Modeling magneto-optical trapping of CaF molecules

Tarbutt, M. R.; Steimle, Timothy C.

doi:10.1103/physreva.92.053401

Cited by 57 publications

(78 citation statements)

References 14 publications

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“…In some cases, a dc MOT can still be achieved due to remixing that occurs naturally in the multilevel structure of molecules. CaF offers this structure due to the spacing of the F ¼ 1 and F ¼ 2 hyperfine ground states, where one can exploit a "dual frequency" [25] effect to achieve strong trapping and cooling forces. The relevant energy levels for CaF are shown in Figs.…”

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Radio Frequency Magneto-Optical Trapping of CaF with High Density

et al. 2017

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We demonstrate significantly improved magneto-optical trapping of molecules using a very slow cryogenic beam source and either rf modulated or dc magnetic fields. The rf magneto-optical trap (MOT) confines 1.0ð3Þ × 105 CaF molecules at a density of 7ð3Þ × 10 6 cm −3 , which is an order of magnitude greater than previous molecular MOTs. Near Doppler-limited temperatures of 340ð20Þ μK are attained. The achieved density enables future work to directly load optical tweezers and create optical arrays for quantum simulation. DOI: 10.1103/PhysRevLett.119.103201 The field of ultracold molecules is rapidly expanding, pushed forward by favorable prospects for advances in quantum simulation [1,2], quantum information [3,4], quantum chemistry [5,6], and precision measurements [7,8]. The rich internal structure of molecules, including rotational and vibrational modes, as well as their long-range and anisotropic dipolar interactions, make diatomic molecules ideal extensions of current work in these fields. While great progress has been made by assembling bi-alkalis [9-11], direct cooling of molecules allows one to realize an increase in chemical diversity. This diversity is of particular interest in the case of 2 Σ molecules, where the unpaired electron spin would allow one to realize lattice spin models [1,12] and the onset of topologically ordered states [13].The same internal degrees of freedom that make molecules so interesting for scientific applications add further complexity to the cooling and trapping process. Despite this, several groups have sought to cool molecules using direct laser cooling with simultaneous application of multiple laser frequencies, in particular, the construction of molecular MOTs. Magneto-optical traps (MOTs) have long been the workhorse of cold atom experiments, producing (sub-)Doppler-limited temperatures of many atomic species. Recently, following the first demonstration of 2D magneto-optical compression of YO [14], the first dc and rf molecular MOTs were created with SrF [15][16][17]. A major challenge in reaching this point was the very low capture velocity of the molecular MOT due to many internal molecular states and the resulting low photon scattering rate. To extend the MOT to other species and improve the number of trapped molecules, laser slowing of YO [18] and CaF [19,20], rf magneto-optical compression of CaF [21], and, very recently, a MOT of CaF based on static magnetic fields (dc MOT) were demonstrated [22].

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“…Radio-frequency sidebands produced by a series of acousto-optic modulators (AOMs) address all hyperfine transitions. The polarization of each hyperfine component can be set independently, allowing the use of the optimal polarization scheme for both the dc [25] and rf MOTs [ Fig. 1(b) MOT…”

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Radio Frequency Magneto-Optical Trapping of CaF with High Density

et al. 2017

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“…A pulse of CaF emitted at time t ¼ 0 from a cryogenic buffer gas source [34] is decelerated by frequency-chirped counter-propagating laser light [35]. The slowest molecules are captured in a dual-frequency MOT [25,36], where the main laser drives the A 2 Π 1=2 ðv¼0; J ¼1=2Þ←X 2 Σ þ ðv¼0;N ¼1Þ transition, with intensity I and detuning δ. …”

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Role of Minerals in Hydrogen Sulfide Generation during Steam-Assisted Recovery of Heavy Oil

et al. 2018

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We demonstrate coherent microwave control of the rotational, hyperfine, and Zeeman states of ultracold CaF molecules, and the magnetic trapping of these molecules in a single, selectable quantum state. We trap about 5 × 10 3 molecules for almost 2 s at a temperature of 70ð8Þ μK and a density of 1.2 × 10 5 cm −3 . We measure the state-specific loss rate due to collisions with background helium. DOI: 10.1103/PhysRevLett.120.163201 Techniques for producing and controlling ultracold molecules are advancing rapidly, motivated by a wide range of applications. These include precise measurements that test fundamental physics [1,2], quantum state resolved collisions and chemistry [3], quantum computation [4][5][6] and simulation [7,8], and the study of dipolar quantum gases [9]. These applications call for trapped molecules in a single, selectable quantum state, and they typically require coherent control over the rotational and hyperfine states. Such control has recently been achieved [10-13] for bialkali molecules produced by associating ultracold atoms [14][15][16][17][18]. Great efforts are also being made to cool molecules directly, for example, by optoelectrical Sisyphus cooling [19] or direct laser cooling and magneto-optical trapping [20][21][22][23][24][25]. These methods can produce ultracold molecules with greater chemical diversity and with large electric and magnetic dipoles, as is often desired. The magneto-optical trap (MOT) is an excellent tool for collecting and cooling molecules, and it promises to be the starting point for many applications of ultracold molecules, just as it has been for ultracold atoms. However, it does not allow quantum state control, provides limited phase-space density, and has a limited lifetime due to optical pumping into states not addressed by the lasers. Thus, molecules in a MOT must be transferred into a conservative trap where the lifetime can be long, the quantum state can be selected and preserved, and the phase-space density can be increased, for example, by sympathetic, evaporative, or Raman sideband cooling. Magnetic traps have been crucial for exploiting ultracold atoms, and they have previously been used to confine molecules produced at ∼100 mK by buffer-gas cooling and Stark and Zeeman deceleration [26][27][28][29][30][31][32][33]. Here, we demonstrate coherent control and magnetic trapping of laser-cooled molecules, which are key steps towards the applications discussed above. Starting from a MOT of CaF [25], we compress the cloud to increase its density, cool the molecules to sub-Doppler temperature [23], optically pump them into a single internal state, transfer them coherently to a selectable rotational, hyperfine and Zeeman level, and then confine them in a magnetic trap.Our setup is the same as used previously [23,25], with the addition of microwave components to drive the rotational transition. A pulse of CaF emitted at time t ¼ 0 from a cryogenic buffer gas source [34] is decelerated by frequency-chirped counter-propagating laser light [35]. The slowest mo...

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“…Here we treat the case where both laser beams, with different polarizations, drive the same level in a socalled dual (or bichromatic or two color) magneto-optical trap. In a recent study of magneto-optical trapping of CaF molecules published in [44], it has been found that such a configuration should allow one to realize a MOT of CaF. If the authors put forth the proposition to benefit from this effect to enhance MOT forces, we aim at giving requirements and details to get such forces as well as the underlying mechanism for both J → J and J → J − 1 schemes.…”

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“…More interestingly, it could be used to cool and trap diatomic molecules on the X 2 Σ(N ′′ = 1, v ′′ = 0) → A 2 Π 1/2 (N ′ = 0, v ′ = 0) transition, molecular negative ions such as C − 2 studied in this article, and also some atoms, such as La − that exhibits a J = 2 → J = 1 transition [45]. In the experimental configuration used for SrF [5,8], two lasers with opposite polarization have been used because of the opposite Landé factor; it seems probable that the process discussed here plays a significant role in the efficient trapping and cooling due to extra near resonance frequencies provided by sidebands originally created to cover the hyperfine splitting [44]. Adding other lasers may even improve cooling and trapping, especially for higher J values or more complicated schemes involving a hyperfine structure or non-linear Zeeman shift.…”

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Bichromatic magneto-optical trapping forJ→J,J−1configurations

et al. 2016

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A magneto-optical trap (MOT) of atoms or molecules is studied when two lasers of different detunings and polarization are used. Especially for J → J, J − 1 transitions, a scheme using more than one frequency per transition and different polarization is required to create a significant force. Calculations have been performed with the simplest forms of the J → J − 1 case (i.e. J ′′ = 1 → J ′ = 0) and J → J case (i.e. J ′′ = 1/2 → J ′ = 1/2). A one dimensional (1D) model is presented and a complete 3D simulation using rate equations confirm the results. Even in the absence of Zeeman effect in the excited state, where no force is expected in the single laser field configuration, we show that efficient cooling and trapping forces are restored in our configuration. We study this mechanism for the C − 2 molecular anion as a typical example of the interplay between the two simple transitions J → J, J − 1. Laser cooling and magneto-optical trapping of atoms typically involves J → J + 1 closed transitions driven by counter-propagating circularly polarized laser fields (J is the total angular momentum). On the contrary laser forces on molecule, a more recent subject despite the pioneer experiments [1,2], typically involve N ′′ = 1 → N ′ = 0 transitions (N is the rotational quantum number) between X 2 Σ(v ′′ = 0) and A 2 Π 1/2 (v ′ = 0) vibronic levels [3][4][5]. Including the electron spin leads to J ′′ = 1/2, 3/2 → J ′ = 1/2 transitions. Theoretical study of the correct choice of circular polarization for magnetooptical trapping depending on the angular momenta, J ′′ and J ′ , and on the g-factors, g ′′ and g ′ (respectively of the lower and upper states) has been performed in Ref [6]. It has been found heuristically that the trapping force is weak whenever g ′ is small compared to g ′′ . This is a serious limitation because in pure Hund's case (a) or (b), A 2 Π 1/2 does not present any Zeeman effect [7], so g ′ = 0 prevents any force. However experiments, such as that on SrF [8], were possible because of rotational and spin-orbit Π − Σ mixing allowing a small non zero value for g ′ (∼ 0.1 [6]). In addition to this weak force, J ′′ = 1/2, 3/2 → J ′ = 1/2 transitions present one or two dark states [9, 10] which leads to experimental difficulties if a stronger confining force is desired. Yet stronger force can be produced by rapidly switching the magnetic field gradient and laser beam polarization on a timescale (typically in the sub-microsecond range which is not a simple experimental task) preventing the adiabatic following of the atomic states as done in reference [3] .In this letter we suggest that efficient magneto-optical forces can be restored in all J ′′ → J ′ cases, even for g ′ = 0, in a very simple way, by simply adding one laser field of opposite polarization with a different detuning. We treat the simplest J → J − 1 case (that * Corresponding author: anne.cournol@u-psud.fr is J ′′ = 1 → J ′ = 0) and J → J case (that is J ′′ = 1/2 → J ′ = 1/2). An analytical one dimensional (1D) model is presented and help get t...

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Modeling magneto-optical trapping of CaF molecules

Cited by 57 publications

References 14 publications

Radio Frequency Magneto-Optical Trapping of CaF with High Density

Radio Frequency Magneto-Optical Trapping of CaF with High Density

Role of Minerals in Hydrogen Sulfide Generation during Steam-Assisted Recovery of Heavy Oil

Bichromatic magneto-optical trapping forJ→J,J−1configurations

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