Boson sampling with self-generation of squeezing via interaction of photons and atoms

TL;DR

This paper proposes a new method for boson sampling using a multimode resonator with atoms and photons that self-generate squeezing, eliminating the need for external photon sources and complex interferometers, potentially enabling quantum advantage.

Contribution

It introduces a novel scheme for boson sampling that replaces traditional interferometers with a self-squeezing resonator involving atom-photon interactions, simplifying implementation and scaling.

Findings

The scheme can generate multimode squeezed states without external sources.

The joint probability distribution can be computed via a matrix hafnian.

Experiments are feasible with current cavity-QED and cold-gas technology.

Abstract

We suggest a novel scheme for generating multimode squeezed states for the boson sampling implementation. The idea is to replace a commonly used linear interferometer by a multimode resonator containing a passive optical element consisting of two-level atoms dispersively interacting with photons and self-generating a squeezed compound state of both bosons -- photons and atoms. The suggested scheme does not need (a) on-demand external sources of photons in squeezed or Fock quantum states and (b) numerous interchannel couplers which introduce phase noise and losses that prevent scaling up the system and achieving quantum advantage. The idea is illustrated by a setup based on a Bose-Einstein-condensed gas confined in a multimode resonator, one of whose optical modes is in the classical coherent regime. The joint probability distribution of photon and/or noncondensed atom numbers is calculated via a matrix hafnian that, for certain parameters of the system, is hardly to be effectively calculated by classical computers. Such experiments are at reach via existing cavity-QED and cold-gas technology.