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Physical Review A

Spectral response of magnetically trapped Bose gases to weak microwave fields

Peter Federsel, Carola Rogulj, Tobias Menold, József Fortágh, Andreas Günther

Published Sep 1, 2015• 5 citations
Publisher

Abstract

Microwave fields can be used to drive local spin transitions in quantum gases and for outcoupling of cold atomic beams from magnetic traps. In this paper, we derive an analytic theory for the outcoupling rate as a response to weak microwave fields of varying frequency and power. The theory holds for thermal clouds and Bose-Einstein condensates. It allows for calculating transition rates in arbitrary magnetic trap geometries and includes the effect of gravity. We verify our theory by measuring the flux of outcoupled atoms at the single-particle level. The derived spectral response is important for magnetic noise spectroscopy with quantum gases, and for probing quantum gas dynamics with single atom detectors in real time.

DOI
10.1103/physreva.92.033601

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Microwave fields can be used to drive local spin transitions in quantum gases and for outcoupling of cold atomic beams from magnetic traps. In this paper, we derive an analytic theory for the outcoupling rate as a response to weak microwave fields of varying frequency and power. The theory holds for thermal clouds and Bose-Einstein condensates. It allows for calculating transition rates in arbitrary magnetic trap geometries and includes the effect of gravity. We verify our theory by measuring the flux of outcoupled atoms at the single-particle level. The derived spectral response is important for magnetic noise spectroscopy with quantum gases, and for probing quantum gas dynamics with single atom detectors in real time.
Bose-Einstein condensates of ultracold atoms can be used to sense fluctuations of the magnetic field by means of transitions into untrapped hyperfine states. It has been shown recently that counting the outcoupled atoms can yield the power spectrum of the magnetic noise. We calculate the spectral resolution function, which characterizes the condensate as a noise measurement device in this scheme. We use the description of the radio-frequency outcoupling scheme of an atom laser, which takes into account the gravitational acceleration. Employing both an intuitive and the exact three-dimensional and fully quantum mechanical approach, we derive the position-dependent spectral resolution function for condensates of different size and shape.
We report on the spectral analysis and the local measurement of intensity correlations of microwave fields using ultracold quantum gases. The fluctuations of the electromagnetic field induce spin flips in a magnetically trapped quantum gas and generate a multimode atom laser. The output of the atom laser 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 atom-laser 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.
We study the dynamics of a magnetically trapped Bose-Einstein condensate in the presence of an external electromagnetic-field coupling trapped, untrapped, and antitrapped Zeeman sublevels. For large condensates an approximate analytical solution of the coupled Gross-Pitaevskii equations is given in the regime of strong outcoupling. The theory is developed for the cases of rf outcoupling within a hyperfine manifold of states, microwave outcoupling connecting states in two different hyperfine manifolds, and Raman outcoupling.
Study of the physical properties of Bose condensed gases has recently become a very active topic due to the experimental realizations of Bose-Einstein condensation in magnetically trapped gases of alkali atoms. In this paper we theoretically study the microwave electronic spin resonance of a weakly interacting Bose gas. For a Bose gas above the critical temperature for Bose-Einstein condensation, the microwave radiation induced by the driving microwave field in the electronic spin resonance exhibits the ordinary Rabi oscillation damped by the inhomogeneous Doppler dephasing. For a Bose gas with a condensate, the induced radiation is composed of two components. One is the strong coherent Rabi oscillation from the condensate. The other is a modulated Rabi oscillation due to the noncondensed part of the gas. We show that the modulation of Rabi oscillation of the noncondensed gas is directly related to the elementary collective excitation of atoms in the gas.
The study of physical properties of Bose condensed gases has recently become a very active topic due to the experimental realization of Bose-Einstein condensation in the magnetically trapped gases of alkali atoms. In this paper we theoretically study the Rabi oscillation of a weakly interacting Bose gas in the regime of microwave electronic spin resonance. For a Bose gas above the critical temperature for Bose-Einstein condensation, the microwave radiation induced by the driving microwave field exhibits the ordinary Rabi oscillation damped by the inhomogeneous Doppler dephasing. For a Bose gas with a condensate, the microwave radiation is composed of two components. One is the strong coherent Rabi oscillation from the condensate. The other is a modulated Rabi oscillation due to the noncondensed part of the gas. We show that the modulation of Rabi oscillation of the noncondensed gas is directly relative to the elementary collective excitation of atoms in the gas.
Abstract We consider the interaction of a magnetically trapped Bose–Einstein condensate of Rubidium atoms with the stationary microwave radiation field sustained by a coplanar waveguide resonator. This coupling allows for the measurement of the magnetic field of the resonator by means of counting the atoms that fall out of the condensate due to hyperfine transitions to non-trapped states. We determine the quantum efficiency of this detection scheme and show that weak microwave fields at the single-photon level can be sensed.