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arXiv:1702.04481 · Physical Review A

Measuring the polarization of electromagnetic fields using Rabi-rate measurements with spatial resolution: Experiment and theory

Joannis Koepsell, Tobias Thiele, Johannes Deiglmayr, Andreas J. Wallraff, Frédéric Merkt

Published May 24, 2017• 15 citations
arXivHTMLPDF

Abstract

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 $35s$ and $35p$ 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.

DOI
10.1103/physreva.95.053860

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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∼25.6GHz\ensuremath{\sim}25.6\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}\ensuremath∼25.6GHz 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.
Rydberg atoms efficiently link photons between the radio-frequency (rf) and optical domains. They furnish a medium in which the presence of an rf field imprints on the transmission of a probe laser beam by altering the coherent coupling between atomic quantum states. The immutable atomic energy structure underpins quantum-metrological rf-field measurements and has driven intensive efforts to realize inherently self-calibrated sensing devices. Here, we investigate spectroscopic signatures owing to the quantization of atomic angular momentum. Using an electromagnetically induced transparency (EIT) sensing scheme, specific combinations of atomic terms are shown to give rise to universal, distinctive fingerprints in the detected optical fields upon rotating a linearly polarized rf field. Employing a dressed state picture, we identify two types of atomic angular momentum ladders that display strikingly disparate spectroscopic characteristics, including the distinctive absence or presence of a central spectral EIT peak. Our study adds important insights into the prospects of Rydberg atomic gases for quantum-metrological electric field characterization including polarimetry. In particular, it calls into question prevailing interpretations of SI-traceable Rydberg atom electrometers.
Matter-wave interferometry has many possible uses, ranging from tests of funda- mental physics to applications in sensing. In order to achieve this interferometry, quantum superpositions of spatially-separated components need to be generated. There are several possible methods to accomplish this using Rydberg atoms; this thesis presents the experimental investigation of two of these. Both of these methods use inhomogeneous electric fields to spatially split beams of Rydberg atoms. In the first method, field distributions were generated above two-dimensional electrode structures and used to transversely split beams of helium Rydberg atoms into pairs of components spatially separated by up to 15.6 mm. Effects of amplitude modulation of the electric fields of this beam splitter were shown to cause particle losses through transitions into unconfined Rydberg-Stark states. This led to further studies of the depolarisation of Rydberg-Stark states in radio-frequency electric fields. Through this work it is shown that both ‘resonant’ and ‘non-resonant’ broadband modulation with amplitudes on the order of 10 mV·cm⁻¹ are sufficient to cause significant depolarisation of initially prepared quantum states on a timescale of 5 μs in a static offset electric field of 0.43 V·cm⁻¹. In a second class of experiments, matter-wave interferometry has been per- formed with helium atoms in high Rydberg states. In this work a series of mi- crowave and electric field gradient pulses were used to create a spatial separation between two components of a coherent superposition of states, while ensuring that the momenta of these components were equal at the end of the process to enable matter-wave interference to be observed. For the Rydberg states used, the spatial extent of the Rydberg electron wavefunction was ∼ 320 nm and displacements of up to 150 pm were observed between the pairs of matter-wave components at the end of the interferometry sequences.
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 $\ifmmode\pm\else\textpm\fi{}900\phantom{\rule{0.28em}{0ex}}\mathrm{nT}$ 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.
We demonstrate a method for determining the magnitude of the angle of arrival (AoA) of a linearly polarized radio-frequency (RF) field using the angle-dependent spectral amplitudes of AC Stark-shifted electromagnetically induced transparency (EIT) resonances. An off-resonant RF field produces distinct Stark shifts of the ∣mJ∣|m_J|∣mJ​∣ sublevels, while their relative excitation strengths depend strongly on the relative orientation of the RF and optical polarizations. Under the controlled polarization geometry considered here, this dependence enables determination of the AoA magnitude without requiring RF phase measurements or spatially separated sensing locations. We experimentally demonstrate the method at RF frequencies of 1.27 GHz, 2 GHz, 3 GHz, and 4 GHz using a subwavelength cesium vapor cell. Within the 20∘−40∘20^\circ-40^\circ20∘−40∘ region of highest angular sensitivity, the estimated repeatability-based 1σ1σ1σ AoA uncertainty ranges from approximately 0.6∘0.6^\circ0.6∘ to 2∘2^\circ2∘ across the investigated RF frequencies. A model combining Floquet-Shirley calculations of the RF-dressed Rydberg states with a coherent hyperfine-to-fine-structure optical excitation model qualitatively reproduces the experimental observations. These results establish a path toward compact, phase-independent AoA sensing using spatially localized Rydberg-atom spectroscopy.
Electric Rydberg-atom interferometry has been performed with helium atoms in coherent superpositions of the 1s56s3S11s56s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s56s3S1​ and 1s57s3S11s57s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s57s3S1​ Rydberg levels. The experiments were carried out in a longitudinal geometry with the atoms traveling at 2000 m/s in pulsed supersonic beams. After laser photoexcitation from the 1s2s3S11s2s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s2s3S1​ metastable level, coherent manipulation of the population of the Rydberg states was achieved using sequences of microwave pulses. The difference in the static electric dipole polarizabilities of the 1s56s3S11s56s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s56s3S1​ and 1s57s3S11s57s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s57s3S1​ levels allowed superpositions of external momentum states to be generated when inhomogeneous electric fields were used to exerted forces on the atoms prepared in superpositions of these internal states. Interference fringes, with contributions arising from the spatial separation of these Rydberg-atom wave packets in the direction of propagation of the atomic beam, were identified through changes in the internal-state populations as the magnitudes and durations of the time-dependent electric-field gradient pulses were adjusted. The maximal displacement of the atomic wave packets for which interference fringes were observed was $\ensuremath{\sim}0.75\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$, limited by the longitudinal velocity spread in the atomic beam and the characteristics of the inhomogeneous electric-field distribution in the apparatus. The experimental data are in good quantitative agreement with the results of numerical calculations of the time evolution of the atomic states under the experimental conditions.
Atoms form the basis of precise measurement for many quantities (time, acceleration, rotation, magnetic field, etc.). Measurements of microwave frequency electric fields by traditional methods (i.e. engineered antennas) have limited sensitivity and can be difficult to calibrate properly. Highly-excited (Rydberg) neutral atoms have very large electric-dipole moments and many dipole allowed transitions in the range of 1 - 500 GHz. It is possible to sensitively probe the electric field in this range using the combination of two quantum interference phenomena: electromagnetically induced transparency and the Autler-Townes effect. This technique allows for very sensitive field amplitude, polarization, and sub-wavelength imaging measurements. These quantities can be extracted by measuring properties of a probe laser beam as it passes through a warm rubidium vapor cell. Thus far, Rydberg microwave electrometry has relied upon the absorption of the probe laser. We report on our use of polarization rotation, which corresponds to the real part of the susceptibility, for measuring the properties of microwave frequency electric fields. Our simulations show that when a magnetic field is present and directed along the optical propagation direction a polarization rotation signal exists and can be used for microwave electrometry. One central advantage in using the polarization rotation signal rather than the absorption signal is that common mode laser noise is naturally eliminated leading to a potentially dramatic increase in signal-to-noise ratio.