Microwave field imaging with ultracold atoms
Cold atoms as non-invasive high-resolution sensors for microwave fields
Microwaves are an essential part of modern communication technology. Mobile phones and laptops, for example, are equipped with integrated microwave circuits for wireless communication and satellite navigation. In the design and development of these circuits, computer simulations play an important role. Such simulations have to rely on approximations and are not always reliable. Therefore, measurements are required to test the circuits and to verify their performance. To enable efficient testing and specific improvement, one would ideally like to measure all components of the microwave field directly and with very high spatial resolution.
Microwaves are difficult to detect with high resolution. In existing techniques for measuring microwaves (see ), the field distribution has to be scanned point-by-point, so that data acquisition is slow. Moreover, most techniques only allow for a measurement of the amplitudes, but not of the phases of the microwave field. Furthermore, macroscopic probe heads used for the measurement can distort the microwave field and result in poor spatial resolution. We have developed a novel technique that avoids these drawbacks and allows for the direct and complete imaging of microwave magnetic fields with high spatial resolution (see ). In this technique, tiny clouds of laser-cooled ultracold atoms serve as non-invasive probes for the microwave field. Ultracold atoms react very sensitively to applied electromagnetic fields. Moreover, because all atoms of a given species are the same and their properties are well-known, these atomic sensors are calibrated by nature.
Figure 1: Illustration of the working principle of the microwave field imaging technique. (a) Ground state hyperfine levels of 87Rb atoms in a static magnetic field. Initially, the atoms are trapped in the hyperfine state |F,mF>=|1,-1>. The three relevant transitions |1,-1>↔|2,m2> (m2=-2,-1,0) are indicated. The corresponding transition frequencies ωγ (γ=-,π,+) are split by ωL due to the Zeeman effect. The resonant Rabi frequencies Ωγ are also indicated. (b) The atom chip used in these experiments. We note that it is not necessary to use a chip-based setup. Inset: Atom cloud near the coplanar waveguide structure (CPW) whose microwave magnetic field is examined. (c) Experimental sequence. Left: The trap is switched off and the atom cloud expands. Right: A microwave pulse is applied to the CPW, resonant with one of the transitions ωγ. Its magnetic field of amplitude B(r) drives Rabi oscillations with position-dependent Ωγ(r) between |1,-1> (red) and the corresponding state |1,m2> (blue). The resulting atomic density distribution n1(r) (n2(r)) in F=1 (F=2) is detected.
In our experiment (see ), the microwave field to be imaged drives a transition between two hyperfine states of the atoms. The probability of finding an atom in either state thereby oscillates with a Rabi frequency which depends on the local microwave field strength at the position of the atom. After applying the microwave field for some time, its spatial field distribution is therefore imprinted onto the hyperfine state distribution in the atomic cloud. From this distribution, which we image onto a CCD-camera, we can reconstruct the microwave field.
How it works
Inside a room-temperature vacuum chamber, we place a magnetically trapped cloud of 104 laser-cooled Rubidium-87 atoms close to the microwave structure to be characterized (see Figure 1). Initially, the atoms are prepared in hyperfine sublevel |1,-1> of the electronic ground state. We switch off the trap and release the atoms to free fall. During a hold-off time dtho, the cloud drops due to gravity and expands due to its thermal velocity spread, filling the region to be imaged. We maintain a homogeneous static magnetic field B0, which provides the quantization axis and splits the hyperfine transition frequencies ωγ (γ=-,π,+) by the Larmor frequency ωL=μBB0/2ћ. When the atoms fill the region of interest, a microwave signal on the microwave circuit is subsequently switched on for a duration dtmw (typically some tens of microseconds). We select one of the transitions by setting the microwave frequency to ω=ωγ. The microwave magnetic field couples to the atomic magnetic moment and drives Rabi oscillations at frequency Ωγ on the resonant transition, with Ωγ(r) proportional to Bγ(r). The Rabi frequency thus directly reflects the microwave magnetic field polarization component Bγ(r) at position r that drives the transition. In particular, Bπ is the projection of the microwave magnetic field B onto B0, and B+ (B-) is the right (left) handed circular polarization component in the plane perpendicular to B0.
After the resonant microwave pulse, a spatial distribution of atomic populations in F=1 and F=2 results. The probability to detect an atom at position r in F=2 is p2(r)=n2(r)/(n1(r)+n2(r))=sin2(Ωγdtmw/2). Here, n1(r) (n2(r)) is the density of atoms in F=1 (F=2), which can be measured using state-selective absorption imaging (see ). Thus, the microwave field strength is imprinted onto the atomic population, which can be imaged onto a CCD camera. An overview of such images of p2(r) is shown in Figure 2. The different images correspond to different microwave polarization components near the coplanar waveguide structure (CPW) that is integrated on our atom chip (see ).
From the measured p2(r) we can reconstruct Ωγ(r) and thus the spatial distribution of the microwave magnetic field component Bγ(r) by measuring p2(r) for different values of the microwave power Pmw, as discussed in .
Figure 2: Imaging of microwave magnetic field components near the CPW structure. The images show the measured probability p2(r) to find an atom in F=2 after applying the microwave pulse. Columns correspond to measurements on the three different transitions ωγ, rows to three different orientations of B0. The imaging beam is reflected from the chip surface at a small angle. As a result, on each picture, the direct image and its reflection on the chip surface are visible. The dashed line separates the two.
(see also our list of publications)
 S. Sayil, D. V. Kerns, and S. E. Kerns, A survey of contactless measurement and testing techniques, IEEE 24 25 (2005).
 P. Böhi, M. F. Riedel, T. W. Hänsch, and P. Treutlein, Imaging of microwave fields using ultracold atoms, Appl. Phys. Lett. 97 051101 (2010).
 M. R. Matthews, D. S. Hall, D. S. Jin, J. R. Ensher, C. E. Wieman, and E. A. Cornell, Dynamical Response of a Bose-Einstein Condensate to a discontinuous change in internal state, Phys. Rev. Lett. 81 243 (1998).
 P. Böhi, M. F. Riedel, J. Hoffroge, J. Reichel, T. W. Hänsch, and P. Treutlein, Coherent manipulation of Bose-Einstein condensates with state-dependent microwave potentials on an atom chip, Nature Physics 5, 592 (2009).