Abstract
Large optical nonlinearities can have numerous applications, ranging from the generation of cat-states for optical quantum computation, through to quantum sensing where the sensitivity exceeds Heisenberg scaling in the resources. However, the generation of ultra-large optical nonlinearities has proved immensely challenging experimentally. We describe a novel protocol where one can effectively generate large optical nonlinearities via the conditional application of a linear operation on an optical mode by an ancilla mode, followed by a measurement of the ancilla and corrective operation on the probe mode. Our protocol can generate high quality optical Schr{\"{o}}dinger cat states useful for optical quantum computing and can be used to perform sensing of an unknown rotation or displacement in phase space, with super-Heisenberg scaling in the resources. We finally describe a potential experimental implementation using atomic ensembles interacting with optical modes via the Faraday effect.
Highlights
Optical nonlinearities, and the Kerr nonlinear oscillator, have been the focus of much research within quantum optics since the investigations by Milburn and Holmes [1] and Yurke and Stoler [2]
We presented a protocol that can generate a nonlinearity via a conditional linear operation and measurement with feedback
We show how to deterministically generate highly nonlinear quantum states of the probe mode which can be very pure
Summary
The Kerr nonlinear oscillator, have been the focus of much research within quantum optics since the investigations by Milburn and Holmes [1] and Yurke and Stoler [2]. We show that, curiously, one can imprint a nonlinear Hamiltonian (in our case a Kerr) on an optical mode (which we will denote as the probe mode) using only a conditional linear operation from an ancilla mode which is measured. (3) can be used to engineer near perfect nonclassical Kerr cats for use in optical quantum computation and metrology; and (4) can be implemented using optical modes interacting with atomic ensembles via the Faraday effect.
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