Schemes for nondestructive quantum gas microscopy of single atoms in an optical lattice

We propose a quantum gas microscope for ultracold atoms that enables nondestructive atom detection, thus evading higher-band excitation and change of the internal degrees of freedom. We show that photon absorption of a probe beam cannot be ignored even in dispersive detection to obtain a signal-to-noise ratio greater than unity because of the shot noise of the probe beam under a standard measurement condition. The first scheme we consider for the nondestructive detection, applicable to an atom that has an electronic ground state without spin degrees of freedom, is to utilize a magic-wavelength condition of the optical lattice for the transition for probing. The second is based on the dispersive Faraday effect and squeezed quantum noise and is applicable to an atom with spins in the ground state. In this second scheme, a scanning microscope is adopted to exploit the squeezed state and reduce the effective losses. Application to ultracold ytterbium atoms is discussed.