Two- and three-body problem with Floquet-driven zero-range interactions

Sykes, Andrew G.; Landa, H.; Petrov, D. S.

doi:10.1103/physreva.95.062705

Cited by 6 publications

(6 citation statements)

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“…Techniques involving radio-frequency (RF) magnetic fields are of exceptional importance since they are highly adjustable in experiments [4,5]. Indeed, the additional magnetic RF field modulation enables the investigation of cold molecule formation [6][7][8] or heteronuclear association/dissociation processes in a microgravity environment [9], association of Efimov trimers [10][11][12][13] or manipulation of Feshbach collisions [14][15][16]. Beyond cold physics, external fields are also used in ultrafast physics where short laser pulses probe photoionization processes [17].…”

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confidence: 99%

Nonadiabatic Molecular Association in Thermal Gases Driven by Radio-Frequency Pulses

et al. 2019

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The molecular association process in a thermal gas of 85 Rb is investigated where the effects of the envelope of the radio-frequency field are taken into account. For experimentally relevant parameters our analysis shows that with increasing pulse length the corresponding molecular conversion efficiency exhibits low-frequency interference fringes which are robust under thermal averaging over a wide range of temperatures. This dynamical interference phenomenon is attributed to Stückelberg phase accumulation between the low-energy continuum states and the dressed molecular state which exhibits a shift proportional to the envelope of the radio-frequency pulse intensity.External fields are widely used in order to probe, tune and control various aspects of atomic matter. For example, in the field of ultracold atomic physics dc magnetic fields constitute the main experimental means for the creation and manipulation of molecules via Feshbach resonances [1][2][3]. Techniques involving radio-frequency (RF) magnetic fields are of exceptional importance since they are highly adjustable in experiments [4,5]. Indeed, the additional magnetic RF field modulation enables the investigation of cold molecule formation [6][7][8] or heteronuclear association/dissociation processes in a microgravity environment [9], association of Efimov trimers [10][11][12][13] or manipulation of Feshbach collisions [14][15][16]. Beyond cold physics, external fields are also used in ultrafast physics where short laser pulses probe photoionization processes [17]. In such systems the pulse envelope plays a crucial role since it induces a time-dependent AC-Stark shift of the energy levels of the system whereas the light-pulse derivatives yield a dynamic interference in photoionization cross-sections [18][19][20][21][22][23][24][25], [26].In this letter, the RF-induced association process in an ultracold thermal gas is investigated and it is shown that the RF field envelope plays a crucial role. This allows us to extend the concept of dynamical interference in strong field ionization into the realm of ultracold physics and to explore its impact on the production of cold molecules. In Ref.[7] experimental evidences suggested that RF association in a thermal gas can exhibit Rabi-like oscillations in the molecular conversion efficiency (MCE) as a function of the duration of the RF field. On the other hand, the corresponding theoretical studies in Ref. [6] show that in this range of parameters any coherence in the MCE is completely smeared out by thermal averaging. Evidently, these studies still pose an intriguing question for the RF association processes in thermal gases: Under what con-ditions does the RF molecule formation display interference fringes that survive thermal averaging? Our study tackles this question: a gas of 85 Rb atoms with density n = 10 11 cm 3 is considered for which the gas temperature varies from T = 20 nK up to T = 50 nK , and for an RF field driving frequency that can associate continuum states near the dissociation threshold. In t...

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confidence: 99%

Nonadiabatic Molecular Association in Thermal Gases Driven by Radio-Frequency Pulses

et al. 2019

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“…Therefore, following the poles of the driven problem in kplane for such a potential should be possible (a-priori) as shown here for a finite range potential. A further study of the possibility to tailor scattering and resonances using Floquet driving, in particular of atomic systems [71], is a promising direction to apply the techniques developed in this work. Indeed, the singular points analyzed in the current work can be found in an explicit calculation em-ploying QDT with the polarization interaction (α = 4) of a cotrapped ion-atom system [98].…”

Section: Discussionmentioning

confidence: 99%

“…Interacting cold atoms or molecules [68] are often subject to oscillating fields [69,70]. The generalization to settings with a potential of spherical symmetry in the exterior region is straightforward, and the case of zero-range interaction has been recently treated in [71]. Overlapping a trap for neutral atoms with a periodically driven Paul trap for ions [72] was suggested and realized [73,74], followed by the demonstration of a trapped ion immersed in a dilute atomic Bose-Einstein condensate [75,76], and many other experiments.…”

Section: Arxiv:170809828v2 [Quant-ph] 5 May 2018mentioning

confidence: 99%

Singularities of Floquet scattering and tunneling

Landa¹

2018

Phys. Rev. A

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We study quasi-bound states and scattering with short range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S-matrix can cross the real energy axis as a function of the drive amplitude, making the S-matrix nonanalytic at a singular point. For the corresponding quasi-bound states that can tunnel out of (or get captured within) a potential well, this results in a discontinuous jump in both the angular momentum and energy of emitted (absorbed) waves. We also analyze elastic and inelastic scattering of slow particles in the time dependent potential. For a drive amplitude at the singular point, there is a total absorption of incoming low energy (s-wave) particles and their conversion to high energy outgoing (mostly p-) waves. We examine the relation of such Floquet singularities, lacking in an effective time independent approximation, with well known "spectral singularities" (or "exceptional points"). These results are based on an analytic approach for obtaining eigensolutions of time-dependent periodic Hamiltonians with mixed cylindrical and spherical symmetry, and apply broadly to particles interacting via power law forces and subject to periodic fields, e.g. co-trapped ions and atoms.

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“…To perform these calculations, we require to solve the scattering problem with respect to the Hamiltonian H R ˆ( ) of equation ( 16). Since the interaction potential V t R ˆ( ) of this Hamiltonian is a periodic function of time, we use Floquet scattering theory with the formalism of Sykes, Landa, and Petrov in [29].…”

Section: Floquet Scatteringmentioning

confidence: 99%

Scattering amplitude and two-body loss of ultracold alkaline-earth atoms in a shaking synthetic magnetic field

Zhang

2022

Commun. Theor. Phys.

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The idea of manipulating the interaction between ultracold fermionic alkaline-earth (like) atoms via a laser-induced periodical synthetic magnetic field was proposed in [Phys. Rev. B {\bf 97}, 155156 (2018)]. In that work it was shown that in the presence of the shaking synthetic magnetic field, two atoms in $^1$S$_0$ and $^3$P$_0$ states experiences a periodical interaction in a rotated frame, and the effective inter-atomic interaction was approximated as the time-averaged operator of this time-dependent interaction. This technique is supposed to be efficient for $^{173}$Yb atoms which has large natural scattering length. Here we exam this time-averaging approximation and derive the rate of the two-body loss induced by the shaking of the synthetic magnetic field, by calculating the zero-energy inter-atomic scattering amplitude corresponding to the explicit periodical interaction. We find that for the typical cases with shaking angular frequency $\lambda$ of the synthetic magnetic field being of the order of $(2\pi)$kHz, the time-averaging approximation is applicable only when the shaking amplitude is small enough. Moreover, the two-body loss rate increases with the shaking amplitude, and is of the order of $10^{-10}$${\rm cm}^{3}{\rm s}^{-1}$ or even larger when the time-averaging approximation is not applicable. Our results are helpful for the quantum simulations with ultracold gases of fermionic alkaline-earth (like) atoms.

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Two- and three-body problem with Floquet-driven zero-range interactions

Cited by 6 publications

References 92 publications

Nonadiabatic Molecular Association in Thermal Gases Driven by Radio-Frequency Pulses

Nonadiabatic Molecular Association in Thermal Gases Driven by Radio-Frequency Pulses

Singularities of Floquet scattering and tunneling

Scattering amplitude and two-body loss of ultracold alkaline-earth atoms in a shaking synthetic magnetic field

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