Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1306.1387 · Physical Review A

Imaging of relaxation times and microwave field strength in a microfabricated vapor cell

Andrew Horsley, Guanxiang Du, Matthieu Pellaton, C. Affolderbach, G. Mileti, Philipp Treutlein

Published Dec 16, 2013• 69 citations
arXivHTMLPDF

Abstract

We present a characterization technique for atomic vapor cells, combining time-domain measurements with absorption imaging to obtain spatially resolved information on decay times, atomic diffusion, and coherent dynamics. The technique is used to characterize a 5-mm-diameter, 2-mm-thick microfabricated Rb vapor cell, with N${}_{2}$ buffer gas, placed inside a microwave cavity. Time-domain Franzen and Ramsey measurements are used to produce high-resolution images of the population (${T}_{1}$) and coherence (${T}_{2}$) lifetimes in the cell, while Rabi measurements yield images of the ${\ensuremath{\sigma}}_{\ensuremath{-}}$, $\ensuremath{\pi}$, and ${\ensuremath{\sigma}}_{+}$ components of the applied microwave magnetic field. For a cell temperature of $90{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}$C, the ${T}_{1}$ times across the cell center are found to be a roughly uniform $265\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}$s, while the ${T}_{2}$ times peak at around $350\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}$s. We observe a ``skin'' of reduced ${T}_{1}$ and ${T}_{2}$ times around the edge of the cell due to the depolarization of Rb after collisions with the silicon cell walls. Our observations suggest that these collisions are far from being 100$%$ depolarizing, consistent with earlier observations made with Na and glass walls. Images of the microwave magnetic field reveal regions of optimal field homogeneity, and thus coherence. Our technique is useful for vapor cell characterization in atomic clocks, atomic sensors, and quantum information experiments.

DOI
10.1103/physreva.88.063407

Related papers

Spatially resolved measurement of relaxation times in a microfabricated vapor cell

Andrew Horsley, Guanxiang Du, Philipp Treutlein +3 more

We present a new characterisation technique for atomic vapor cells, combining time-domain measurements with absorption imaging to obtain spatially resolved information on decay times, atomic diffusion and coherent dynamics. The technique is used to characterise a microfabricated Rb vapor cell, with N2buffer gas, placed inside a microwave cavity. High-resolution images of the population (T1) and coherence (T2) lifetimes in the cell are presented. Atom-wall collisions and atomic diffusion result in a `skin' of reduced T1and T2times around the edge of the cell. The technique also allows polarisation-resolved imaging of the microwave magnetic field inside the cell. Our technique is useful for vapor cell characterisation in atomic clocks, atomic sensors, and quantum information experiments.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•Jul 1, 2013•1 citation

Imaging Microwave and DC Magnetic Fields in a Vapor-Cell Rb Atomic Clock

C. Affolderbach, Guanxiang Du, Thejesh Bandi +3 more

We report on the experimental measurement of the dc and microwave magnetic field distributions inside a recently developed compact magnetron-type microwave cavity mounted inside the physics package of a high-performance vapor-cell atomic frequency standard. Images of the microwave field distribution with sub-100-μm lateral spatial resolution are obtained by pulsed optical-microwave Rabi measurements, using the Rb atoms inside the cell as field probes and detecting with a CCD camera. Asymmetries observed in the microwave field images can be attributed to the precise practical realization of the cavity and the Rb vapor cell. Similar spatially resolved images of the dc magnetic field distribution are obtained by Ramsey-type measurements. The T2relaxation time in the Rb vapor cell is found to be position dependent and correlates with the gradient of the dc magnetic field. The presented method is highly useful for experimental in situ characterization of dc magnetic fields and resonant microwave structures, for atomic clocks or other atom-based sensors and instrumentation.

arXiv:1505.07739•IEEE Transactions on Instrumentation and Measurement•Jul 21, 2015•46 citations

High resolution field imaging with atomic vapor cells

Andrew Horsley

In this thesis, I report on the development of imaging techniques in atomic vapor cells. This is a relatively unexplored area, despite the ubiquitous use of imaging in experiments with ultracold atoms. Our main focus is in high resolution imaging of microwave near fields, for which there is currently no satisfactory established technique. We detect microwave fields through Rabi oscillations driven by the microwave on atomic hyperfine transitions. The technique can be easily modified to also image dc magnetic fields. In addition, we have developed techniques to image vapor cell processes such as atomic T1 and T2 relaxation. These provide a new window into vapor cell physics, which we have used to obtain spatially resolved information on Rb interactions with the cell walls, and to estimate the Rb relaxation probability in a collision with the cell wall. \n \nAs a first application of our imaging techniques, we imaged the dc and microwave magnetic fields inside a state-of-the-art vapor cell atomic clock. This new clock characterisation technique should lead to real improvements in clock performance, and is in the process of being adopted by the atomic clock community. \n \nWe have developed a widefield, high resolution imaging setup using a microfabricated vapor cell, which we have used to image microwave and dc magnetic vector fields. With the addition of a 480 nm laser, the setup can be configured to image microwave electric fields. Our camera-based imaging system records 2D images with a 6x6 mm2 field of view at a rate of 10 Hz. It provides up to 50 um spatial resolution, and allows imaging of fields as close as 150 um above structures, through the use of extremely thin external cell walls. This is crucial in allowing us to take practical advantage of the high spatial resolution, as feature sizes in near-fields are on the order of the distance from their source, and represents an order of magnitude improvement in surface-feature resolution compared to previous vapor cell experiments. We demonstrate a microwave magnetic field sensitivity of 1.4 uT/sqrt-Hz per 50x50x140 um3 voxel, at present limited by the speed of our imaging system. Since we image 120x120 voxels in parallel, a single scanned sensor would require a sensitivity of at least 12 nT/sqrt-Hz to produce images with the same sensitivity. \n \nThe spatial resolution, distance of approach, and sensitivity of our high resolution setup are sufficient for characterising 6.8 GHz microwave fields above a range of real world devices. However, frequency tunability is essential for wider applications of our imaging technique. Industry is particularly interested in techniques for imaging high frequency microwaves, above 18 GHz, where simulations become increasingly unreliable. I have shown that our technique can be extended to image microwaves of any frequency, in principle from dc to 100s of GHz, by using a large dc magnetic field to Zeeman shift the hyperfine ground state transitions to the desired frequency. I present results from a proof-of-principle setup, where we have used a 0.8 T solenoid to detect and image microwaves from 2.3 GHz to 26.4 GHz. \n

•Jan 1, 2015•1 citation

Impact of static-magnetic-field-gradients on relaxation times in a Rb vapor cell

Mohammadreza Gharavipour, C. Affolderbach, Florian Gruet +4 more

We apply an innovative method called Optically-Detected Spin-Echo to measure the intrinsic coherence relaxation time in the buffer-gas vapor cell of a Rb atomic clock [1]. This method suppresses the influence of static-magnetic-field-gradients across the cell which is a source of relaxation processes. Such studies are of interest for high-performance Rb atomic clocks, where both intrinsic population and coherence relaxation times (T1and T2, respectively) of the “clock transition” (52S1/2|Fg= 1, mF= 0〉 ↔ |Fg= 2, mF= 0〉) are relevant.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•Jul 1, 2017•0 citations

Simple microwave field imaging technique using hot atomic vapor cells

Pascal Böhi, Philipp Treutlein

We demonstrate a simple technique for microwave field imaging using alkali atoms in a vapor cell. The microwave field to be measured drives Rabi oscillations on atomic hyperfine transitions, which are detected in a spatially resolved way using a laser beam and a camera. Our vapor cell geometry enables single-shot recording of two-dimensional microwave field images with 350 μm spatial resolution. Using microfabricated vapor cell arrays, a resolution of a few micrometers seems feasible. All vector components of the microwave magnetic field can be imaged. Our apparatus is simple and compact and does not require cryogenics or ultra-high vacuum.

arXiv:1207.4964•Applied Physics Letters•Oct 29, 2012•69 citations

Broad Instantaneous Bandwidth Microwave Spectrum Analyzer with a Microfabricated Atomic Vapor Cell

Yongqi Shi, Thomas Ruster, Melvyn Ho +3 more

We report on broad instantaneous bandwidth microwave spectrum analysis with hot Rb 87 atoms in a microfabricated vapor cell in a large magnetic field gradient. The sensor is a MEMS atomic vapor cell filled with isotopically pure Rb 87 and N 2 buffer gas to localize the motion of the atoms. The microwave signals of interest are coupled through a coplanar waveguide to the cell, inducing spin-flip transitions between optically pumped ground states of the atoms. A static magnetic field with large gradient maps the frequency spectrum of the input microwave signals to a position-dependent spin-flip pattern on absorption images of the cell recorded with a laser beam onto a camera. In our proof-of-principle experiment, we demonstrate a microwave spectrum analyzer that has ≈ 1 GHz instantaneous bandwidth centered around 13 GHz, 3 MHz frequency resolution, 2 kHz refresh rate, and a − 23 dBm single-tone microwave power detection limit in 1 s measurement time. A theoretical model is constructed to simulate the image signals by considering the processes of optical pumping, microwave interaction, diffusion of Rb 87 atoms, and laser absorption. We expect to reach more than 25 GHz instantaneous bandwidth in an optimized setup, limited by the applied magnetic field gradient. Our demonstration offers a practical alternative to conventional microwave spectrum analyzers based on electronic heterodyne detection. Published by the American Physical Society 2024

arXiv:2403.15155•Physical Review X•Nov 13, 2024•4 citations
We present a characterization technique for atomic vapor cells, combining time-domain measurements with absorption imaging to obtain spatially resolved information on decay times, atomic diffusion, and coherent dynamics. The technique is used to characterize a 5-mm-diameter, 2-mm-thick microfabricated Rb vapor cell, with N2{}_{2}2​ buffer gas, placed inside a microwave cavity. Time-domain Franzen and Ramsey measurements are used to produce high-resolution images of the population (T1{T}_{1}T1​) and coherence (T2{T}_{2}T2​) lifetimes in the cell, while Rabi measurements yield images of the \ensuremathσ\ensuremath−{\ensuremath{\sigma}}_{\ensuremath{-}}\ensuremathσ\ensuremath−​, \ensuremathπ\ensuremath{\pi}\ensuremathπ, and \ensuremathσ+{\ensuremath{\sigma}}_{+}\ensuremathσ+​ components of the applied microwave magnetic field. For a cell temperature of 90\ensuremath∘90{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}90\ensuremath∘C, the T1{T}_{1}T1​ times across the cell center are found to be a roughly uniform 265\ensuremathμ265\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}265\ensuremathμs, while the T2{T}_{2}T2​ times peak at around 350\ensuremathμ350\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}350\ensuremathμs. We observe a ``skin'' of reduced T1{T}_{1}T1​ and T2{T}_{2}T2​ times around the edge of the cell due to the depolarization of Rb after collisions with the silicon cell walls. Our observations suggest that these collisions are far from being 100% depolarizing, consistent with earlier observations made with Na and glass walls. Images of the microwave magnetic field reveal regions of optimal field homogeneity, and thus coherence. Our technique is useful for vapor cell characterization in atomic clocks, atomic sensors, and quantum information experiments.
We present a new characterisation technique for atomic vapor cells, combining time-domain measurements with absorption imaging to obtain spatially resolved information on decay times, atomic diffusion and coherent dynamics. The technique is used to characterise a microfabricated Rb vapor cell, with N2buffer gas, placed inside a microwave cavity. High-resolution images of the population (T1) and coherence (T2) lifetimes in the cell are presented. Atom-wall collisions and atomic diffusion result in a `skin' of reduced T1and T2times around the edge of the cell. The technique also allows polarisation-resolved imaging of the microwave magnetic field inside the cell. Our technique is useful for vapor cell characterisation in atomic clocks, atomic sensors, and quantum information experiments.
We report on the experimental measurement of the dc and microwave magnetic field distributions inside a recently developed compact magnetron-type microwave cavity mounted inside the physics package of a high-performance vapor-cell atomic frequency standard. Images of the microwave field distribution with sub-100-μm lateral spatial resolution are obtained by pulsed optical-microwave Rabi measurements, using the Rb atoms inside the cell as field probes and detecting with a CCD camera. Asymmetries observed in the microwave field images can be attributed to the precise practical realization of the cavity and the Rb vapor cell. Similar spatially resolved images of the dc magnetic field distribution are obtained by Ramsey-type measurements. The T2relaxation time in the Rb vapor cell is found to be position dependent and correlates with the gradient of the dc magnetic field. The presented method is highly useful for experimental in situ characterization of dc magnetic fields and resonant microwave structures, for atomic clocks or other atom-based sensors and instrumentation.
In this thesis, I report on the development of imaging techniques in atomic vapor cells. This is a relatively unexplored area, despite the ubiquitous use of imaging in experiments with ultracold atoms. Our main focus is in high resolution imaging of microwave near fields, for which there is currently no satisfactory established technique. We detect microwave fields through Rabi oscillations driven by the microwave on atomic hyperfine transitions. The technique can be easily modified to also image dc magnetic fields. In addition, we have developed techniques to image vapor cell processes such as atomic T1 and T2 relaxation. These provide a new window into vapor cell physics, which we have used to obtain spatially resolved information on Rb interactions with the cell walls, and to estimate the Rb relaxation probability in a collision with the cell wall. \n \nAs a first application of our imaging techniques, we imaged the dc and microwave magnetic fields inside a state-of-the-art vapor cell atomic clock. This new clock characterisation technique should lead to real improvements in clock performance, and is in the process of being adopted by the atomic clock community. \n \nWe have developed a widefield, high resolution imaging setup using a microfabricated vapor cell, which we have used to image microwave and dc magnetic vector fields. With the addition of a 480 nm laser, the setup can be configured to image microwave electric fields. Our camera-based imaging system records 2D images with a 6x6 mm2 field of view at a rate of 10 Hz. It provides up to 50 um spatial resolution, and allows imaging of fields as close as 150 um above structures, through the use of extremely thin external cell walls. This is crucial in allowing us to take practical advantage of the high spatial resolution, as feature sizes in near-fields are on the order of the distance from their source, and represents an order of magnitude improvement in surface-feature resolution compared to previous vapor cell experiments. We demonstrate a microwave magnetic field sensitivity of 1.4 uT/sqrt-Hz per 50x50x140 um3 voxel, at present limited by the speed of our imaging system. Since we image 120x120 voxels in parallel, a single scanned sensor would require a sensitivity of at least 12 nT/sqrt-Hz to produce images with the same sensitivity. \n \nThe spatial resolution, distance of approach, and sensitivity of our high resolution setup are sufficient for characterising 6.8 GHz microwave fields above a range of real world devices. However, frequency tunability is essential for wider applications of our imaging technique. Industry is particularly interested in techniques for imaging high frequency microwaves, above 18 GHz, where simulations become increasingly unreliable. I have shown that our technique can be extended to image microwaves of any frequency, in principle from dc to 100s of GHz, by using a large dc magnetic field to Zeeman shift the hyperfine ground state transitions to the desired frequency. I present results from a proof-of-principle setup, where we have used a 0.8 T solenoid to detect and image microwaves from 2.3 GHz to 26.4 GHz. \n
We apply an innovative method called Optically-Detected Spin-Echo to measure the intrinsic coherence relaxation time in the buffer-gas vapor cell of a Rb atomic clock [1]. This method suppresses the influence of static-magnetic-field-gradients across the cell which is a source of relaxation processes. Such studies are of interest for high-performance Rb atomic clocks, where both intrinsic population and coherence relaxation times (T1and T2, respectively) of the “clock transition” (52S1/2|Fg= 1, mF= 0〉 ↔ |Fg= 2, mF= 0〉) are relevant.
We demonstrate a simple technique for microwave field imaging using alkali atoms in a vapor cell. The microwave field to be measured drives Rabi oscillations on atomic hyperfine transitions, which are detected in a spatially resolved way using a laser beam and a camera. Our vapor cell geometry enables single-shot recording of two-dimensional microwave field images with 350 μm spatial resolution. Using microfabricated vapor cell arrays, a resolution of a few micrometers seems feasible. All vector components of the microwave magnetic field can be imaged. Our apparatus is simple and compact and does not require cryogenics or ultra-high vacuum.
We report on broad instantaneous bandwidth microwave spectrum analysis with hot Rb 87 atoms in a microfabricated vapor cell in a large magnetic field gradient. The sensor is a MEMS atomic vapor cell filled with isotopically pure Rb 87 and N 2 buffer gas to localize the motion of the atoms. The microwave signals of interest are coupled through a coplanar waveguide to the cell, inducing spin-flip transitions between optically pumped ground states of the atoms. A static magnetic field with large gradient maps the frequency spectrum of the input microwave signals to a position-dependent spin-flip pattern on absorption images of the cell recorded with a laser beam onto a camera. In our proof-of-principle experiment, we demonstrate a microwave spectrum analyzer that has ≈ 1 GHz instantaneous bandwidth centered around 13 GHz, 3 MHz frequency resolution, 2 kHz refresh rate, and a − 23 dBm single-tone microwave power detection limit in 1 s measurement time. A theoretical model is constructed to simulate the image signals by considering the processes of optical pumping, microwave interaction, diffusion of Rb 87 atoms, and laser absorption. We expect to reach more than 25 GHz instantaneous bandwidth in an optimized setup, limited by the applied magnetic field gradient. Our demonstration offers a practical alternative to conventional microwave spectrum analyzers based on electronic heterodyne detection. Published by the American Physical Society 2024