General limit to nondestructive optical detection of atoms

We demonstrate that there is a fundamental limit to the sensitivity of phase-based detection of atoms with light for a given maximum level of allowable spontaneous emission. This is a generalization of previous results for two- and three-level atoms. The limit is due to an upper bound on the phase shift that can be imparted on a laser beam for a given excited-state population. Specifically, we show that no single-pass optical technique using classical light, based on any number of lasers or coherences between any number of levels, can exceed the limit imposed by the two-level atom. This puts significant restrictions on potential nondestructive optical measurement schemes.

Figure 1

Examples of lasers and atomic energy level schemes that are allowable in our analysis. (a) Shows the two-level atom. This can be connected only by a single laser, or else it would be possible to return to the ground state without returning to the original momentum state. (b) Shows a Raman transition with two laser fields. Each laser still causes only one transition, but the excited state for each of those transitions is identical, so in our notation $\mid U_{11}⟩\equiv \mid U_{21}⟩$. (c) Shows a more exotic system where each laser causes multiple transitions but the atoms will still return to the starting state without momentum diffusion. In this example, all four states are multiply defined in the $\mid U_{jl}⟩,\mid L_{jl}⟩$ notation.