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Physical Review A

Absolute static-field magnetometry, magnetic gradiometry, and vector electrometry with circular Rydberg atoms

Junwen Zou, S. D. Hogan

Published Jun 26, 2023• 6 citations
Publisher

Abstract

Helium atoms in pulsed supersonic beams have been prepared in the circular Rydberg state with principal quantum number $n=55$ using the crossed-fields method. High-resolution microwave spectroscopy of the transition from this state to the $n=56$ circular state, at frequencies close to 38.5 GHz, was performed to measure static magnetic and electric fields along the axis of propagation of the beams with quantum-state-selective detection by pulsed-electric-field ionization. Magnetic fields of between 1.3 and 1.6 mT were measured to a relative precision of $\ifmmode\pm\else\textpm\fi{}900\phantom{\rule{0.28em}{0ex}}\mathrm{nT}$ by rf spectroscopy and $\ifmmode\pm\else\textpm\fi{}1.3\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{T}$ by microwave spectroscopy, with absolute calibration, accounting for Doppler shifts and effects of weak stray electric fields to $\ifmmode\pm\else\textpm\fi{}2.0\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{T}$ and a spatial resolution of $\ifmmode\pm\else\textpm\fi{}0.87$ mm. Magnetic-field gradients could be determined to a precision of $\ifmmode\pm\else\textpm\fi{}1.49\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{T}/\mathrm{mm}$ ($\ifmmode\pm\else\textpm\fi{}53$ nT/mm) over a baseline of 1.74 mm (35 mm). To perform these measurements, static electric fields and contributions from the motional Stark effect were minimized, and residual electric fields in each of the three spatial dimensions in the apparatus were measured to an absolute precision of between $\ifmmode\pm\else\textpm\fi{}85$ and $\ifmmode\pm\else\textpm\fi{}750\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{V}/\mathrm{cm}$. The methods used in this work can be transferred to experiments with other atoms or molecules. They are therefore well suited for applications in minimally invasive, absolute static-field magnetometry and electrometry, for example, at hybrid interfaces between Rydberg atoms and superconducting circuits; in tests of bound-state QED or the weak equivalence principle with atomic or molecular hydrogen, antihydrogen, or positronium; and in measurements of the absolute neutrino mass by cyclotron radiation emission spectroscopy.

DOI
10.1103/physreva.107.062820

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Helium atoms in pulsed supersonic beams have been prepared in the circular Rydberg state with principal quantum number n=55n=55n=55 using the crossed-fields method. High-resolution microwave spectroscopy of the transition from this state to the n=56n=56n=56 circular state, at frequencies close to 38.5 GHz, was performed to measure static magnetic and electric fields along the axis of propagation of the beams with quantum-state-selective detection by pulsed-electric-field ionization. Magnetic fields of between 1.3 and 1.6 mT were measured to a relative precision of \ifmmode±\else\textpm\fi900nT\ifmmode\pm\else\textpm\fi{}900\phantom{\rule{0.28em}{0ex}}\mathrm{nT}\ifmmode±\else\textpm\fi900nT by rf spectroscopy and \ifmmode±\else\textpm\fi1.3\textmuT\ifmmode\pm\else\textpm\fi{}1.3\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{T}\ifmmode±\else\textpm\fi1.3\textmuT by microwave spectroscopy, with absolute calibration, accounting for Doppler shifts and effects of weak stray electric fields to \ifmmode±\else\textpm\fi2.0\textmuT\ifmmode\pm\else\textpm\fi{}2.0\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{T}\ifmmode±\else\textpm\fi2.0\textmuT and a spatial resolution of \ifmmode±\else\textpm\fi0.87\ifmmode\pm\else\textpm\fi{}0.87\ifmmode±\else\textpm\fi0.87 mm. Magnetic-field gradients could be determined to a precision of \ifmmode±\else\textpm\fi1.49\textmuT/mm\ifmmode\pm\else\textpm\fi{}1.49\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{T}/\mathrm{mm}\ifmmode±\else\textpm\fi1.49\textmuT/mm (\ifmmode±\else\textpm\fi53\ifmmode\pm\else\textpm\fi{}53\ifmmode±\else\textpm\fi53 nT/mm) over a baseline of 1.74 mm (35 mm). To perform these measurements, static electric fields and contributions from the motional Stark effect were minimized, and residual electric fields in each of the three spatial dimensions in the apparatus were measured to an absolute precision of between \ifmmode±\else\textpm\fi85\ifmmode\pm\else\textpm\fi{}85\ifmmode±\else\textpm\fi85 and \ifmmode±\else\textpm\fi750\textmuV/cm\ifmmode\pm\else\textpm\fi{}750\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{V}/\mathrm{cm}\ifmmode±\else\textpm\fi750\textmuV/cm. The methods used in this work can be transferred to experiments with other atoms or molecules. They are therefore well suited for applications in minimally invasive, absolute static-field magnetometry and electrometry, for example, at hybrid interfaces between Rydberg atoms and superconducting circuits; in tests of bound-state QED or the weak equivalence principle with atomic or molecular hydrogen, antihydrogen, or positronium; and in measurements of the absolute neutrino mass by cyclotron radiation emission spectroscopy.
Circular Rydberg states with n=70n=70n=70 have been prepared in helium using a modified version of the crossed-fields method. This approach to the preparation of high-nnn circular Rydberg states overcomes limitations of the standard crossed-fields method which arise at this, and higher, values of nnn. The experiments were performed with atoms traveling in pulsed supersonic beams that were initially laser photoexcited from the metastable 1s2s3S11s2s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s2s3S1​ level to the 1s73s3S11s73s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s73s3S1​ level by resonance-enhanced two-color two-photon excitation in a magnetic field of 16.154 G. These excited atoms were then polarized using a perpendicular electric field of 0.844 V/cm, and transferred by a pulse of microwave radiation to the state that, when adiabatically depolarized, evolves into the n=70n=70n=70 circular state in zero electric field. The excited atoms were detected by state-selective electric field ionization. Each step of the circular state preparation process was validated by comparison with the calculated atomic energy-level structure in the perpendicular electric and magnetic fields used. Of the atoms initially excited to the 1s73s3S11s73s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s73s3S1​ level, $\ensuremath{\sim}80%$ were transferred to the n=70n=70n=70 circular state. At these high values of $n, \mathrm{\ensuremath{\Delta}}n=1$ circular-to-circular Rydberg state transitions occur at frequencies below 20 GHz. Consequently, atoms in these states, and the circular state preparation process presented here, are well suited to hybrid cavity QED experiments with Rydberg atoms and superconducting microwave circuits.
Helium atoms have been prepared in the circular $|n=55,\ensuremath{\ell}=54,{m}_{\ensuremath{\ell}}=+54\ensuremath{\rangle}$ Rydberg state using the crossed electric and magnetic fields method. The atoms, initially traveling in pulsed supersonic beams, were photoexcited from the metastable 1s2s3S11s2s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s2s3S1​ level to the outermost, ${m}_{\ensuremath{\ell}}=0$ Rydberg-Stark state with n=55n=55n=55 in the presence of a strong electric field and weak perpendicular magnetic field. Following excitation, the electric field was adiabatically switched off causing the atoms to evolve into the circular state with ${m}_{\ensuremath{\ell}}=+54$ defined with respect to the magnetic-field quantization axis. The circular states were detected by ramped electric-field ionization along the magnetic-field axis. The dependence of the circular state production efficiency on the strength of the excitation electric field, and the electric-field switch-off time was studied, and microwave spectroscopy of the circular-to-circular $|55,54,+54\ensuremath{\rangle}\ensuremath{\rightarrow}|56,55,+55\ensuremath{\rangle}$ transition at $\ensuremath{\sim}38.5$ GHz was performed.
When internal states of atoms are manipulated using coherent optical or radio-frequency (rf) radiation, it is essential to know the polarization of the radiation with respect to the quantization axis of the atom. We first present a measurement of the two-dimensional spatial distribution of the electric-field amplitude of a linearly polarized pulsed rf electric field at $\ensuremath{\sim}25.6\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}$ and its angle with respect to a static electric field. The measurements exploit coherent population transfer between the 35s35s35s and 35p35p35p Rydberg states of helium atoms in a pulsed supersonic beam. Based on this experimental result, we develop a general framework in the form of a set of equations relating the five independent polarization parameters of a coherently oscillating field in a fixed laboratory frame to Rabi rates of transitions between a ground and three excited states of an atom with arbitrary quantization axis. We then explain how these equations can be used to fully characterize the polarization in a minimum of five Rabi-rate measurements by rotation of an external bias field, or, knowing the polarization of the driving field, to determine the orientation of the static field using two measurements. The presented technique is not limited to Rydberg atoms and rf fields but can also be applied to characterize optical fields. The technique has the potential for sensing the spatiotemporal properties of electromagnetic fields, e.g., in metrology devices or in hybrid experiments involving atoms close to surfaces.
In highly excited Rydberg atoms, the excited electron is in a large, loosely bound orbit. Hence, in contrast with the ground states, the Rydberg states are very sensitive to external electric field and can be ionized in rather weak fields. The low ionization threshold of Rydberg states results in effective state-specific detection by the selective field ionization technique. \t In this thesis, high-resolution spectroscopy of Rydberg states of Rubidium using millimeter wave transitions and selective field ionization has been used as a probe of external electric and magnetic fields. Laser cooling and trapping techniques in a magneto-optical trap (MOT) are employed to have a high density and narrow velocity distribution for the atomic sample. In this work the magnetic field inhomogeneity inherent in a MOT is minimized and the stray electric field present at the trap region is compensated in order to have resolved spectra. The Stark line broadening of the spectra obtained in this work may be used to determine the electric field distribution in an expanding ultra-cold neutral plasma.
Experimental results of studying the spectrum of the microwave 37 P -37 S transition of Rydberg sodium atoms in a weak magnetic field (≤7 G) are reported. The populations of the Rydberg states were measured using the method of selective ionization with a pulsed electric field. When the magnetic field was parallel to the ionizing electric field, a good agreement between the calculated and experimental spectral shapes was observed, making it possible to determine the unknown polarization of the microwave radiation. In the case of the orthogonal configuration of the fields, the resonance structure was suppressed in the field ionization signals due to the strong influence of the magnetic field on the electron trajectories in the detection system.
A coherent electric analogue of the Stern-Gerlach experiment has been performed with helium atoms in Rydberg states. The atoms, travelling in pulsed supersonic beams, were prepared in superpositions of Rydberg states with different static electric dipole polarisabilities using pulses of microwave radiation. State-dependent forces were then exerted on them, transverse to their direction of propagation, using inhomogeneous electric fields. These fields were generated between a pair of electrodes in a wedge configuration. The forces applied resulted in the coherent evolution of each atomic wavepacket into a superposition of spatially separated momentum states. The classical paths of least action associated with these momentum states evolved over time up to a separation of ∼2 nm. The coherent evolution of the atoms, and hence the superposition of atomic wavepackets in this ‘half-loop’ electric Rydberg-atom interferometer, was monitored by measuring the internal Rydberg state populations at the end of each measurement cycle. The experimental data are in good quantitative agreement with the results of semiclassical calculations of the phase evolution of the atomic superposition states which account for contributions from Stark shifts, the momentum differences between the classical paths of least action through the apparatus, and the spatial separation of the atomic wavepackets.