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Physical Review A

Detection of nonclassical states using a Kerr medium

Mark S. Hillery

Published Oct 1, 1991• 22 citations
Publisher

Abstract

It is possible to determine whether the input state to a Kerr medium is nonclassical by measuring the total noise of the output state. For a classical input state the total noise at the output has a minimum value that depends on the photon number and the interaction time. If the total noise is found to be less than this value, then it can be concluded that the input state was nonclassical. A certain class of generalized coherent states can be detected in this way.

DOI
10.1103/physreva.44.4578

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It is possible to determine whether the input state to a Kerr medium is nonclassical by measuring the total noise of the output state. For a classical input state the total noise at the output has a minimum value that depends on the photon number and the interaction time. If the total noise is found to be less than this value, then it can be concluded that the input state was nonclassical. A certain class of generalized coherent states can be detected in this way.
The total noise of a field state is a measure of the fluctuations of the field amplitude. It is a minimum for coherent states. As the behavior of a state becomes more nonclassical, its total noise increases. This is shown first for several specific types of nonclassical states, among them squeezed and sub-Poissonian states. These results are generalized by using nonclassical distance to measure how nonclassical a field state is. A lower bound for the total noise is derived that is an increasing function of nonclassical distance. From it one can conclude that highly nonclassical states have large amplitude fluctuations.
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 12(|0⟩+|20⟩). Finally, we suggest one possible application of this state in the field of optomechanics.
The total noise of a state is the sum of the fluctuations in the real part of the field amplitude and those in the imaginary part. It is a measure of the total fluctuations in the field amplitude and is a minimum for coherent states. Several examples of nonclassical fields are considered, and it is shown that as nonclassical behavior increases so does total noise. For example, total noise increases as a state becomes more squeezed or as the photon statistics become more sub-Poissonian. This result is then generalized by using the concept of nonclassical distance. Nonclassical distance δ is a measure of the extent to which the behavior of a field state differs from that of classical states. A lower bound for the total noise is derived which is an increasing function of δ. This means that the more nonclassical a state is the greater its total noise must be.
We construct a distinct class of nonlinear displaced Kerr states by application of the displacement operator upon a state which is prepared by sending the well-known photon-added coherent state through a normal Kerr medium. A sketch for the experimental setup for preparing the state is suggested. We evaluate some statistical properties such as the photon number distribution, Mandel’s Q parameter, Husimi-Q and Wigner functions, and quadrature squeezing for the nonlinear displaced Kerr state and then analyze the nonclassicality in terms of these standard parameters. We reduce the infinite-level problem to a truncated discrete two-level system by using a low Kerr parameter approximation and then convert the generated nonclassicality into bipartite entanglement between the two modes of an output state of a linear optical device.
Non-Gaussian quantum states of light are essential resources for quantum information processing and precision metrology. Among them, generalized coherent states (GCS), which naturally arise from the evolution of a coherent state with a nonlinear medium, exhibit useful quantum features such as Wigner negativity and metrological advantages [Phys. Rev. Res. 5, 013165 (2023)]. Because these states remain coherent to all orders, their nonclassical character cannot be revealed through standard intensity-intensity correlation measurements. Here, we demonstrate that the intensity-field correlation function alone provides a simple and experimentally accessible witness of nonclassicality. For GCSs, any deviation of this normalized correlation from unity signals nonclassical behavior. We derive analytical results for Kerr-generated states and extend the analysis to statistical mixtures of GCSs. The proposed approach enables real-time, low-complexity detection of quantum signatures in non-Gaussian states, offering a practical tool for experiments across a broad range of nonlinear regimes.