arXiv subjects

J. L. Cohen

Publications and source records attributed to J. L. Cohen.

5 recordsLinked to original sources

arXiv1999

Filtered Talbot lens: Producing $λ/2n$-periodic atomic patterns with standing wave fields having period $λ$

We propose a scheme to create high-contrast, periodic atom density distributions having period $λ/2n$ using the Talbot effect, where $% λ$ is the wave length of the optical fields that scatter the atoms and $n$ is a positive integer. This {\em filtered Talbot lens} is comprised of two standing-wave optical fields. An atomic beam propagates perpendicular to the fields. The first field, which is far-detuned from the atomic transition frequency, acts as an array of lenses that focuses the atoms. The second field, positioned at the atom optical focus of the first, is resonant with the atomic transition frequency and acts as an amplitude mask, leaving unperturbed only those atoms that pass through its nodes. At distances following the interaction with the second field that are equal to an integral fraction of the Talbot length, atomic density gratings having period $λ/2n$ are formed.

physics.atom-ph↗

arXiv1999

Atom focusing by far-detuned and resonant standing wave fields: Thin lens regime

The focusing of atoms interacting with both far-detuned and resonant standing wave fields in the thin lens regime is considered. The thin lens approximation is discussed quantitatively from a quantum perspective. Exact quantum expressions for the Fourier components of the density (that include all spherical aberration) are used to study the focusing numerically. The following lens parameters and density profiles are calculated as functions of the pulsed field area $θ$: the position of the focal plane, peak atomic density, atomic density pattern at the focus, focal spot size, depth of focus, and background density. The lens parameters are compared to asymptotic, analytical results derived from a scalar diffraction theory for which spherical aberration is small but non-negligible ($θ\gg 1$). Within the diffraction theory analytical expressions show that the focused atoms in the far detuned case have an approximately constant background density $0.5(1-0.635θ^{- 1/2})$ while the peak density behaves as $% 3.83θ^{1/2}$, the focal distance or time as $θ^{-1}(1+1.27θ^{- 1/2})$, the focal spot size as $0.744θ^{-3/4}$, and the depth of focus as $1.91θ^{- 3/2}$. Focusing by the resonant standing wave field leads to a new effect, a Rabi- like oscillation of the atom density. For the far-detuned lens, chromatic aberration is studied with the exact Fourier results. Similarly, the degradation of the focus that results from angular divergence in beams or thermal velocity distributions in traps is studied quantitatively with the exact Fourier method and understood analytically using the asymptotic results. Overall, we show that strong thin lens focusing is possible with modest laser powers and with currently achievable atomic beam characteristics.

physics.atom-ph↗

arXiv1999

Talbot Oscillations and Periodic Focusing in a One-Dimensional Condensate

An exact theory for the density of a one-dimensional Bose-Einstein condensate with hard core particle interactions is developed in second quantization and applied to the scattering of the condensate by a spatially periodic impulse potential. The boson problem is mapped onto a system of free fermions obeying the Pauli exclusion principle to facilitate the calculation. The density exhibits a spatial focusing of the probability density as well as a periodic self-imaging in time, or Talbot effect. Furthermore, the transition from single particle to many body effects can be measured by observing the decay of the modulated condensate density pattern in time. The connection of these results to classical and atom optical phase gratings is made explicit.

physics.atom-ph↗

arXiv1998

Quasiperiodic Atom Optics, Focusing, and Wave packet Rephasing

We propose a laser field configuration which acts as a quasiperiodic atom optical diffraction grating. Analytical and computational results for the atomic center-of-mass wavefunction after the grating reveal a quasiperiodic density pattern, a semiclassical focusing effect, and a quasiperiodic self-imaging of the atomic wavefunction analogous to a Talbot effect.

physics.atom-ph↗

arXiv1998

High resolution amplitude and phase gratings in atom optics

An atom-field geometry is chosen in which an atomic beam traverses a field interaction zone consisting of three fields, one having frequency $Ω=c/λ$ propagating in the $\hat{z}$ direction and the other two having frequencies $Ω+δ_{1}$ and $Ω+δ_{2}$ propagating in the -$\hat{z}$ direction. For $n_{1}δ_{1}+n_{2}δ_{2}=0$ and $|δ_{1}| T,|δ_{2}| T\gg 1$, where $n_{1}$ and $n_{2}$ are positive integers and $T$ is the pulse duration in the atomic rest frame, the atom-field interaction results in the creation of atom amplitude and phase gratings having period $% λ/[2(n_{1}+n_{2})]$. In this manner, one can use optical fields having wavelength $λ$ to produce atom gratings having periodicity much less than $λ$.

physics.atom-ph↗