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Physical Review A

Atom recoil during coherent light scattering from many atoms

F. Robicheaux, Shihua Huang

Published Jan 9, 2019• 16 citations
Publisher

Abstract

The recoil momentum and energy of ultracold atoms is studied for situations where collective scattering or emission of photons is important. Effects due to the dipole-dipole interaction are emphasized. For two and many atoms confined in optical traps, calculations of the energy and momentum with respect to atomic separation are performed. When the atomic separation is comparable to or larger than the transition wavelength, the ultracold atoms' recoil energy depends mainly on collective spontaneous decay rather than forces from the cooperative frequency shift. Calculations for a laser pulse reflecting from an atomic array suggest that the recoil energy of atoms can be substantially larger than might be expected from an independent atom picture.

DOI
10.1103/physreva.99.013410

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The recoil momentum and energy of ultracold atoms is studied for situations where collective scattering or emission of photons is important. Effects due to the dipole-dipole interaction are emphasized. For two and many atoms confined in optical traps, calculations of the energy and momentum with respect to atomic separation are performed. When the atomic separation is comparable to or larger than the transition wavelength, the ultracold atoms' recoil energy depends mainly on collective spontaneous decay rather than forces from the cooperative frequency shift. Calculations for a laser pulse reflecting from an atomic array suggest that the recoil energy of atoms can be substantially larger than might be expected from an independent atom picture.
The recoil of atoms in arrays due to the emission or absorption of photons is studied for subwavelength interatomic spacing. The atoms in the array interact with each other through collective dipole-dipole interactions and with the incident laser field in the low-intensity limit. Shining uniform light on the array gives rise to patterns of excitation and recoil in the array. They arise due to the interference of different eigenmodes of excitation. The relation between the recoil and the decay dynamics is studied when the array is in its excitation eigenstates. The recoil experienced by a subradiant collective decay is substantially larger than that from independent atom decay. A method to calculate the rate of recoil when steady state has been achieved with a constant influx of photons is also described.
The recoil of atoms in arrays due to the emission or absorption of photons is studied for subwavelength interatomic spacing. The atoms in the array interact with each other through collective dipole-dipole interactions and with the incident laser field in the low-intensity limit. Shining uniform light on the array gives rise to patterns of excitation and recoil in the array. They arise due to the interference of different eigenmodes of excitation. The relation between the recoil and the decay dynamics is studied when the array is in its excitation eigenstates. The recoil experienced by a subradiant collective decay is substantially larger than that from independent atom decay.
The recoil of atoms in dense ensembles during light-matter interactions is studied using quantized vibrational states for the atomic motion. The recoil resulting from the forces due to the near-field collective dipole interactions and far-field laser and decay interactions are explored. The contributions to the recoil and the dependence on the trap frequency of the different terms of the Hamiltonian and Lindbladian are studied. These calculations are compared with previous results using the impulse model in the slow-oscillation approximation. Calculations in highly subradiant systems show enhanced recoil indicating that recoil effects cannot be ignored in such cases.
The coherent photon scattering of atoms in an atomic array is studied. It is found that due to cooperative photon exchanges, the excitation probability of an atom in an array parallel to the direction of laser propagation ($\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{k}}$) will either grow or decay along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{k}}$, depending on the detuning of the laser. The symmetry of the system for atomic separations of $a=j\ensuremath{\lambda}/2$ causes the excitation distribution and scattered radiation to abruptly become symmetric about the center of the array, where jjj is an integer and $\ensuremath{\lambda}$ is the transition wavelength. For atomic separations of $a<\ensuremath{\lambda}/2$, a collection of nonradiating states ($\mathrm{\ensuremath{\Gamma}}\ensuremath{\sim}0$) disrupts the described trend. In order to interpret this surprising result, a band-structure calculation in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit is conducted, where the decay rates and the collective Lamb shifts of the eigenmodes versus quasimomentum are obtained. This calculation shows that the collective exchange of photons in an array strongly affects its scattered radiation, allowing one to easily manipulate the collective Lamb shift and directly excite either superradiant or subradiant eigenmodes by correctly choosing the angle of the driving laser.
We study the scattering of light by a single ultracold trapped atom initially in the ground state of the trapping harmonic potential. We have found interesting features of scattering in the regime where the atomic recoil energy is much larger than the separation between oscillatory trap levels. Although we present the quantum-mechanical expression for the scattering cross section, special attention is paid to the semiclassical analysis of the process. We show that the major characteristics of the scattering might be deduced from two conservation laws: conservation of energy and momentum in absorption and emission of photon process separately. These conservation laws impose a strong correlation between scattered light characteristics and the position of the trapped atom at the moment of photon emission. \textcopyright{} 1996 The American Physical Society.
An ensemble of periodically ordered atoms coherently scatters the light of an incident laser beam. The scattered and the incident light may interfere and give rise to a light intensity modulation and thus to optical dipole forces which, in turn, emphasize the atomic ordering. This positive feedback is at the origin of the collective atomic recoil laser (CARL). We demonstrate this dynamics using ultracold atoms confined by dipole forces in a unidirectionally pumped far red‐detuned high‐finesse optical ring cavity. Under the influence of an additional dissipative force exerted by an optical molasses the atoms, starting from an unordered distribution, spontaneously form a density grating moving at constant velocity. Additionally, steady state lasing is observed in the reverse direction if the pump laser power exceeds a certain threshold. We compare the dynamics of the atomic trajectories to the behavior of globally coupled oscillators, which exhibit phase transitions from incoherent to coherent states if the coupling strength exceeds a critical value.