Nonlinear interferometer as a resource for maximally entangled photonic states for Heisenberg-limited interferometry

Christopher C. Gerry, Richard A. Campos

Christopher C. Gerry, Adil Benmoussa, Richard A. Campos

Nonlinear interferometers are Mach-Zehnder interferometers with Kerr media in either one or both arms. We refer to these devices, respectively, as the asymmetric and symmetric nonlinear interferometers. In the asymmetric case, with one input mode in the vacuum, it is possible to generate maximally entangled photonic states or superpositions of such states. We consider the device as a resource of entangled states for applications to Heisenberg-limited interferometry. Interferometry with the maximally entangled states cannot be performed by simply subtracting the output photocounts as in standard interferometry. Instead, one must perform parity measurements on only one of the output beams. We show that the symmetric nonlinear interferometer, with one input mode in the vacuum, may be used to perform such parity measurements. The same device is shown to produce, with an input coherent state and upon projective measurements, even or odd coherent states, examples of the Schr\"odinger-cat states.

Florian Kaiser, Lutfi Arif Ngah, Amandine Issautier +9 more

Christopher C. Gerry, Adil Benmoussa

Maximally entangled photonic states of a two-mode field have applications in Heisenberg-limit interferometry and in photolithography where they may be used to transfer images with resolutions exceeding the Rayleigh diffraction limit. In a recent paper by one of us [C. C. Gerry, Phys. Rev. A 61, 043811 (2000)] it was shown that a nonlinear four-wave mixer could produce the requisite states for input states containing only even photon numbers. For superpositions of even number states the output is just a superposition of maximally entangled even states. In the present paper we extend the earlier work to consider both even coherent states and squeezed vacuum states as inputs and study their applications to interferometry and lithography.

Juan P. Torres, Konrad Banaszek, Ian A. Walmsley

Christopher C. Gerry

A model of a four-wave mixer operated in a nonlinear regime, studied by Yurke and Stoler [Phys. Rev. A 35, 4846 (1987)], is reexamined. Yurke and Stoler have shown that this device, under a certain condition, acts as an even-odd filter, switching even-photon-number states from the pump mode to the signal mode. An initial coherent state in the pump is converted into an entanglement of even and odd coherent states with vacuum states in the output signal and pump modes. We point out that under a different condition and with an even-photon-number state initially in the pump and a vacuum in the signal, the device creates a maximally entangled state between the number state and the vacuum. Using the device to replace the first beamsplitter of a Mach-Zehnder interferometer, phase uncertainties at the Heisenberg limit $(\ensuremath{\Delta}\ensuremath{\varphi}=1/n)$ can be obtained. Since number states are difficult to generate, we point out that an even coherent state obtained from the output of one device can be used as input to a second to achieve the phase uncertainties $\ensuremath{\Delta}\ensuremath{\varphi}{=1/n}_{e},$ where ${n}_{e}$ is the average photon number of the even coherent state.