Squeezing in a nonlocal photon fluid

Quantum fluids of light are an emerging tool employed in quantum many-body physics. Their amazing properties and versatility allow using them in a wide variety of fields including gravitation, quantum information, and simulation. However the implications of the quantum nature of light in nonlinear optical propagation are still missing many features. We theoretically predict classical spontaneous squeezing of a photon fluid in a nonlocal nonlinear medium. By using the so called Gamow vectors, we show that the quadratures of a coherent state get squeezed and that a maximal squeezing power exists. Our analysis holds true for temporal and spatial optical propagation in a highly nonlocal regime. These results lead to advances in the quantum photon fluids research and may inspire applications in fields like metrology and analogs of quantum gravity.

Figure 1

(a) Uncertainty principle $\mathrm{\Delta }{u}^2\mathrm{\Delta }{v}^2$ behavior as function of $\gamma$. The inset shows that the phase space distribution area changes with $\gamma$ and hence with $P$ and $\sigma$, while the phase space distribution form varies from circular to elliptical during the propagation. (b) Normalized quadratures $u$ (blue line) and $v$ (red line) uncertainties and uncertainty principle $\mathrm{\Delta }{u}^2\mathrm{\Delta }{v}^2$ (magenta line). Squares represent the theoretical behavior for the two normalized quadratures $u$ (blue squares) and $v$ (red squares) in a semilogarithmic scale after Eq. (14) with $P=100$ and $\sigma =15$. Green dot-dashed curve provides the expected result in the hydrodynamical regime after Eq. (19). Dashed lines evidence the three region limits. (c) Same as (b) for the temporal case with $P=100$ and $T=10$. The inset is the convolution integral $\mathcal{R}\left(t\right)$ behavior as function of time (blue line). The green dashed curve is the series expansion trend around the convolution maximum at $\overline{t}$.

Figure 2

(a) Numerical solution of Eq. (3) with $P=100$ and $\sigma =15$. (b) Wigner function calculated after Eq. (3) of the evolved beam in panel (a) at $z=2$, with ${\overline{k}}_x=257$; the inset shows the Wigner function of the initial condition of panel (a). (c) Numerical solution of Eq. (21) with $P=100$ and $T=10$. (d) The same as (b) for the evolved beam in panel (c) with ${\overline{k}}_t=128$.