Quantum demolition measurement of photon statistics by atomic beam deflection

Abstract

We consider the deflection of a resonant two-level atom by a quantized electromagnetic field using the Jaynes-Cummings Hamiltonian. We show that a joint measurement of the atomic momentum and an appropriate field variable allows us to reconstruct the original photon statistics even for this demolition Hamiltonian. We demonstrate that the momentum distribution of atoms scattered at the nodes of the standing wave also follows the original photon statistics of the field. In this sense a recent experiment on the optical Stern-Gerlach effect [T. Sleator et al., Phys. Rev. Lett. 68, 1996] measures the intensity fluctuations of the standing wave.

Quantum atomic lithography via cross-cavity optical Stern–Gerlach setup

“…2 we display the 2D momentum distribution in the dimensionless space ℘ x ∕Λ × ℘ y ∕Λ, computed for the interaction parameters (a) Λ 5 and (b) Λ 20. As expected, the resolution of the distribution function becomes better as the interaction parameter Λ is increased [2][3][4]. Moreover, the components of transverse momentum acquired by the atoms are given by a summation over the Fourier transforms F m;n ℘; ϕ, which, because of their dependence on the e −iρ℘ cosθ−ϕ− n p Λ term [see Eq.…”

“…At the beginning of the 1990s, the optical Stern-Gerlach (OSG) effect [1] was explored in a number of studies [2][3][4], with a view to extracting information about a cavity field state through its interaction with an atomic meter. Relying on the fact that the momentum distribution of scattered atoms follows the photon statistics of the field state, strategies have been devised to reconstruct the statistics [2] and even the full state of a cavity mode [3].…”

“…Relying on the fact that the momentum distribution of scattered atoms follows the photon statistics of the field state, strategies have been devised to reconstruct the statistics [2] and even the full state of a cavity mode [3]. These OSG strategies differ from other measurement devices in quantum optics, such as quantum nondemolition [5] and homodyne techniques [6], that have been extensively explored from the 1990s until now [7].…”

Phase Space as Arena for Atomic Motion in a Quantized Light Field

“…We can for example consider the properties of the quantum fleld ignoring the transverse motion of the atom or vice versa concentrate on the motion while ignoring the field variables. Moreover we can, of course, investigate the entanglement between the atomic and field variables via joint measurements [8,12]. In the present paper, however, we confine ourselves to the measurements of the atomic motion only.…”

Quantum Measurements in Atom Optics

“…Holland et ale (1991) have shown that if the frequency of the light is sufficiently detuned from the atomic resonance and the cavity Q is sufficiently high, the momentum distribution of the scattered atoms constitutes a QND readout of the photon number observable. For the case of a resonant two-level atom, Herkommer et al (1992) have shown that a joint measurement of the atomic momentum and an appropriate field variable allows us to reconstruct the original photon statistics even for this demolition Hamiltonian. Proposals for experiments have been put forward by Treussart et al (1994) and Matsko et al (1994).…”