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Physical Review A

Microwave ac Zeeman force for ultracold atoms

Charles Fancher, Andrew J. Pyle, Andrew P. Rotunno, S. Aubin

Published Apr 27, 2018• 14 citations
Publisher

Abstract

We measure the ac Zeeman force on an ultracold gas of $^{87}\mathrm{Rb}$ due to a microwave magnetic field targeted to the 6.8 GHz hyperfine splitting of these atoms. An atom chip produces a microwave near field with a strong amplitude gradient, and we observe a force over three times the strength of gravity. Our measurements are consistent with a simple two-level theory for the ac Zeeman effect and demonstrate its resonant, bipolar, and spin-dependent nature. We observe that the dressed-atom eigenstates gradually mix over time and have mapped out this behavior as a function of magnetic field and detuning. We demonstrate the practical spin selectivity of the force by pushing or pulling a specific spin state while leaving other spin states unmoved.

DOI
10.1103/physreva.97.043430

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Atom chip based interferometry holds signicant promise for embedded precise measurements of time, accelerations, rotations, and magnetic fields. It can enable compact sensors for various carriers like planes, boats, and drones, making it advantageous for navigation applications. When measuring acceleration with a cold atom interferometer, it is necessary to separate the two states during the interferometry sequence. Microwave dressed potentials generated from CPWs within a magnetic trap are one approach to achieve such on-chip manipulation. Two specic challenges arise in this process. First, the microwave field emitted by a waveguide introduces an AC Zeeman shifts, leading to a bias phase in the interferometer output. Precise determination of this bias is necessary for accurate parameter readout. Second, positioning the atom trap accurately between the two waveguides is crucial to obtain the necessary symmetry during separation; otherwise, the contrast of the interferometer is signicantly reduced. To address these challenges, we present a method for measuring AC Zeeman shifts using Ramsey interferometry.

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We measure the ac Zeeman force on an ultracold gas of 87Rb^{87}\mathrm{Rb}87Rb due to a microwave magnetic field targeted to the 6.8 GHz hyperfine splitting of these atoms. An atom chip produces a microwave near field with a strong amplitude gradient, and we observe a force over three times the strength of gravity. Our measurements are consistent with a simple two-level theory for the ac Zeeman effect and demonstrate its resonant, bipolar, and spin-dependent nature. We observe that the dressed-atom eigenstates gradually mix over time and have mapped out this behavior as a function of magnetic field and detuning. We demonstrate the practical spin selectivity of the force by pushing or pulling a specific spin state while leaving other spin states unmoved.
Ultracold atom experiments use a gas of neutral atoms with temperatures less than 100 µK above absolute zero and offer unmatched experimental control of quantum states and coherence, which has allowed ultracold atom-based measurements to be some of the most precise to date. While ultracold atom experiments can control almost all atomic degrees of freedom, spin-dependent trapping and spatial manipulation has remained difficult if not inaccessible. We are developing a method of spin-dependent trapping and spatial manipulation for ultracold neutral atoms using the AC Zeeman force produced by a microwave magnetic near-field gradient generated by an atom chip. We measure the AC Zeeman force on ultracold rubidium atoms by observing its effect on the motion of atoms in free-fall and on those confined in a trap. We have studied the force as a function of microwave frequency detuning from a hyperfine transition at 6.8 GHz at several magnetic field strengths and have observed its characteristic bipolar and resonant features predicted by two-level dressed atom theory. We find that the force is several times the strength of gravity in our setup, and that it can be targeted to a specific hyperfine transition while leaving other hyperfine states and transitions relatively unaffected. We find that our measurements are reasonably consistent with parameter-free theoretical predictions.
We measure the ac Zeeman force acting on ultracold 87Rb^{87}\mathrm{Rb}87Rb atoms due to a radio frequency (rf) field driving intramanifold Zeeman transitions near 8 MHz. We observe about 2.5 times the force of gravity for $\ensuremath{\approx}14$ mW of rf power acting on atoms $\ensuremath{\approx}100\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{m}$ from the atom chip. Our measurements are consistent with theoretical predictions and demonstrate the spin-state dependence of the force, as well as its resonant and bipolar behavior. We demonstrate the ac Stern-Gerlach effect by spatially separating a spin mixture, using initial detuning to determine which spins are ac Zeeman high- and low-field seekers. With an eye towards using this force for atom trapping, we observe the time dependence of dressed state spin mixing as a function of detuning and power.
Spin-specific trapping and mechanical control of ultracold atoms is difficult with current techniques, but offers the possibility of exploring new physics systems, such as spin-dependent trapped atom interferometers, as well as quantum gates, 1D many-body spin gases, and novel cooling schemes. Microwave near-field potentials based on the AC Zeeman effect provide a mechanism for such spin-specific control of atoms: in principle, independent potentials can be targeted to different spin states simultaneously. A broadband microwave atom chip can be used to generate both AC Zeeman trapping potentials and a microwave lattice for long distance trap positioning. We present recent experimental results on the successful trapping of ultracold rubidium atoms in an AC Zeeman atom chip trap using RF intra-hyperfine manifold transitions. Notably, these traps suppress the potential roughness encountered in traditional micro-magnetic chip traps.
We demonstrate the accurate determination of the magnetic strength of a microwave field utilizing the dressed cesium atom as a sensor. A bias magnetic field is initially used to split the Zeeman levels of the ground state. Its value is carefully selected to ensure that the microwave field to be measured is closely resonant to a pair of selected hyperfine Zeeman levels ( | F = 3 , m F = 3 ⟩ and | F = 4 , m F = 4 ⟩ ), while other states are neglected. This approach significantly simplifies the interaction model. A weak radio-frequency magnetic field is utilized to drive atoms away from the specified magnetic quantum number state to its neighbor, whose population imbalance is supervised by optical readout. The long atomic transverse relaxation time due to the antirelaxation coatings of alkali-metal-vapor cells makes it possible to precisely depict the interaction between atoms and the microwave field. Consequently, the microwave field can be accurately determined with an uncertainty of less than 1% even beyond 100 nT, corresponding to a radio-frequency spectral line broadening less than 100 Hz. The features we have identified enable us to expand the possibilities of developing new metrology for measuring microwave fields in an alternative way.
The spectacular progress in the field of ultracold quantum gases is intimately connected with the availability of sophisticated techniques for quantum-level control of internal states, motional states, and collisional interactions. Atom chips provide such control in compact, robust, and scalable setups, which makes them attractive for both applications and fundamental studies. In this thesis I report on experiments that use a new method for coherent manipulation of ultracold atoms. The method is based on microwave near-fields, provided by a waveguide structure that is fully integrated on an atom chip. We generate microwave near-field potentials that combine the versatility of optical traps with the robustness and tailorability of static magnetic microtraps. These potentials depend on the internal atomic state, and we use them for state-selective splitting of Rb Bose-Einstein condensates. We show for the first time combined coherent manipulation of internal and motional states on an atom chip, realizing a trapped-atom interferometer with internal state labeling of the interferometer paths. Moreover, we use microwave near-field potentials for the preparation of spin-squeezed states for quantum-enhanced metrology through controlling state-dependent collisional interactions. In addition, very promising proposals exist for the implementation of a quantum phase gate using these potentials. Measuring microwave fields is important for engineering of microwave devices as well as in science, e.g. to characterize the field homogeneity in the interaction regions of an atomic clock. We develop a novel technique that uses clouds of uncondensed ultracold atoms as sensitive, tunable and non-invasive probes for microwave field imaging with micrometer spatial resolution. The microwave magnetic field components drive Rabi oscillations on atomic hyperfine transitions whose frequency can be tuned with a static magnetic field. Readout is accomplished using state-selective absorption imaging. Quantitative data extraction is simple and it is possible to reconstruct the amplitudes and phases of the different microwave magnetic field components. While we demonstrate 2D imaging, an extension to 3D imaging is straightforward. We use the method to determine the microwave near-field distribution around the on-chip waveguide and reconstruct the corresponding current distribution. For our experimental parameters, the method provides a microwave magnetic field sensitivity of 0.2 mG, which can even be improved further with variants discussed. The experiments presented in this thesis open the path for the realization of portable quantum-enhanced interferometer devices, the implementation of a quantum phase gate as well as for a new generation of microwave field sensors.
Atom chip based interferometry holds signicant promise for embedded precise measurements of time, accelerations, rotations, and magnetic fields. It can enable compact sensors for various carriers like planes, boats, and drones, making it advantageous for navigation applications. When measuring acceleration with a cold atom interferometer, it is necessary to separate the two states during the interferometry sequence. Microwave dressed potentials generated from CPWs within a magnetic trap are one approach to achieve such on-chip manipulation. Two specic challenges arise in this process. First, the microwave field emitted by a waveguide introduces an AC Zeeman shifts, leading to a bias phase in the interferometer output. Precise determination of this bias is necessary for accurate parameter readout. Second, positioning the atom trap accurately between the two waveguides is crucial to obtain the necessary symmetry during separation; otherwise, the contrast of the interferometer is signicantly reduced. To address these challenges, we present a method for measuring AC Zeeman shifts using Ramsey interferometry.