Abstract:

It is well-known that electromagnetic field can have different spatial modes, e.g., Hermite-Gaussian or Laguerre-Gaussian modes. Quantum mechanically, each of this spatial modes can have different quantum states and thus may be squeezed in one of its associated conjugate quadratures via different quantum approaches. Fast growing interests have been focused on how to simultaneously squeeze a large number of spatial modes but not a single one owing to its promising applications in diverse fields including quantum imaging processing beyond the standard quantum limit, multipartite quantum entanglement and parallel quantum computation.

In particular, it has been verified experimentally that four-wave mixing (FWM) can be employed to efficiently generate multi-spatial-mode squeezed light. However, up to date, the record has been limited up to 75 squeezed spatial modes. Here, by carefully analyzing the FWM process, we identify that the optical diffraction is the key factor which limits the number of squeezed spatial modes, and also propose a plausible approach to realize more than 106 squeezed spatial modes by manipulating the diffraction in the system. The mechanism to manipulate diffraction is based on the intrinsic properties the FWM process itself which only requires tuning of involved laser parameters like beam widths, intensities and detunings. It should be able to be easily realized in current experimental settings.

Furthermore, we will show how to realize beam focusing and reduction of quantum uncertainty in width at the few photon level in a similar setting. This surprising effect of simultaneous focusing and reduction of width uncertainty is enabled by multi-spatial-mode squeezing, and is not possible via any classical optical approach or single-spatial-mode squeezing.