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Multipole Analysis of Radio-Frequency Experiments in Ultra-Cold Atoms

Betzalel Bazak, Evgeny Z. Liverts, Nir Barnea

Published Jul 25, 2012• 0 citations
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Abstract

Using the multipole expansion we analyze photo induced reactions in an ultra-cold atomic gas composed of identical neutral bosons. While the Frank-Condon factor dominates the photo induced spin-flip reactions, we have found that for frozen-spin process the reaction rate is governed by the $r^2$ and quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number $k$ acquires an extra $k^4$ factor in comparison to the spin-flip process. Comparing the relative strength of the $r^2$ and quadrupole modes in dimer photoassociation we predict that the mutual importance of these two modes changes with temperature and scattering length.

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Multipole analysis of radio-frequency reactions in ultracold atoms

Betzalel Bazak, Evgeny Z. Liverts, Nir Barnea

Using the multipole expansion, we analyze photoinduced reactions in an ultracold atomic gas composed of identical neutral bosons. While the Franck-Condon factor dominates the photoinduced spin-flip reactions, we have found that for a frozen-spin process in which the atomic spins are conserved, the reaction rate is governed by the monopole ${r}^{2}$ and the quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number $k$ acquires an extra ${k}^{4}$ factor in comparison to the spin-flip process. Comparing the relative strength of the ${r}^{2}$ and quadrupole modes in dimer photoassociation, we predict that the mutual importance of these two modes changes with temperature and scattering length.

arXiv:1207.5936•Physical Review A•Oct 10, 2012•6 citations

Photoassociation of universal Efimov trimers

Betzalel Bazak, Nir Barnea

Abstract In view of recent experiments in ultracold atomic systems, the photoassociation of Efimov trimers, composed of three identical bosons, is studied utilizing the multipole expansion. We study both the normal hierarchy case, where one-body current is dominant, and the strong hierarchy case, relevant for photoassociation in ultracold atoms, where two-body current is dominant. For identical particles in the normal hierarchy case, the leading contribution comes from the r 2 s -mode operator and from the quadrupole d -mode operator. The s -mode reaction is found to be dominant at low temperature, while as the temperature increases the d -mode becomes as significant. For the strong hierarchy case, the leading contribution comes from a 2-body s -wave δ operator. In both cases log periodic oscillations are found in the cross section. For large but finite scattering length the amplitude of the oscillations becomes larger in comparison to infinite scattering length case. We apply our theory to photoassociation of 7 Li ultracold atoms and show a good fit to the available experimental results.

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Photoassociation of a cold-atom–molecule pair: Long-range quadrupole-quadrupole interactions

Maxence Lepers, Olivier Dulieu, Viatcheslav Kokoouline

The general formalism of the multipolar expansion of electrostatic interactions is applied to the calculation of the potential energy between an excited atom (without fine structure) and a ground-state diatomic molecule at large mutual separations. Both partners exhibit a permanent quadrupole moment so that their mutual long-range interaction is dominated by a quadrupole-quadrupole term, which is attractive enough to bind trimers. Numerical results are given for an excited Cs($6{}^{2}P$) atom and a ground-state ${\mathrm{Cs}}_{2}$ molecule. The prospects for achieving photoassociation of a cold-atom--dimer pair are thus discussed and found promising. The formalism can be generalized to the long-range interaction between molecules to investigate the formation of cold tetramers.

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Theoretical investigation of an ultracold atom-dimer reaction for three identical bosons

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We study the atom-dimer collision reaction for a three bosonic $^{7}\mathrm{Li}$ system using a multichannel model. We calculate the atom-dimer scattering length and dimer relaxation rate for all three $^{7}\mathrm{Li}$ atoms in $|f=1,{m}_{f}=1\ensuremath{\rangle}$ (case I) or $|f=1,{m}_{f}=0\ensuremath{\rangle}$ (case II) in an external magnetic field. The dimer is considered as the Feshbach dimer in both cases. In case I there are two atom-dimer resonances, whereas in case II only one atom-dimer resonance induced by the second excited trimer state is observed. It is found that $d$-wave two-body interaction plays an appreciable role in the entire considered magnetic field regime in case I but only when $B>$ 890 G in case II. We calculate the state-to-state transition probability and normalized transition probability from the incoming atom-dimer channel to the deep atom-dimer hyperfine channel. A propensity that the second-deepest hyperfine channels of atom-dimer collision reaction are dominant in all product channels is revealed for both $s$- and $d$-wave dimers.

Physical Review A•Dec 19, 2023•0 citations

Effective control of cold collisions with radio-frequency fields

Yijue Ding, José Paulo D'Incao, Chris H. Greene

We study $^{87}\mathrm{Rb}$ cold collisions in a static magnetic field and a single-color radio-frequency (RF) field by employing the multichannel quantum defect theory in combination with the Floquet method to solve the two-body time-dependent Schr\"odinger equation. Our results show that RF fields can modify the two-body scattering length by a large scale through Feshbach resonances in both low- and high-static magnetic-field regimes. Such RF-induced Feshbach resonances can be applied to quenching experiments or control of interactions in spinor condensates. Here, we also show that, analogously to photoassociation, RF fields can also associate cold atoms into molecules at a useful rate.

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Two-color photoassociation spectra of ultra-cold Cs (60D5/2)2 Rydberg molecule

Bai Jing-Xu, Xiaoxuan Han, Bai Su-Ying +3 more

The long-range multipole interactions between ultra-cold Rydberg atoms form adiabatic potentials, one of which shows a binding potential that can be used to bind Rydberg-Rydberg molecules. Rydberg-atom molecule, known as macrodimer due to its larger size (~μm), has the properties of the abundant vibrational energy levels and large electric dipole moment and so on. Compared with Rydberg atom, the Rydberg molecule, including Rydberg-ground molecule and Rydberg-Rydberg molecule, is susceptible to manipulate by an external field and possesses potential applications in the weak-signal detection, the quantum gas correlation measurement and the vacuum fluctuation and so on. In this paper, we investigate a (60D5/2)2 Rydberg macrodimer theoretically and experimentally. In the calculation, we take into account the multipole interaction of a Rydberg-atom pair, including dipole-dipole, dipole-quadrupole, dipole-octupole and quadrupole-quadrupole interaction and so on. The adiabatic potential of 60D5/2 Rydberg-atom pair is obtained by diagonalizing the interaction Hamiltonian on a grid of internuclear separations, R. The potential depth and binding length of the Rydberg molecular potential well are obtained. In experiment, we prepare the ultra-cold Cs (60D5/2)2 Rydberg molecules by a two-color photoassociation method in a cesium ultracold atom trap. The first-color (pulse-A) resonantly excites a seed Rydberg atom A, and the second color (pulse-B) is detuned and resonantly excites the second Rydberg atom B near to the atom A. Both pulse-A and pulse-B are two-photon excitations (852 nm + 510 nm), between which their 852-nm lasers have the same frequency, whereas the 510-nm laser frequency of the pulse-A is set to be resonant with the atomic transition and the frequency of the pulse-B is detuned by using a double-passed acousto-optic modulator. When the pulse-B is detuned to the molecular binding energy, atom-A and-B are bonded, forming an ultra-cold Cs (60D5/2)2 Rydberg molecule. The two-color photoassociation spectra of Rydberg-Rydberg molecules are detected by the field ionization of Rydberg atoms and molecules with a ramped electric field. Molecular spectra are compared with calculated adiabatic molecular potentials, which yields the binding energy and equilibrium internuclear distance. The two-color photoassociation method used in this work has a doubly resonant character that results in the enhanced excitation rate.

Acta Physica Sinica•Jan 1, 2018•0 citations
Using the multipole expansion we analyze photo induced reactions in an ultra-cold atomic gas composed of identical neutral bosons. While the Frank-Condon factor dominates the photo induced spin-flip reactions, we have found that for frozen-spin process the reaction rate is governed by the r2r^2r2 and quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number kkk acquires an extra k4k^4k4 factor in comparison to the spin-flip process. Comparing the relative strength of the r2r^2r2 and quadrupole modes in dimer photoassociation we predict that the mutual importance of these two modes changes with temperature and scattering length.
Using the multipole expansion, we analyze photoinduced reactions in an ultracold atomic gas composed of identical neutral bosons. While the Franck-Condon factor dominates the photoinduced spin-flip reactions, we have found that for a frozen-spin process in which the atomic spins are conserved, the reaction rate is governed by the monopole r2{r}^{2}r2 and the quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number kkk acquires an extra k4{k}^{4}k4 factor in comparison to the spin-flip process. Comparing the relative strength of the r2{r}^{2}r2 and quadrupole modes in dimer photoassociation, we predict that the mutual importance of these two modes changes with temperature and scattering length.
Abstract In view of recent experiments in ultracold atomic systems, the photoassociation of Efimov trimers, composed of three identical bosons, is studied utilizing the multipole expansion. We study both the normal hierarchy case, where one-body current is dominant, and the strong hierarchy case, relevant for photoassociation in ultracold atoms, where two-body current is dominant. For identical particles in the normal hierarchy case, the leading contribution comes from the r 2 s -mode operator and from the quadrupole d -mode operator. The s -mode reaction is found to be dominant at low temperature, while as the temperature increases the d -mode becomes as significant. For the strong hierarchy case, the leading contribution comes from a 2-body s -wave δ operator. In both cases log periodic oscillations are found in the cross section. For large but finite scattering length the amplitude of the oscillations becomes larger in comparison to infinite scattering length case. We apply our theory to photoassociation of 7 Li ultracold atoms and show a good fit to the available experimental results.
The general formalism of the multipolar expansion of electrostatic interactions is applied to the calculation of the potential energy between an excited atom (without fine structure) and a ground-state diatomic molecule at large mutual separations. Both partners exhibit a permanent quadrupole moment so that their mutual long-range interaction is dominated by a quadrupole-quadrupole term, which is attractive enough to bind trimers. Numerical results are given for an excited Cs(62P6{}^{2}P62P) atom and a ground-state Cs2{\mathrm{Cs}}_{2}Cs2​ molecule. The prospects for achieving photoassociation of a cold-atom--dimer pair are thus discussed and found promising. The formalism can be generalized to the long-range interaction between molecules to investigate the formation of cold tetramers.
We study the atom-dimer collision reaction for a three bosonic 7Li^{7}\mathrm{Li}7Li system using a multichannel model. We calculate the atom-dimer scattering length and dimer relaxation rate for all three 7Li^{7}\mathrm{Li}7Li atoms in $|f=1,{m}_{f}=1\ensuremath{\rangle}$ (case I) or $|f=1,{m}_{f}=0\ensuremath{\rangle}$ (case II) in an external magnetic field. The dimer is considered as the Feshbach dimer in both cases. In case I there are two atom-dimer resonances, whereas in case II only one atom-dimer resonance induced by the second excited trimer state is observed. It is found that ddd-wave two-body interaction plays an appreciable role in the entire considered magnetic field regime in case I but only when B>B>B> 890 G in case II. We calculate the state-to-state transition probability and normalized transition probability from the incoming atom-dimer channel to the deep atom-dimer hyperfine channel. A propensity that the second-deepest hyperfine channels of atom-dimer collision reaction are dominant in all product channels is revealed for both sss- and ddd-wave dimers.
We study 87Rb^{87}\mathrm{Rb}87Rb cold collisions in a static magnetic field and a single-color radio-frequency (RF) field by employing the multichannel quantum defect theory in combination with the Floquet method to solve the two-body time-dependent Schr\"odinger equation. Our results show that RF fields can modify the two-body scattering length by a large scale through Feshbach resonances in both low- and high-static magnetic-field regimes. Such RF-induced Feshbach resonances can be applied to quenching experiments or control of interactions in spinor condensates. Here, we also show that, analogously to photoassociation, RF fields can also associate cold atoms into molecules at a useful rate.
The long-range multipole interactions between ultra-cold Rydberg atoms form adiabatic potentials, one of which shows a binding potential that can be used to bind Rydberg-Rydberg molecules. Rydberg-atom molecule, known as macrodimer due to its larger size (~μm), has the properties of the abundant vibrational energy levels and large electric dipole moment and so on. Compared with Rydberg atom, the Rydberg molecule, including Rydberg-ground molecule and Rydberg-Rydberg molecule, is susceptible to manipulate by an external field and possesses potential applications in the weak-signal detection, the quantum gas correlation measurement and the vacuum fluctuation and so on. In this paper, we investigate a (60D5/2)2 Rydberg macrodimer theoretically and experimentally. In the calculation, we take into account the multipole interaction of a Rydberg-atom pair, including dipole-dipole, dipole-quadrupole, dipole-octupole and quadrupole-quadrupole interaction and so on. The adiabatic potential of 60D5/2 Rydberg-atom pair is obtained by diagonalizing the interaction Hamiltonian on a grid of internuclear separations, R. The potential depth and binding length of the Rydberg molecular potential well are obtained. In experiment, we prepare the ultra-cold Cs (60D5/2)2 Rydberg molecules by a two-color photoassociation method in a cesium ultracold atom trap. The first-color (pulse-A) resonantly excites a seed Rydberg atom A, and the second color (pulse-B) is detuned and resonantly excites the second Rydberg atom B near to the atom A. Both pulse-A and pulse-B are two-photon excitations (852 nm + 510 nm), between which their 852-nm lasers have the same frequency, whereas the 510-nm laser frequency of the pulse-A is set to be resonant with the atomic transition and the frequency of the pulse-B is detuned by using a double-passed acousto-optic modulator. When the pulse-B is detuned to the molecular binding energy, atom-A and-B are bonded, forming an ultra-cold Cs (60D5/2)2 Rydberg molecule. The two-color photoassociation spectra of Rydberg-Rydberg molecules are detected by the field ionization of Rydberg atoms and molecules with a ramped electric field. Molecular spectra are compared with calculated adiabatic molecular potentials, which yields the binding energy and equilibrium internuclear distance. The two-color photoassociation method used in this work has a doubly resonant character that results in the enhanced excitation rate.