Noise spectroscopy with a quantum gas

Abstract

We report on the spectral analysis and the local measurement of intensity correlations of microwave fields using ultra cold quantum gases. The fluctuations of the electromagnetic field induce spin flips in a magnetically trapped quantum gas and generate a multi-mode atomlaser. The output of the atomlaser is measured with high temporal resolution on the single atom level, from which the spectrum and intensity correlations of the generating microwave field are reconstructed. We give a theoretical description of the atomlaser output and its correlations in response to resonant microwave fields and verify the model with measurements on an atom chip. The measurement technique is applicable for the local analysis of classical and quantum noise of electromagnetic fields, for example on chips, in the vicinity of quantum electronic circuits. [5], are well characterized by the electron counting statistics and the corresponding field noise. This becomes especially important, as novel materials such as artificial honeycomb crystals [6] predict quantum effects in the electron transport even at room temperature, due to the formation of topological protected states [7]. Such quantum transport phenomena might be measured by means of a recently proposed quantum galvanometer [8], in which the low frequency current noise of a nano-device is coherently coupled to an atomic quantum gas and analyzed via state selective single atom detection.Here, we demonstrate the basic operation of the quantum galvanometer and extend it to quantum correlation measurements. Using a Bose-Einstein condensate, we coherently probe artificial, low frequency magnetic field fluctuations (noise) by shifting them electronically into the microwave (mw) regime, close to an atomic resonance. These fluctuations, generate a multi-mode atomlaser, with an output directly connected to the original field fluctuations. Using a sensitive detector, we analyze this output on the single atom level and show, how the power spectral density and the intensity correlations of the microwave field can be reconstructed. We give a theoretical description for the output of the multi-mode atomlaser, including decoherence effects.Experimental setup: The experiment is illustrated in Fig. 1a. Using an atom-chip based cold atom apparatus[9], we prepare Bose-Einstein condensates and thermal ensembles of 87 Rb atoms in the 5S 1/2 , F = 2, m F = 2 ground state. The atoms are magnetically trapped in a harmonic configuration with trap frequencies ω (x,y,z) = 2π × (85, 70, 16)Hz and offset field B z,off ≈ 0.93G. If this cloud is exposed to resonant microwave radiation, spin flips to the anti-trapped 5S 1/2 , F = 1, m F = 1 state occur. Here, we irradiate microwaves of various spectra to demonstrate the measurement of noise spectra and correlations. In particular, we apply amplitude modulation to a microwave carrier at ω c ≈ 2π × 6.834GHz with a variable function A (t) in the kHz regime. Here, A(t) mimics the low frequency field noise, which in the quantum galvanometer case is intrinsically (...

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