Imaging of microwave fields using ultracold atoms

Abstract

We report a technique that uses clouds of ultracold atoms as sensitive, tunable, and noninvasive 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 distribution of microwave magnetic field amplitudes and phases. While we demonstrate two-dimensional imaging, an extension to three-dimensional imaging is straightforward. We use the method to determine the microwave near-field distribution around a coplanar waveguide integrated on an atom chip. © 2010 American Institute of Physics. ͓doi:10.1063/1.3470591͔ Today, monolithic microwave integrated circuits ͑MMICs͒ are of great importance in science and technology. In particular, they constitute key building blocks of today's communication technology. 1 MMICs also serve as main components of superconducting quantum processors. 2 In our group, a simple MMIC structure has recently been used as a tool for quantum coherent manipulation of ultracold atoms on an atom chip. 3 Function and failure analysis is of crucial importance for the design of MMICs as well as for simulation verification. 4 External port measurements ͑e.g., using a network analyzer͒ offer only limited insight. The microwave ͑mw͒ near-field distribution on the device gives much more information, enabling specific improvement. Therefore, different methods have been developed to measure the spatial distribution of mw near-fields. 5 These methods use diverse physical effects to measure the mw electric or magnetic field. They have in common that they scan the field distribution point-by-point.Here we propose and experimentally demonstrate a highly parallel method that allows for non-invasive and complete ͑amplitudes and phases͒ imaging of the mw magnetic field distribution using clouds of ultracold atoms. 6 In this method, the mw magnetic field drives resonant Rabi oscillations 7 between two atomic hyperfine levels that can be detected using state-selective absorption imaging. 8 The method offers micrometer spatial resolution and a mw magnetic field sensitivity in the 10 −8 T range at frequencies of a few gigahertz. It is a frequency-domain, single-shot technique to measure a two-dimensional field distribution. The method can be extended to measure three-dimensional ͑3D͒ distributions slice by slice. Data extraction is simple, it offers a high dynamic range, and it is intrinsically calibrated since only well-known atomic properties enter in the analysis.For the proof-of-principle experiment presented here, we use our atom chip setup, 3 see Fig. 1. The chip has integrated mw coplanar waveguide ͑CPW͒ structures that were designed for quantum manipulation of ultracold atoms. 3 To demonstrate our method, we analyze the mw magnetic field near this structure. In general, the device to be tested does ...

Quantum-limited measurement of magnetic-field gradient with entangled atoms

“…The transition frequency of 87 Rb atoms can be tuned by using an external static magnetic field [6], the range of the frequencies of the detected magnetic field is about a few GHz to 10 GHz [6,31].…”

“…1. Here we consider the two hyperfine spin states of atoms to be coupled to the magnetic fields via their magnetic dipoles [6,13]. Recently, a BEC has been shown to be transported to a distance about 1 mm by using a conveyor belt [14].…”

Stability of a trapped-atom clock on a chip

“…The clock transition is interrogated via two-photon (microwave + radiofrequency) coupling, where the microwave is detuned 500 kHz above the |1 to |F = 2, m F = 0 transition (figure 1). The microwave is coupled to a three-wire coplanar waveguide on the atom chip [43,45]. The interaction of the atoms with the waveguide evanescent field allows to reach single photon Rabi frequencies of a few kHz with moderate power ∼ 0 dBm.…”

Sensitive imaging of electromagnetic fields with paramagnetic polar molecules

“…The ratio of the minimal detectable magnetic fields in experiments with cold atoms [18] and molecules is given by B at min /B mol min = 2cd 12 α /( √ 3µ B )(assuming the same interaction time τ , the same number of particles and the same detection efficiency in both cases), which for typical molecules with d ∼ 1 a.u. amounts to ∼100-fold higher sensitivity using the proposed scheme.…”

“…imaging of the field amplitudes and phases at many spatial points at the same time. Recently Böhi et al proposed to use ultracold atoms for sensitive parallel imaging of microwave fields with frequencies in the range 2.5 − 14 GHz [18]. The method relies on measuring the phase difference between two hyperfine states of 87 Rb, accumulated due to an interaction with the magnetic component of the microwave field.…”