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Measurement of the permanent electric dipole moment of ultracold ground state 85 Rb 133 Cs molecules by microwave coherent spectroscopy

Ting Gong, Zhonghua Ji, Jiaqi Du, Yanting Zhao, Liantuan Xiao, Suotang Jia

Published Dec 19, 2020• 3 citations
Publisher

Abstract

We demonstrate measurement of the permanent electric dipole moment (EDM) of 85 Rb 133 Cs molecules in the absolute vibrational ground state by microwave (MW) coherent spectroscopy. The rotational states of the considered molecules, which are formed from short-range photoassociation of mixed cold atoms, are nondegenerated under external electric field. To measure the EDM based on electric-field-induced shifts of the sublevels of X 1 Σ + ( v = 0, J = 1) rotational state, we utilized a MW coherent spectroscopy, which has a higher resolution than depletion spectroscopy and one-photon MW spectroscopy and can also eliminate the influence from Stark shift of the excited state existing in both spectroscopies above. In order to acquire accurate electric intensity, electromagnetic induced transparency spectroscopy of 85 Rb Rydberg atoms is used to implement the calibration. The permanent EDM of 85 Rb 133 Cs molecules is finally determined to be 1.266(15) D, which agrees with the theoretical calculations and is comparable with the value of its isotopic molecule.

DOI
10.1364/oe.411249

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We demonstrate measurement of the permanent electric dipole moment (EDM) of 85 Rb 133 Cs molecules in the absolute vibrational ground state by microwave (MW) coherent spectroscopy. The rotational states of the considered molecules, which are formed from short-range photoassociation of mixed cold atoms, are nondegenerated under external electric field. To measure the EDM based on electric-field-induced shifts of the sublevels of X 1 Σ + ( v = 0, J = 1) rotational state, we utilized a MW coherent spectroscopy, which has a higher resolution than depletion spectroscopy and one-photon MW spectroscopy and can also eliminate the influence from Stark shift of the excited state existing in both spectroscopies above. In order to acquire accurate electric intensity, electromagnetic induced transparency spectroscopy of 85 Rb Rydberg atoms is used to implement the calibration. The permanent EDM of 85 Rb 133 Cs molecules is finally determined to be 1.266(15) D, which agrees with the theoretical calculations and is comparable with the value of its isotopic molecule.
The ultralong-range Cs2 Rydberg molecules consisting of a Rydberg, nD5/2 ( principal quantum number n =35-38), and a ground state atom, 6S1/2 (F=4) are prepared by a two-photon photoassociation spectroscopy in an ultracold Cs gas. This kind of molecule is bound with the low energy scattering and has a permanent dipole moment. We observe two Rydberg-ground state molecular spectra, one is deep-bound molecule, TΣ state, bound by triplet s-wave scattering length and the other one is shallow-bound molecule, S,TΣ state, bound by mixed singlet-triplet s-wave scattering length. The binding energy of Rydberg-ground molecules are attained by analyzing the two photon photoassociation spectrum, corresponding permanent dipole moment is measured by applying an external electric field, which is compared to the calculation.
We present the formation of ultracold (85)Rb(133)Cs molecules in the (5)0(+) electronic state by photoassociation and their detection via resonance-enhanced two-photon ionization. Up to v = 47 vibrational levels including the lowest v = 0 vibrational and lowest J = 0 levels are identified with rotationally resolved high resolution photoassociation spectra. Precise Dunham coefficients are determined for the (5)0(+) state with high accuracy, then the Rydberg-Klein-Rees potential energy curve is derived. The electric dipole moments with respect to the vibrational numbers of the (5)0(+) electronic state of (85)Rb(133)Cs molecule are also measured in the range between 1.9 and 4.8 D. These comprehensive studies on previously unobserved rovibrational levels of the (5)0(+) state are helpful to understand the molecular structure and discover suitable transition pathways for transferring ultracold atoms to deeply bound rovibrational levels of the electronic ground state.
We measure the rotational populations of ultracold 85 Rb 133 Cs molecules in the lowest vibrational ground state by a depletion spectroscopy and quantify the molecular production rate based on the measurement of single ion signal area. The 85 Rb 133 Cs molecules in the are formed from the short-range molecular state. A home-made external-cavity diode laser is used as the depletion laser to measure the rotational populations of the formed molecules. Based on the determination of single ion signal, the production rates of molecules in the J = 0 and J = 2 rotational levels are derived to be 4800 mole/s and 7200 mole/s, respectively. The resolution and quantification of molecules in rotational states are facilitative for the manipulation of rotational quantum state of ultracold molecules.
Coherence and Collisions in Ultracold 87^{87}87Rb133^{133}133Cs Molecules
This thesis presents work towards the development of a quantum simulator based on 87^{87}87Rb133^{133}133Cs molecules using a bulk sample of up to ~4000 molecules at temperatures of ~1 µK. We demonstrate coherent control over the molecules' internal state using resonant microwave fields. We test this coherence by performing high resolution Ramsey spectroscopy of the first rotational transition and observing how the contrast of the spectroscopic fringes decay. We are able to affect the coherence of the superposition using an external laser field, as the two component states have a significant differential AC Stark shift. We extend this microwave control by including an additional microwave field, demonstrating the Autler-Townes effect with hyperfine state resolution and transfer between two hyperfine states in N=0N=0N=0. We study the internal structure of the molecule in the presence of external fields focussing on controlling the differential AC Stark shift between the rotational ground state and the first excited state. We investigate the effect of the off-resonant light on the internal structure in static magnetic and electric fields. In the DC electric field we use two models to describe the molecular structure, demonstrating that at modest values of the electric field the nuclear spin angular momentum is decoupled from the rotational angular momentum of the molecule, this enables us to construct a set of optimum trapping parameters for states with MN=0M_N=0MN​=0. Through careful measurements of the molecular lifetime we are able to determine that molecular losses are limited by two-body collisions. By introducing a time dependent intensity modulation to our optical trap we are further able to determine that the dominant loss process in bulk samples of ultracold 87^{87}87Rb133^{133}133Cs molecules is the laser excitation of collision complexes. Finally, we investigate the collisional properties of 87^{87}87Rb133^{133}133Cs with 87^{87}87Rb and 133^{133}133Cs atoms. We find that the loss is caused by single molecule-single atom collisions and sub-universal over a wide range of magnetic fields.
We report the creation of a sample of over 1000 ultracold 87Rb133Cs^{87}\mathrm{Rb}^{133}\mathrm{Cs}87Rb133Cs molecules in the lowest rovibrational ground state, from an atomic mixture of 87Rb^{87}\mathrm{Rb}87Rb and 133Cs^{133}\mathrm{Cs}133Cs, by magnetoassociation on an interspecies Feshbach resonance followed by stimulated Raman adiabatic passage (STIRAP). We measure the binding energy of the RbCs molecule to be $hc\ifmmode\times\else\texttimes\fi{}3811.576(1)\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}1}$ and the $|{v}^{\ensuremath{'}\ensuremath{'}}=0,{J}^{\ensuremath{'}\ensuremath{'}}=0⟩$ to $|{v}^{\ensuremath{'}\ensuremath{'}}=0,{J}^{\ensuremath{'}\ensuremath{'}}=2⟩$ splitting to be $h\ifmmode\times\else\texttimes\fi{}2940.09(6)\text{ }\text{ }\mathrm{MHz}$. Stark spectroscopy of the rovibrational ground state yields an electric dipole moment of 1.225(3)(8) D, where the values in parentheses are the statistical and systematic uncertainties, respectively. We can access a space-fixed dipole moment of 0.355(2)(4) D, which is substantially higher than in previous work.
This thesis presents the development of a toolbox for the coherent control of ultracold polar molecules. Such systems of molecules promise the creation of long-lived, highly dipolar quantum gases with applications spanning the fields of quantum state controlled chemistry, quantum information, quantum simulation, and precision measurement. However, the addition of vibrational and rotational degrees of freedom leads to molecular systems being significantly more complex than their widely used atomic counterparts. In this work we demonstrate full control of the quantum state down to the hyperfine level of an optically trapped sample of ultracold bosonic 87Rb133 Cs molecules, and exploit that control to begin an investigation into the collision processes which take place in an ultracold molecular gas. We create a sample of up to ∼ 4000 optically trapped molecules in their rovibronic and hyperfine ground state. We characterise the molecules by measuring their temperature, binding energy, and molecule-frame electric dipole moment. We perform spectroscopy of the first rotationally excited state with hyperfine state resolution using microwaves to determine accurate values of rotational and hyperfine coupling constants. We use coherent π pulses to perform complete transfer population between selected hyperfine levels of the ground, first-excited, and second-excited rotational states. We investigate the effect of the off-resonant light of our optical dipole trap on the rotational and hyperfine structure of the molecules. Through a combination of high-resolution microwave spectroscopy and parametric heating measurements, we characterise the polarisability of the 87Rb133Cs molecule. We demonstrate that coupling between neighbouring hyperfine states manifests in rich structure with many avoided crossings in any rotational state other than the ground state. This coupling may be tuned by rotating the polarisation of the linearly polarised trapping light. Finally, we study the lifetime of polar bosonic 87Rb133Cs molecules in our 3D optical dipole trap. We examine the lifetime of the molecules as a function of dipole trap intensity, magnetic field, and hyperfine and rotational state. Despite the chemical stability of the 87Rb133 Cs molecule, we observe lifetimes of ∼1 s corresponding to 2-body decay rates close to the universal limit.