Localization of Atoms by Homodyne Measurement

T. Richter

A. M. Herkommer, H. J. Carmichael, Wolfgang P. Schleich

We study a continuous homodyne measurement of the field transmitted from an optical cavity. In particular, we investigate the back-action of this measurement onto an atom whose centre-of-mass motion is entangled with the cavity field. Using the method of quantum trajectories we calculate analytically and numerically the time evolution of the entangled quantum state, and demonstrate the localization of the atom relative to the nodes of the cavity field. We compare the quantum trajectory formalism of the continuous homodyne measurement to a projection onto quadrature eigenstates of the field and show that in the long-time limit both descriptions are identical.

Stephen J. Kadlecek, Jennifer Sebby-Strabley, Nathan Harrison +1 more

R. L. de Matos Filho, W. Vogel

Squeezing in resonance fluorescence was predicted more than a decade ago,1 but it has not been observed until now. There are lwo problems in connection with such an experiment. First, in a homodyne measurement of the photon statistics the observable effect is limited by the detection and collection efficiencies and is therefore extremely small.2 Second, since the squeezing effect is phase sensitive, the atom must be localized very well. To overcome these problems, homodyne intensity-correlation measurements of the fluorescence from a trapped ion have been proposede.3

Sajid Qamar, Muhammad Suhail Zubairy

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.