Superfluidity of light in nematic liquid crystals

Optical analog experiments have captured a lot of interest in recent years by offering a strategy to test theoretical models and concepts that would be otherwise untestable. The approach relies on the similarity between the mathematical model for light propagation in nonlinear optical media and the model to be mimicked. In particular, the analogy between light and a quantum fluid with superfluidlike properties has been studied extensively. Still, while most of these studies use thermo-optical media to perform these experiments, the possibility of using nematic liquid crystals to perform such optical analog experiments remains to be analyzed. This work explores how this medium can constitute an alternative to materials more commonly used in optical analogs, such as thermo-optical media, and how its tunable properties can be advantageous to explore and better control fluidlike properties of light. Moreover, we explore the analogy between the propagation of light and a quantum fluid, and propose a pump-probe experiment to measure the dispersion relation of the superfluid analog.

Figure 1

Bogoliubov-like dispersion relation of the photon-fluid analog in NLCs. (a) The dispersion for the parameters $A=0.1, \nu =200$, and $q=1.0$ (solid line). For comparison, the local ($\nu =0$, dash-dotted curve) and the linear cases (dotted line) are also represented. The dependence of the dispersion relation on the parameters (b) $q$ ($\nu =200$) and (c) $\nu$ ($q=0.1$).

Figure 2

$\left|\zeta \right(k\left)\right|$ as a function of the wave number, for $\nu =100, q=1.0, A=0.1$, and $D_0=1\times {10}^{-8}$.

Figure 3

Representation of the pump-probe experiment, where a flat beam interferes with a perturbation beam at the entrance of the NLC cell. The resulting beam propagates along the cell. By comparing the initial and final intensity profiles and measuring the displacement of the intensity maxima, $\mathrm{\Delta }x$, it is possible to reconstruct the dispersion relation of the fluid of light using Eqs. (14) or (15). By varying the angle at which the beams interfere, one can change the wave number of the perturbations. Simultaneously, a quasistatic electric field applied perpendicular to the direction of propagation provides some tuning of the properties of the system.

Figure 4

Evolution of the intensity patterns of light inside the NLC cell for different regimes. (a) The typical evolution of the intensity pattern for large wave numbers and (b) the same pattern for small wave numbers, i.e., in the deep sonic regime. In both cases, the solid red line tracks the position of an intensity maximum obtained from numerical simulations, while the dashed green line describes the approximation obtained from Eq. (15). The dash-dotted blue line depicts the linear approximation provided by Eq. (14). The numerical simulations were performed by evolving the initial state $E(x,z=0)=A+D_0{e}^{ikx}$ using Eqs. (1) and (2) with $A=0.1, D_0=1\times {10}^{-8}, \nu =100$, and $q=0.1$. $X$ and $Z$ are dimensionless.

Figure 5

Numerical simulations of the pump-probe experiment. The experiment was simulated considering large propagation distances and expression (14) was used to retrieve the dispersion relation.

Figure 6

Numerical results for the evolution of the intensity patterns of light inside the NLC cell. These simulations correspond to the same initial conditions and parameters used in Fig. 4 with the addition of a white noise signal of $10\%$ on top of the perturbation. $X$ and $Z$ are dimensionless.

Figure 7

Results of numerical simulations of the pump-probe experiment in the presence of noise. As in Fig. 5, the experiment was simulated considering large propagation distances and expression (14) was used to retrieve the dispersion relation.