Analyzing Feshbach resonances: A<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">Li</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:mmultiscripts><mml:mo>−</mml:mo><mml:mmultiscripts><mml:mi mathvariant="normal">Cs</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>133</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>case study

We observe two consecutive heteronuclear Efimov resonances in an ultracold Li-Cs mixture by measuring three-body loss coefficients as a function of magnetic field near a Feshbach resonance. The first resonance is detected at a scattering length of a (0) − = −320(10) a0 corresponding to ∼ 7(∼ 3) times the Li-Cs (Cs-Cs) van der Waals range. The second resonance appears at 5.8(1.0) a (0) − close to the unitarity-limited regime at the sample temperature of 450 nK. Indication of a third resonance is found in the atom loss spectra. The scaling of the resonance positions is close to the predicted universal scaling value of 4.9 for zero temperature. Deviations from universality might be caused by finite-range and temperature effects, as well as magnetic field dependent Cs-Cs interactions.The control of interactions in ultracold atomic systems via magnetically tunable Feshbach resonances opens up new pathways for the investigation of few-and manybody physics [1]. One intriguing example is the access to the universal regime, which is characterized by a magnitude of the scattering length a exceeding all other length scales of the system. In the limit of at least two resonant pairwise interactions, an infinite series of three-body bound-states, the so called Efimov states, exists [2][3][4]. Counterintuitively, these trimers persist even for a < 0, where the two body potential does not support a boundstate. The ratio between two subsequent trimer energies follows a discrete scale invariance with a universal scaling factor of exp(−2π/s 0 ). Here, s 0 only depends on the quantum statistics of the constituent atoms, their mass ratio, and the number of resonant interactions [3, 5]. This scale invariance is also reflected in those values of a where the energy of the bound-states coincides with the threshold of three free atoms for a < 0, resulting in enhanced three-body loss. When the position of the first resonance is given by a − only depends on the characteristic range r 0 of the interatomic van der Waals potential [6][7][8][9][10][11]. The universal scaling factor acquires a value of 22.7 for equal mass constituents and features a drastic reduction in heteronuclear massimbalanced systems of two heavy and one light particle [3, 5], resulting e.g. in a factor of 4.9 for a 6 Li-133 Cs mixture.In ultracold atom experiments, Efimov resonances become evident in the three-body loss coefficient L 3 in the rate equation for atom lossṅ = −L 3 n 3 . Here, n denotes the number density of atoms, and L 3 ∝ C(a)a 4 . The Efimov physics are contained in the dimensionless, logperiodic function C(a). Thus far, Efimov resonances have been studied in several equal mass systems [6,7,[12][13][14][15][16][17][18], where the scaling between different resonances is predicted to follow C(a) = C(22.7a). This large scaling factor demands a level of temperature and magnetic field control which makes the observation of an excited Efimov states highly involved. There had been indication of such an excited state in a three-component Fermi gas of 6 Li atoms ...

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“…extensive study of Li-Cs Feshbach resonances via three different models [30]. Inserting these quantities into the relation…”

Section: (C) and (D)mentioning

confidence: 99%

Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance

et al. 2014

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“…The MQDT-FT technique has been successfully applied to ultracold atomic collisions in the presence of an external magnetic field [23,34,35]. We follow here the method employed in a very recent study of the Li-Cs heteronuclear system [28].…”

Section: Ft Machinerymentioning

confidence: 99%

“…In systems where magnetic dipole-dipole or quadrupole interactions are important, it could be desirable to include offdiagonal coupling terms in l, but those are often sufficiently weak that they can be treated perturbatively. The short-range quantum defects μ sr do depend on l, but most of that l-dependence is known analytically; a small ldependent correction can be applied as in [28].…”

Section: Ft Machinerymentioning

confidence: 99%

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Quantum defect theory description of weakly bound levels and Feshbach resonances in LiRb

et al. 2015

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The multichannel quantum defect theory (MQDT) in combination with the frame transformation (FT) approach is applied to model the Fano-Feshbach resonances measured for 7 Li 87 Rb and 6 Li 87 Rb Marzok et al (2009 Phys. Rev. A 79 012717). The MQDT results show a level of accuracy comparable to that of previous models based on direct, fully numerical solutions of the the coupled channel Schrödinger equations. Here, energy levels deduced from 2-photon photoassociation (PA) spectra for 7Li 85 Rb are assigned by applying the MQDT approach, obtaining the bound state energies for the coupled channel problem. Our results confirm that MQDT yields a compact description of PA observables as well as the Fano-Feshbach resonance positions and widths.

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“…The theoretical studies of FRs have been performed by using coupled-channel (CC) theory [10,11 ] as well as some approximate models, such as effective-range theory [12,13], the asymptotic bound-state model [14,15], and multichannel quantum-defect theory (MQDT) [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. MQDT is computa tionally both accurate and economical, thus it has been widely applied to the investigation of cold and ultracold collisions in not only atom-atom [19] and atom-ion [20] systems, but also atom-molecule [21] and molecule-molecule [22] systems. In recent years, MQDT has been extended to describe more complex issues such as high-partial problems [23,24] and reaction collisions [25,26].…”

Section: Introductionmentioning

confidence: 99%

Simple model for predicting and analyzing magnetically induced Feshbach resonances

Wang

et al. 2015

Phys. Rev. A

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We present a simple theoretical model for describing ultracold-atomic collision dynamics and Feshbach resonances (FRs) without onerous numerical computation. An effective quantum-defect phase shift 5yff is derived and the reference potentials are shown acting as an assistant tool in the calculation. With the help of singlet and triplet scattering lengths as and aT, as well as an adjustable parameter ysr, this model can be used to reliably predict FRs. An application example of sLi-40K collision shows that the results given by the simple model agree quite well with both the relevant experimental data and the coupled-channel calculations.

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Analyzing Feshbach resonances: ALi6−Cs133case study

Cited by 30 publications

References 61 publications

Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance

Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance

Quantum defect theory description of weakly bound levels and Feshbach resonances in LiRb

Simple model for predicting and analyzing magnetically induced Feshbach resonances

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