We use a small Bose-Einstein condensate on an atom chip as an interferometric scanning probe to map out a microwave field near the chip surface with a few micrometers resolution. With the use of entanglement between the atoms, our interferometer overcomes the standard quantum limit of interferometry by 4 dB and maintains enhanced performance for interrogation times up to 10 ms. This corresponds to a microwave magnetic field sensitivity of 77 pT/√Hz in a probe volume of 20 μm(3). Quantum metrology with entangled atoms is useful in measurements with high spatial resolution, since the atom number in the probe volume is limited by collisional loss. High-resolution measurements of microwave near fields, as demonstrated here, are important for the development of integrated microwave circuits for quantum information processing and applications in communication technology.
We use a small Bose-Einstein condensate on an atom chip as an interferometric scanning probe to map out a microwave field near the chip surface with a few micrometers resolution. With the use of entanglement between the atoms, our interferometer overcomes the standard quantum limit of interferometry by 4 dB and maintains enhanced performance for interrogation times up to 10 ms. This corresponds to a microwave magnetic field sensitivity of 77 pT/√Hz in a probe volume of 20 μm(3). Quantum metrology with entangled atoms is useful in measurements with high spatial resolution, since the atom number in the probe volume is limited by collisional loss. High-resolution measurements of microwave near fields, as demonstrated here, are important for the development of integrated microwave circuits for quantum information processing and applications in communication technology.
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.
The controlled generation of entanglement forms the basis for currently emerging ‘quantum technologies’, such as quantum simulation, computation, and metrology. In the field of quantum metrology, multi-particle entangled states, such as spin-squeezed states, are investigated as a means to improve measurement precision beyond the ‘standard quantum limit’. This limit arises from the quantum noise inherent in measurements on a finite number of uncorrelated particles and limits today’s best atomic clocks. Atom chips combine exquisite coherent control of ultracold atoms with a compact and robust setup, suggesting their use for quantum metrology with portable atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. In this thesis, I present experiments where we generate for the first time multi-particle entanglement on an atom chip. We achieve this by controlling elastic collisional interactions with a state-dependent potential. We employ this novel technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they are a useful resource for quantum metrology, as they could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit. The state-dependent potential is created with the help of a coplanar microwave guide, which is integrated on our atom chip. In the vicinity of this waveguide a microwave nearfield is formed. When a Bose-Einstein condensate of 87Rb is brought into this near-field, the hyperfine energy levels of the atoms are shifted differentially due to the AC Zeeman effect. The strong gradients in the field can be used to state-selectively shift the minimum of a static magnetic atom trap and thus coherently split an ensemble of atoms which have been prepared in a superposition of two internal states. During this process, nonlinear atomic interactions lead to the formation of a spinsqueezed state. I tomographically analyze the produced state, reconstruct its Wigner function, and deduce that it is at least four-particle entangled. I compare our results with a dynamical multi-mode simulation which takes not only the atomic motion and internal state dynamics but also particle losses into account and find good agreement. Moreover, I use this comparison to identify technical noise sources in our experiment, which currently limit the achieved amount of squeezing, and make suggestions on how to eliminate them in future experiments. Our method can in principle create a very large amount of squeezing and entanglement and is applicable to a wide variety of atomic systems, in particular to those for which no convenient Feshbach resonance exists. We envisage the implementation of this technique in portable atomic clocks and interferometers operating beyond the standard quantum limit. Furthermore, it is a valuable tool for experiments on many-body quantum physics and could enable quantum information processing on atom chips.
We report on the design and performance of a cryogenic (300 mK) near-field scanning microwave microscope. It uses a microwave resonator as the near-field sensor, operating at a frequency of 6 GHz and microwave probing amplitudes down to 100 μV, approaching low enough photon population (N ∼ 1000) of the resonator such that coherent quantum manipulation becomes feasible. The resonator is made out of a miniaturized distributed fractal superconducting circuit that is integrated with the probing tip, micromachined to be compact enough such that it can be mounted directly on a quartz tuning-fork, and used for parallel operation as an atomic force microscope (AFM). The resonator is magnetically coupled to a transmission line for readout, and to achieve enhanced sensitivity we employ a Pound-Drever-Hall measurement scheme to lock to the resonance frequency. We achieve a well localized near-field around the tip such that the microwave resolution is comparable to the AFM resolution, and a capacitive sensitivity down to 6.4 × 10(-20) F/Hz, limited by mechanical noise. We believe that the results presented here are a significant step towards probing quantum systems at the nanoscale using near-field scanning microwave microscopy.
Microwave (MW) field sensing is foundational to modern technology, yet its evolution, reliant on classical antennas, is constrained by fundamental physical limits on field, temporal, and spatial resolutions. Here, we demonstrate an MW electrometry that simultaneously surpasses these constraints by using individual Rydberg atoms in an optical tweezer array as coherent sensors. This approach achieves a field sensitivity within 13% of the standard quantum limit, a response time that exceeds the Chu limit by more than 11 orders of magnitude, and in-situ near-field mapping with λ/3000 spatial resolution. This work establishes Rydberg-atom arrays as a powerful platform that unites quantum-limited sensitivity, nanosecond-scale response time, and sub-micrometer resolution, opening new avenues in quantum metrology and precision electromagnetic field imaging.
Interferometers based on ultracold atoms enable an absolute measurement of inertial forces with unprecedented precision. However, their resolution is fundamentally restricted by quantum fluctuations. Improved resolutions with entangled or squeezed atoms were demonstrated in internal-state measurements for thermal and quantum-degenerate atoms and, recently, for momentum-state interferometers with laser-cooled atoms. Here, we present a gravimeter based on Bose-Einstein condensates with a sensitivity of − 1.7 − 0.5 + 0.4 dB beyond the standard quantum limit. Interferometry with Bose-Einstein condensates combined with delta-kick collimation minimizes atom loss in and improves scalability of the interferometer to very-long-baseline atom interferometers.
Matter–wave interferometry is a powerful tool for high-precision measurements of the quantum properties of atoms, many-body phenomena and gravity. The most precise matter–wave interferometers exploit the excellent localization in momentum space and coherence of the degenerate gases. Further enhancement of the sensitivity and reduction of complexity are crucial conditions for the success and widening of their applications. Here we introduce a multi-state interferometric scheme that offers advances in both these aspects. The coherent coupling between Bose–Einstein condensates in different Zeeman states is used to generate high-harmonic output signals with an enhanced resolution and the maximum possible interferometric visibility. We demonstrate the realization of such an interferometer as a compact, easy to use, atom-chip device. This provides an alternative method for the measurement of the light–atom and surface–atom interactions and enables the application of multi-parameter sensing schemes in cold-atom interferometry.