domain that breaks up into two MF domains at high temperatures. The $+$’s in the figures is fermion parity for the entire chain, and each chain has the same parity for the one configuration drawn. Empty dashed circles denote empty MF edge states; hatched circles denote MF edge states occupied by one particle per row.

Figure 3

Top: The susceptibility of the string-string correlation function $O$ from QMC simulations for different $L$’s at $V_y=4.8t$ and $\mu =0$. The SOs tend to order along the $y$ direction for $T<T_c$. The inset shows a schematic of an ordered domain with MFs forming columns at the ends (dashed lines). The domains shrink for $T>T_c$. Bottom: $T_c$ extrapolated to $L\to \infty$. The solid line is a linear chi-squared fit.

Figure 4

The main panel plots the energy splitting between two sectors defined by $P_j=\pm 1$ for all $x$ rows as a function of chemical potential for Eq. (2) at $T=0.16t$ and $V_y=4.8t$. Inset (a) shows a weak linear increase in density with increasing $\mu$ inside the topological phase ($\mu \lesssim 1.5t$). Inset (b) shows a schematic phase diagram established by the lifting of the degeneracy; see the horizontal arrow. The vertical arrow indicates the thermal phase transition explored in Fig. 3. MFT denotes the mean field theory result.