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arXiv:quant-ph/9608044 · Physical Review A

Bose-stimulated scattering off a cold atom trap

H. David Politzer

Published Feb 1, 1997• 10 citations
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Abstract

The angle and temperature dependence of the photon scattering rate for Bose-stimulated atom recoil transitions between occupied states is compared to diffraction and incoherent Rayleigh scattering near the Bose-Einstein transition for an optically thin trap in the limit of large particle number N. Each of these three processes has a range of angles and temperatures for which it dominates over the others by a divergent factor as N\ensuremath{\rightarrow}\ensuremath{\infty}.

DOI
10.1103/physreva.55.1140

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The angle and temperature dependence of the photon scattering rate for Bose-stimulated atom recoil transitions between occupied states is compared to diffraction and incoherent Rayleigh scattering near the Bose-Einstein transition for an optically thin trap in the limit of large particle number N. Each of these three processes has a range of angles and temperatures for which it dominates over the others by a divergent factor as N\ensuremath{\rightarrow}\ensuremath{\infty}.
We discuss a method for probing a system of cold bosonic atoms in a trap using intense short laser pulses. Above the critical temperature for Bose-Einstein condensation, such a system scatters very weakly. Coherent scattering occurs primarily in the forward direction within a solid angle determined by phase matching conditions for the thermal atomic distribution. Below the critical temperature, the number of scattered photons increases dramatically and the scattered light is emitted into a solid angle determined by the size of the condensate. Quantum statistics of the atoms explicitly effect the spectrum as well as the squeezing properties of the scattered light. The theory accounts for the atom-atom interactions.
We study a novel property of light scattering by Rb atoms confined in a far off-resonance optical dipole force trap. The trapping laser wavelength varies from 780 nm to 860 nm and its intensity is about 1 MW/cm{sup 2}. Spontaneous Raman scattering of photons from the trapping laser can change the ground-state hyperfine quantum number F of the atoms. We observe the relaxation time by measuring the population of the F=3 level after optically pumping the atoms into the F=2 level. Spontaneous photon scatter rates as low as 10{sup 3} s{sup -1} have been observed, corresponding to recoil heating rates below 1 mK/s. For detuning from resonance {Delta} greater than the excited-state fine-structure splitting the total scatter rate, including Rayleigh scattering, decreases as {Delta}{sup 2} while the spontaneous Raman scatter rate decreases as {Delta}{sup 4}. This is due to interference between the Raman scattering amplitudes from the two excited-state fine-structure levels in the Kramers-Heisenberg formula. Because Rayleigh scattering dominates, the atoms` F and M{sub F} quantum numbers are preserved even after many scattering events. This makes far off-resonance optical traps ideal for studies of state-selective collisions and collective phenomena.
We confine 85Rb^{85}\mathrm{Rb}85Rb atoms in an optical dipole force trap with a very large detuning from resonance of up to 65 nm. Confinement times of 200 ms, limited only by background-gas collisions, are obtained without additional cooling. A typical trap contains 1300 atoms at a temperature of 0.4 mK and a peak density of 8\ifmmode\times\else\texttimes\fi{}1011{10}^{11}1011 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. We measure spontaneous photon scatter rates of the trapped atoms to be less than 1.6\ifmmode\times\else\texttimes\fi{}103{10}^{3}103 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, corresponding to recoil heating rates below 0.6 mK/s. The far-detuned trap confines atoms with a strong, nearly conservative optical force and negligible atomic excitation.
We investigate the scattering of intense short laser pulses off trapped cold fermionic atoms. We discuss the sensitivity of the scattered light to the quantum statistics of the atoms. The temperature dependence of the scattered light spectrum is calculated. Comparisons are made with a system of classical atoms that obey Maxwell-Boltzmann statistics. We find the total scattering increases as the fermions become cooler but eventually tails off at very low temperatures (far below the Fermi temperature). At these low temperatures the fermionic degeneracy plays an important role in the scattering, as it inhibits spontaneous emission into occupied energy levels below the Fermi surface. We demonstrate that temperature dependent qualitative changes in the differential and total spectrum can be utilized to probe the quantum degeneracy of a trapped Fermi gas when the total number of atoms is sufficiently large (> 106).(>~{10}^{6}).(> 106). At smaller numbers of atoms, incoherent scattering dominates and it displays weak temperature dependence.
We present a quantitative model for magneto-optical traps operating on narrow transitions, where the transition linewidth and the recoil shift are comparable. We combine a quantum treatment of the light scattering process with a Monte-Carlo simulation of the atomic motion. By comparing our model to an experiment operating on the 5s21S0→5s5p3P1 transition in strontium, we show that it quantitatively reproduces the cloud size, position, temperature and dynamics over a wide range of operating conditions, without any adjustable parameters. We also present an extension of the model that quantitatively reproduces the transfer of atoms into a far off-resonance dipole trap, highlighting its use as a tool for optimizing complex cold atom experiments.