Verifying cross-Kerr induced number squeezing: a case study

Abstract

We analyse an experimental method for creating interesting nonclassical states by processing the entanglement generated when two large coherent states interact in a cross-Kerr medium. We specifically investigate the effects of loss and noise in every mode of the experiment, as well as the effect of ‘binning’ the post-selection outcomes. Even with these imperfections, we find an optimal set of currently achievable parameters which would allow a proof-of-principle demonstration of number squeezing in states with large mean photon number. We discuss other useful states which can be generated with the same experimental tools, including a class of states which contain coherent superpositions of differing photon numbers, e.g. good approximations to the state $\frac{1}{\sqrt{2}}(|0⟩+|20⟩)$. Finally, we suggest one possible application of this state in the field of optomechanics.

Keywords:

• Cross-Kerr
• number squeezing
• photon statistics

Acknowledgements

The original idea for our experimental proposal was conceived in collaboration with: Aephraim Steinberg, Josiah Sinclair, Matin Hallaji and Greg Dmochowski; we thank them for useful discussions towards making a realistic model. Finally, we thank Nicolás Quesada for helpful input and fruitful discussions.

Notes

No potential conflict of interest was reported by the authors.

1 However, if high data rates are crucial, a more sophisticated experiment could use feedback to keep more of the signal photons: one would simply apply a displacement operator whose magnitude was a function of the phase measurement’s outcome, such that the mean photon number in all shots was identical after the displacement. This would allow one to include more of the measurement results while suffering only a small decrease in squeezing [8].

2 We assume most of the inefficiency occurs from detector inefficiencies.

3 An additional limitation is imposed by the theoretical limit $\text{min}[\mathit{\delta }\mathit{\varphi }]=\frac{1}{2|\mathit{\alpha }|}$, which becomes important once other sources of phase noise are removed and for smaller $\mathit{\alpha }$ than considered here.

Additional information

Funding

D.S., K.M., and D.F.V.J acknowledge support from the Canadian Network for Research and Innovation in Machining Technology; Natural Sciences and Engineering Research Council of Canada.