Prepartion Of The Quantum State And Microwave Coherent Control Of Ultracold ⁸⁵Rb¹³³Cs Molecules In Ground State

With the development of laser cooling atomic technology,ultracold molecules have attracted widespread attention due to their unique characteristics.Compared with atoms,molecules have more freedom of vibration and rotation.Polar molecules can realize the manipulation of internal state through the external fields,with its permanent electric dipole moments and long-range anisotropic interactions.These characteristics make ultracold polar molecules can be treated as a good carrier for precise measurement,quantum calculation and quantum simulation.The preparation of molecules in a stable state is a prerequisite for these applications.Ultracold polar molecules in the lowest vibrational ground state have a deeper potential well and will not decay to a lower state.Thus the molecules in the ground state are more stable and hold longer lifetime,and always be used as research objects.There are several methods to prepare ultracold molecules in ground state,direct laser cooling,feshbach resonance combined with stimulated raman adiabatic transfer(STIRAP),and photoassociation(PA).Direct laser cooling of molecules needs to form a closed-cooling transition which can only be applied to a few molecular species.The method of feshbach resonance combined with STIRAP can realize the hyperfine resolution of the ground state molecule.Because it directly constructs the channel for preparing the molecule,the molecular yield is high and is widely used by researchers.Compared with the method of feshbach resonance combined with STIRAP,PA is simpler in experiment and can realize the continuous preparation of molecules,which is also a favored method for preparing molecules.Among them,excited state molecules prepared by short-range PA can directly radiate spontaneously decay to the ground state,which arouses researchers'interests.With the comparation of direct construction of the channel for preparing molecules,the yield of molecules prepared by short-range PA is lower.Researchers investigate the PA spectra of different PA intermediate states and calculate the Frank Condon factors between the intermediate state and atomic state and molecular,they try to explore the intermediate state with large yield of ground state molecules.If an intermediate state can construct an atom-molecule coherent transfer channel,it can greatly increase the yield of ground state molecules.After the preparation of the ultracold ground state molecule,microwave can be used to couple adjacent rotational states of molecules in the lowest vibrational ground state with the appropriate frequency.Microwave manipulation of the internal molecular states has many applications,such as quantum magnetism,topological phase and synthetic dimensions.Quantum computation has certain requirements for the coherence of molecular energy levels.Therefore,many researchers have explored the coherence of the ultracold molecular in ground state.After the preparation of ground state molecules,the measurement of the Rabi oscillation can be realized by microwave coupling the adjacent rotational states,we can obtain the coherence time from the Rabi oscillation measurement.It is known that the Rabi oscillation measurements can only be achieved in ground state molecules which are produced by feshbach resonance combined with STIRAP,such as ultracold ⁴⁰K⁸⁷Rb,²³Na⁴⁰K,⁸⁷Rb¹³³Cs,²³Na⁸⁷Rb molecules and Ca F molecules formed by direct laser cooling.The large electric dipole moment of polar molecules lays the foundation for realizing quantum computing.The existence of electric dipole moment enables polar molecules can be controlled by the dipole-dipole interaction using an external electric field.As early as the 1980s,researchers have carried out theoretical study and experimental measurement of the electric dipole moment of polar molecules.The electric dipole moment measurement of ultracold ⁴⁰K⁸⁷Rb,⁸⁷Rb¹³³Cs,²³Na⁸⁷Rb and molecules which are formed by feshbach resonance combined with STIRAP and ultracold ⁷Li¹³³Cs molecules formed by PA have been completed.However,the electric dipole moment of ultracold ⁸⁵Rb¹³³Cs molecules in ground state has not yet been measured.In this paper,we choose the short-range PA to prepare ultracold ⁸⁵Rb¹³³Cs ground state molecules.Based on the research background we demonstrated above,we have carried out the following research.1.Investigations on the spectrum of 2¹?₁-2³?₁-3³?₁⁺and the characteristic of 3³?₁⁺state.The molecular yield can be greatly enhanced if the intermediate state has both singlet and triplet characters.Here,we have investigated the PA spectrum of2¹?₁-2³?₁-3³?₁⁺states.According to the labeling method of molecular state,we know that the angular momentum?of these three states is 1,and the component J=0should not appear in the vibrational spectrum.However,we find that there are J=0components in the spectroscopy of 3³?₁⁺(v=3)state.And then we have studied the characteristics of 3³?₁⁺(v=3)in detail.We get that the yield of ground state molecules prepared through 3³?₁⁺(v=3)is higher than that of other vibrational energy levels,and the rotational constant is also abrupt when comparing the adjacent vibration energy level,these characters demonstrate the resonance coupling characteristics of 3³?₁⁺(v=3).We realize the rotational distribution measurement of ground state molecules by using depletion spectrum.We also investigate the cascade radiation scheme of ground molecules produced from3³?₁⁺(v=3,J=1).It is found that the molecules prepared by3³?₁⁺(v=3,J=1)have can spontaneously decay to ground state via single pass,which is different from other two-photon cascade radiation scheme.This provides a basis for further preparation of ⁸⁵Rb¹³³Cs molecules in ground state by transferring from atom to molecules using stimulated Raman adiabatic passage.2.Two-level microwave coherent spectrum and coherence time measurementAfter the preparation of the ultracold ground state ⁸⁵Rb¹³³Cs molecules,we realized the Rabi oscillation measurement betweenX¹?⁺(v=0,J=1)andX¹?⁺(v=0,J=2)states by coupling these two states using microwave.A density-matrix formalism that accounts for longitudinal and transverse decay times reproduces both the dynamic evolution during the coherent process and the equilibrium population.3.Three-level microwave coherence spectrum measurement and spectrum analysisBased on the research of two-level microwave coherent Rabi oscillations,a ladder three-level structure was proposed,and the three-level microwave coherence spectra were measured.The molecules are initially populated atX¹?⁺(v=0,J=1)and transferred toX¹?⁺(v=0,J=2)by using a microwave?pulse.After that,we obtain the Rabi oscillation betweenX¹?⁺(v=0,J=2)andX¹?⁺(v=0,J=3)states,and get the coherence time of these two energy levels.Meanwhile,we use a weaker probe microwave field to couple the transition ofX¹?⁺(v=0,J=1)?X¹?⁺(v=0,J=2),and a stronger control microwave field to couple the transition of X¹?⁺(v=0,J=2)?X¹?⁺(v=0,J=3).By scanning the frequency of probe field we obtain a three-level microwave coherence spectrum with the fixed control field frequency.We use the Akaike's information criterion(AIC)criterion to analyze the spectral lineshape of the coherent spectrum,and discussed the observed spectrum splitting and the shift of the central frequency.4.Electric dipole moment measurement of ultracold ⁸⁵Rb¹³³Cs molecules in ground stateBased on the investiagtion of the three-level microwave coherent spectrum,we measured the energy level splitting of the ground stateX¹?⁺(v=0,J=1)under the external electric field,and obtained the electric dipole moment of the ultracold ground state ⁸⁵Rb¹³³Cs molecules.Compared with ⁷Li¹³³Cs molecules prepared by PA,which uses depletion spectroscopy to measure energy level splitting,and ignores the energy level splitting of excited states,here,we adopt the microwave coherence spectroscopy,which holds advantages:the resolution of microwave coherence spectroscopy is three orders of magnitude higher than that of the depletion spectrum;the constructed lambda-type three-level structure can effectively avoid the effect of Stark splitting caused by the upper energy level.5.Electric field intensity calibration by using ⁸⁵Rb Rydberg atomsIn order to obtain a more accurate electric dipole moment of the ultracold ⁸⁵Rb¹³³Cs molecule in ground state,the measurement and calibration of the electric field intensity are also critical.Here,we take advantage of the sensitivity of Rydberg atoms to the external field to calibrate the intensity of the electric field applied to the grid electrode plates.The weaker probe light couples the transition5S_1/2?5P_3/2,and the stronger coupling light couples the transition 5P_3/2?10D_3/2.We can acquire the EIT spectrum by scanning the frequency of coupling laser and detecting the probe laser intensity which is frequency locked.We analyzed the energy level splitting of ⁸⁵Rb Rydberg atom in 10D_3/2state under the external electric field and further calculated its polarizability.Finally,we have realized the calibration of the electric field intensity.