Rydberg atoms make excellent sensors of external electromagnetic fields over a wide range of frequencies including the RF, microwave and terahertz bands. It is often necessary to identify which atomic transitions fall within a particular frequency range and compare their properties. It was primarily written to identify transitions within the THz band (100 GHz to 10 THz) for a 3-photon excitation scheme in caesium. For further details on this use case see [1,2,3]. The function is described here, and examples of use can be found in the Jupyter Notebook.
The function in the Transition_Search.py module searches through all atomic transitions within given parameters to identify those in the frequency range of interest. It relies on the Python package ARC (Alkali Rydberg Calculator), and I cannot be held responsible for any errors therein. (For example the frequency of the transitions will depend on the values of the quantum defects used by ARC which are outdated for caesium. This can result in errors of up to 100 MHz.)
The get_all_trans function creates an array of all possible transitions within a certain frequency range for a specified atom type. It searches through all atomic transitions and stores details of those that have properties within the specified parameter limits.
Args:
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freq_range(tuple of floats): Frequency range in which to search for possible Rydberg transitions (in GHz). For example (500, 700) will search for all transitions between 500 GHz and 700 GHz. -
atom_type(str'Cs'or'Rb', optional): The atomic species to consider. Default is Cs (caesium), Rb is rubidium 87. -
ground(tuple of floats, optional): The state from which we excite to Rydberg in the form$(n,l,j)$ e.g. (7,0,0.5) corresponds to$7S_{1/2}$ . (Default is'default'which corresponds to$7S_{1/2}$ in Caesium, and$6S_{1/2}$ for Rubidium.). -
min_dme(float, optional): the minimum value of the dipole matrix element (DME) to be stored (in units$a_0 e$ ). Transitions with DME less than this will not appear in the output array. Default is 5$a_0 e$ . -
nmax(float, optional): the maximum value of principal quantum number$n$ that will be considered. Default is 80. -
ryd_laser_range(tuple of floats, optional): wavelength range of the laser used to excite from the specified 'ground' state to the$R_1$ Rydberg state (in nm). Default is (700,1000) corresponding to the approximate range of a Titanium:Sapphire laser. -
save(bool, optional): whether the output array should be saved. Filename will be "Transition_Search_{frequency_range}GHz_{atom_type}_from_{ground}.csv". Default isTrue.
Returns:
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data_arr(2darray): details of all transitions within the specified parameter ranges. In order [$n_1$ ,$l_1$ ,$j_1$ ,$n_2$ ,$l_2$ ,$j_2$ , Transition frequency (GHz), DME ($a_0e$ ), Wavelength from chosen 'ground' state to Rydberg state$R_1$ (nm), DME of transition from 'ground' state to Rydberg state$R_1$ ($a_0e$ )]
This function only considers dipole allowed transitions (getDipoleMatrixElement function from ARC (from/to getRadialMatrixElement) which would neglect the angular/polarisation dependence and need to specify type of transition (
[1] Lucy A. Downes et al., Full-Field Terahertz Imaging at Kilohertz Frame Rates Using Atomic Vapor Phys. Rev. X 10 011027 (2020) https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.011027
[2] Lucy A. Downes, Lara Torralbo-Campo and Kevin J. Weatherill, A practical guide to terahertz imaging using thermal atomic vapour New J. Phys. 25 035002 (2023) https://iopscience.iop.org/article/10.1088/1367-2630/acb80c/meta
[3] Lucy A. Downes, A High-speed THz Imaging System based on THz-to-optical Conversion in Atomic Vapour PhD Thesis, Durham University (2020) https://etheses.dur.ac.uk/13797/