Entangled coherent states and optical homodyne measurements

Barry C. Sanders, K. S. Lee, M. S. Kim

We show that optical homodyne measurements of coherent states, and of superpositions of coherent states, can be described using the joint photon-number distribution for entangled coherent states. The quadrature-phase distribution interference fringes for superpositions of macroscopically distinct coherent states (the so-called ``Schr\"odinger cat states'') are shown to arise from interference in the photon-number distribution for entangled coherent states. The entangled squeezed states are introduced here as squeezed superposition states which are optically mixed with an antisqueezed coherent local oscillator field (squeezing in the other quadrature) at a beam splitter, and we discuss the connection between entangled squeezed states and squeezed-state homodyne detection of squeezed light. Finally the relationship between interference in phase space and fringes in the joint photon-number distribution for the entangled squeezed state is explored.

Osamu Hirota, Genta Masada

Francisco A. Domínguez-Serna, Francisco Javier Mendieta-Jiménez, F. Rojas

Jaehak Lee, Jiyong Park, Jaewan Kim +2 more

Homodyne measurement is a crucial tool widely used to address continuous variables for bosonic quantum systems. While an ideal homodyne detection provides a powerful analysis, e.g., to effectively measure quadrature amplitudes of light in quantum optics, it relies on the use of a strong reference field, the so-called local oscillator, typically in a coherent state. Such a strong coherent local oscillator may not be readily available, particularly for a massive quantum system like a Bose-Einstein condensate, posing a substantial challenge in dealing with continuous variables appropriately. It is necessary to establish a practical framework that includes the effects of nonideal local oscillators for a rigorous assessment of various quantum tests and applications. We here develop entanglement criteria beyond a Gaussian regime applicable for this realistic homodyne measurement that do not require assumptions on the state of local oscillators. We discuss the working conditions of homodyne detection to effectively detect non-Gaussian quantum entanglement under various states of local oscillators.

Z. M. McIntyre, W. A. Coish

The authors propose the use of homodyne detection to detect phase shifts and show that this method is optimal for path-entangled coherent states. This is notable because homodyne measurements do not require photon counting, and the resulting sensitivity is independent of the value of the phase shift itself.

Paul A. Knott, Jacob Dunningham