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Physical Review A

Incomplete optical shielding in cold atom traps: three-dimensional Landau-Zener theory

Vladimir Yurovsky, A. Ben‐Reuven

Published May 1, 1997• 13 citations
Publisher

Abstract

Ultracold atom collisions in the presence of a linearly polarized blueshifted laser field are studied theoretically. An analytical solution is presented within the framework of the Landau-Zener approximation. The effect of incomplete shielding is mostly accounted for by incorporating the three-dimensional character of the collisions, using a partial-wave analysis with space degeneracy. A model of two electronic states, including effects of indistinguishability of the colliding atoms, is used. The model associates the incomplete shielding with a process involving two crossing points. The theory is applied to the case of metastable xenon traps, obtaining a fair agreement with the experimental data.

DOI
10.1103/physreva.55.3772

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Incomplete optical shielding in cold sodium atom traps

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A simple two-channel model, based on the semiclassical Landau-Zener (LZ) approximation, with averaging over angle-dependent exponents, is proposed as a fast means for accounting for the incomplete optical shielding of collisions, as observed in recent experiments conducted by Weiner and co-workers on ultracold sodium-atom traps, and its dependence on the laser polarization. The model yields a reasonably good agreement with the recent quantum close-coupling calculations of Julienne and co-workers. The remaining discrepancy between both theories and the data is qualitatively attributed to a partial overlap of the collision ranges at which loss processes and optical shielding occur.

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Inelastic collision rates between two very cold ground-state atoms can be strongly decreased by using an optical shielding laser to repel the colliding atoms at very large internuclear separation so that they never get close to each other. This can be achieved by using a sufficiently intense laser to excite a repulsive state of the quasimolecule formed by the two colliding atoms. We study a simple two-state model and compare the predictions of fully quantum-mechanical close coupling and time-dependent wave packet methods with semiclassical approximations based on the concept of a Landau-Zener curve crossing of field-dressed states. The effect of spontaneous emission in the excited state is treated by the Monte Carlo wave-function method. Calculations are given for a model sodium system at 250 \ensuremath{\mu}K. Strong optical shielding, without significant heating due to the quasimolecular excitation, can be achieved at relatively modest laser power. We find that Landau-Zener models give near quantitative agreement with the fully quantum calculations in spite of the extremely low temperature.

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Research focusing on the formation of ultracold atomic and molecular quantum gases is a continuously expanding field due to its envisioned applications such as quantum-controlled chemistry or quantum simulation. The aim of our theoretical work is to find ways to suppress inelastic or reactive processes between colliding particles in ultracold quantum gases. Using a laser field detuned to the blue of a relevant transition, we propose to couple the initial colliding particle state to a repulsive excited one, thus preventing the particles to come close to each other. This "blueshielding" technique is applied for ultracold quantum gases, close to quantum degeneracy. We investigate the optical shielding in ultracold39K-Cs collision by using close-coupling channel method. As the (3)3Σ+and (2)3Π+molecular states are repulsive in long range[1], one verified effective optical shielding can be realized via driving the transition from the ground α3Σ+state to these excited states in the presence of linear-polarized light. We demonstrate that a strong field with a small blue detuning to the atomic transition is to the benefit of shielding since the Condon point is farther away from the inner region of ground triplet state. The spontaneous emission effect is taken into account by considering excited optical potentials with the modified formula of shielding rate [2]. We expect the shielding efficiency could be improved by using circular-polarized light [3].

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Collisions between laser-cooled metastable xenon atoms in the presence of laser fields provide a good experimental test for ultracold collision theories as the observed ionization can be directly linked to the atomic binary collisions. Hyperfine structure is not present for the even isotopes ${\mathrm{Xe}}^{132}$ and ${\mathrm{Xe}}^{136}$, which simplifies the theoretical work. We present our results and show how these and the results presented in Walhout et al. [Phys. Rev. Lett. 74, 605 (1995)] can be interpreted with suitably adapted two-state models. Our approach suggests one possibility why the strong shielding of collisions predicted by the simple two-state model of Suominen et al. [Phys. Rev. A 51, 1446 (1995)] has not been achieved in the xenon experiment. \textcopyright{} 1996 The American Physical Society.

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Theory of optical shielding in cold atom beams

Vladimir Yurovsky, A. Ben‐Reuven

Experiments were conducted recently (by Weiner and co-workers) on the optical shielding (suppression) of atomic collisions in cold-atom beams, and its variation with the angle between the polarization direction of the shielding light and the direction of approach of the beam. This case is shown here to be a typical example of an optical collision in which quantum interference may persevere between two incident collision partial waves leading to the same output state. This effect depends on the relative collisional phaseshift of the two interfering channels, as well as on the angle of approach, and will vanish when averaging over the latter (as with collisions in the bulk). The extent of variation of this interference effect with the relative phaseshift is quite broad, and may lead, under favorable conditions, to almost complete shielding at a finite value of the shielding-laser power. The latter observation leaves open the possibility of exerting coherent control over the interference effect in order to optimize the shielding.

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Ultracold atom collisions in the presence of a linearly polarized blueshifted laser field are studied theoretically. An analytical solution is presented within the framework of the Landau-Zener approximation. The effect of incomplete shielding is mostly accounted for by incorporating the three-dimensional character of the collisions, using a partial-wave analysis with space degeneracy. A model of two electronic states, including effects of indistinguishability of the colliding atoms, is used. The model associates the incomplete shielding with a process involving two crossing points. The theory is applied to the case of metastable xenon traps, obtaining a fair agreement with the experimental data.
A simple two-channel model, based on the semiclassical Landau-Zener (LZ) approximation, with averaging over angle-dependent exponents, is proposed as a fast means for accounting for the incomplete optical shielding of collisions, as observed in recent experiments conducted by Weiner and co-workers on ultracold sodium-atom traps, and its dependence on the laser polarization. The model yields a reasonably good agreement with the recent quantum close-coupling calculations of Julienne and co-workers. The remaining discrepancy between both theories and the data is qualitatively attributed to a partial overlap of the collision ranges at which loss processes and optical shielding occur.
Inelastic collision rates between two very cold ground-state atoms can be strongly decreased by using an optical shielding laser to repel the colliding atoms at very large internuclear separation so that they never get close to each other. This can be achieved by using a sufficiently intense laser to excite a repulsive state of the quasimolecule formed by the two colliding atoms. We study a simple two-state model and compare the predictions of fully quantum-mechanical close coupling and time-dependent wave packet methods with semiclassical approximations based on the concept of a Landau-Zener curve crossing of field-dressed states. The effect of spontaneous emission in the excited state is treated by the Monte Carlo wave-function method. Calculations are given for a model sodium system at 250 \ensuremath{\mu}K. Strong optical shielding, without significant heating due to the quasimolecular excitation, can be achieved at relatively modest laser power. We find that Landau-Zener models give near quantitative agreement with the fully quantum calculations in spite of the extremely low temperature.
Research focusing on the formation of ultracold atomic and molecular quantum gases is a continuously expanding field due to its envisioned applications such as quantum-controlled chemistry or quantum simulation. The aim of our theoretical work is to find ways to suppress inelastic or reactive processes between colliding particles in ultracold quantum gases. Using a laser field detuned to the blue of a relevant transition, we propose to couple the initial colliding particle state to a repulsive excited one, thus preventing the particles to come close to each other. This "blueshielding" technique is applied for ultracold quantum gases, close to quantum degeneracy. We investigate the optical shielding in ultracold39K-Cs collision by using close-coupling channel method. As the (3)3Σ+and (2)3Π+molecular states are repulsive in long range[1], one verified effective optical shielding can be realized via driving the transition from the ground α3Σ+state to these excited states in the presence of linear-polarized light. We demonstrate that a strong field with a small blue detuning to the atomic transition is to the benefit of shielding since the Condon point is farther away from the inner region of ground triplet state. The spontaneous emission effect is taken into account by considering excited optical potentials with the modified formula of shielding rate [2]. We expect the shielding efficiency could be improved by using circular-polarized light [3].
Collisions between laser-cooled metastable xenon atoms in the presence of laser fields provide a good experimental test for ultracold collision theories as the observed ionization can be directly linked to the atomic binary collisions. Hyperfine structure is not present for the even isotopes Xe132{\mathrm{Xe}}^{132}Xe132 and Xe136{\mathrm{Xe}}^{136}Xe136, which simplifies the theoretical work. We present our results and show how these and the results presented in Walhout et al. [Phys. Rev. Lett. 74, 605 (1995)] can be interpreted with suitably adapted two-state models. Our approach suggests one possibility why the strong shielding of collisions predicted by the simple two-state model of Suominen et al. [Phys. Rev. A 51, 1446 (1995)] has not been achieved in the xenon experiment. \textcopyright{} 1996 The American Physical Society.
Introduction Photoassociation uses optical fields to produce bound molecules from free atoms. Optical fields can also prevent atoms from closely approaching, thereby shielding them from shortrange inelastic or reactive interactions and suppressing the rates of these processes. Recently several groups have demonstrated shielding and suppression by shining an optical field on a cold atom sample. Figure 6.1(a) shows how a simple semiclassical picture can be used to interpret the shielding effect as the rerouting of a ground-state entrance channel scattering flux to an excited repulsive curve at an internuclear distance localized around a Condon point. An optical field, blue detuned with respect to the asymptotic atomic transition, resonantly couples the ground and excited states. In the cold and ultracold regime particles approach on the ground state with very little kinetic energy. Excitation to the repulsive state effectively halts their approach in the immediate vicinity of the Condon point, and the scattering flux then exits either on the repulsive excited state or on the ground state. Figure 6.1(b) shows how this picture can be represented as a Landau–Zener (LZ) avoided crossing of field-dressed potentials. As the blue-detuned suppressor laser intensity increases, the avoided crossing gap around the Condon point widens, and the semiclassical particle moves through the optical coupling region adiabatically. The flux effectively enters and exits on the ground state, and the collision becomes elastic.
Experiments were conducted recently (by Weiner and co-workers) on the optical shielding (suppression) of atomic collisions in cold-atom beams, and its variation with the angle between the polarization direction of the shielding light and the direction of approach of the beam. This case is shown here to be a typical example of an optical collision in which quantum interference may persevere between two incident collision partial waves leading to the same output state. This effect depends on the relative collisional phaseshift of the two interfering channels, as well as on the angle of approach, and will vanish when averaging over the latter (as with collisions in the bulk). The extent of variation of this interference effect with the relative phaseshift is quite broad, and may lead, under favorable conditions, to almost complete shielding at a finite value of the shielding-laser power. The latter observation leaves open the possibility of exerting coherent control over the interference effect in order to optimize the shielding.