Quantum Measurements in Atom Optics

Abstract

We review recent progress in atom optics. We describe new quantum measurements based on the entanglement of quantum states of a light field with atomic external degrees of freedom. Examples include the quantum non-demolition measurement of the photon number in a cavity and the measurement of atomic position.

Generating continuous variable quantum codewords in the near-field atomic lithography

“…Here, revisiting some results of [9,10] on atomic lithography, we show how to embed a qubit in the external degrees of freedom of a free neutral atom. As in [9], we consider a two-level atom passing through an optical cavity and interacting with a single mode of the intracavity electromagnetic field.…”

“…t 2w 0 /v, where w 0 is the cavity mode waist and v is the atom velocity) is short enough so that any variation of the atomic kinetic energy along x due to photon exchanges with the cavity field can be neglected. In this limit the kinetic energy along the cavity axis becomes a constant of motion, equal to its value before the cavity crossing, and therefore can be eliminated from the Hamiltonian of equation (10).…”

“…[9] and [10] on atomic lithography, we show how to embed a qubit in the external degrees of freedom of a free neutral atom. As in Ref.…”

Transmission of Correlated Gaussian Packets Through a Delta-Potential

“…In this case, T (A, B) ≈ B/(2A) = 1 + ρ 2 /(2sZ) 2 . Although this expression is proportional to 1 + ρ 2 = 1 − r 2 −1 , nonetheless we cannot say that it can be obtained from the plane wave transmission coefficient by the replacement → ef , since in the latter case we would obtain from formulas (25) and (26) the new formula T ef = 1 + ρ 2 (p 0 /Z) 2 .…”

“…The dynamics of Gaussian wavepackets possessing nonzero correlation coefficients was studied in [20]. Gaussian correlated packets were used in the analysis of many physical problems, from the wave propagation in optical waveguides [21] and random media [22] to the neutron interferometry [23], cosmology [24] and quantum optics [12,25]. Detailed studies of properties and dynamics of correlated and squeezed coherent states in arbitrary timedependent harmonic potentials were performed in [9,10,[26][27][28][29].…”