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arXiv:1812.05545 · New Journal of Physics

Probing multiple-frequency atom-photon interactions with ultracold atoms

K Luksch, E Bentine, A J Barker, S Sunami, T L Harte, B Yuen, Christopher J. Foot

Published Jul 1, 2019• 10 citations
arXivHTMLPDF

Abstract

Abstract We dress atoms with multiple-radiofrequency (RF) fields and investigate the spectrum of transitions driven by an additional probe field. A complete theoretical description of this rich spectrum is presented, in which we find allowed transitions and determine their amplitudes using the resolvent formalism. Experimentally, we observe transitions up to sixth order in the probe field using RF spectroscopy of Bose–Einstein condensates trapped in single- and multiple-RF-dressed potentials. We find excellent agreement between theory and experiment, including the prediction and verification of previously unobserved transitions, even in the single-RF case.

DOI
10.1088/1367-2630/ab2f60

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Abstract We dress atoms with multiple-radiofrequency (RF) fields and investigate the spectrum of transitions driven by an additional probe field. A complete theoretical description of this rich spectrum is presented, in which we find allowed transitions and determine their amplitudes using the resolvent formalism. Experimentally, we observe transitions up to sixth order in the probe field using RF spectroscopy of Bose–Einstein condensates trapped in single- and multiple-RF-dressed potentials. We find excellent agreement between theory and experiment, including the prediction and verification of previously unobserved transitions, even in the single-RF case.
This thesis presents experimental work to investigate the properties of ultracold rubidium atoms in multiple-radiofrequency dressed potentials and detailed theoretical calculations to understand this system. The use of multiple frequencies rather than a single dressing frequency increases the complexity of the spectrum, and we present theoretical calculations that predict all possible transitions as well as the corresponding strengths. Extensive measurements for dressing with a single and multiple frequencies have verified these predictions, observing transitions up to tenth order in the probe field. We observe previously unknown transitions even for the single-frequency case and have uncovered further transitions which we explain by the non-linearity of the Zeeman effect even at our small field strengths. These results are used to understand the absorption spectrum as the potential transforms from a single to a double well in order to split a Bose-Einstein condensate. This is important for applications since spurious noise leads to atom loss if it is resonant with a transition between eigenstates. We present a new method of splitting, replacing adiabatic ramps with a projection, that reduces the duration of the ramps as well as the spectrum of resonances throughout the ramps, thus reducing losses. The new experimental techniques will allow observation of the thermalisation of a two-dimensional quantum system using ultracold gases. We discuss how multiple-radiofrequency dressed potentials can be used to confine ultracold atoms in two dimensions, and subsequently split the trapped cloud into two parallel sheets. After a varying hold time, the atoms can be released and overlapped to produce interference fringes. Analysis of the fringes determines how the relative phase between the two sheets thermalises. Information can be accumulated to determine the probability distribution of the integrated contrast, which can then be compared to the equilibrium distribution to determine if and how the relative phase thermalises. This promises to answer key questions in non-equilibrium physics.
Time-varying fields are widely used to extend the accessible range of trapping potentials for ultracold atoms. This work explores two very different examples of such fields, in the radiofrequency and optical regimes, whose interactions with trapped atoms can both be described in terms of the dressed atom picture. Forming the basis of this work are radiofrequency dressed adiabatic potentials based on macroscopic trapping coils. Atoms are confined at the south pole of the resultant oblate spheroidal trapping surfaces. This work describes the extension of these potentials by two different methods: the application of multiple dressing radiofrequencies, and addition of a rapidly-scanned optical dipole trap. This is the first experimental demonstration of a multiple-radiofrequency dressed adiabatic potential, explored using ultracold 87Rb atoms confined in a highly configurable double well. Due to the independent generation of each constituent dressing frequency, the depth of each trapping well and the height of the barrier are easily manipulated, enabling precise and reliable transfer of atoms between the available trapping geometries. Experimental work includes an exploration of the potential-shaping capabilities of the three-radiofrequency system, and characterisation of the potential landscape using radiofrequency spectroscopy with good agreement to the eigenvalues numerically calculated using Floquet theory. This initial exploration of multiple-radiofrequency techniques lays the groundwork for applications in studying double well physics in a two-dimensional system, and independent state or species selective manipulation of trapped atoms. The potential shaping capabilities of this method can also be extended by applying additional trapping frequencies. In a supplementary line of experimental work, an optical dipole trapping system has been constructed, and the trapping beam aligned to the lower surface of the radiofrequency dressed trapping shell in order to sculpt the radial confinement. Beam shaping is achieved using an acousto-optic deflector, which can be used to produce either a composite array of static deflected beams, a rapidly-scanned painted potential, or some combination of the two approaches. The development and extension of the experimental apparatus required to implement these enhanced dressed state potentials is explored, and the challenges of their experimental implementation considered.
We study dressed Bose-Einstein condensates in an atom chip radio-frequency trap. We show that in this system sufficiently strong dressing can be achieved to cause the widely used rotating-wave approximation (RWA) to break down. We present a full calculation of the atom-field coupling which shows that the non-RWA contributions quantitatively alter the shape of the emerging dressed adiabatic potentials. The non-RWA contributions furthermore lead to additional allowed transitions between dressed levels. We use rf spectroscopy of Bose-Einstein condensates trapped in the dressed state potentials to directly observe the transition from the RWA to the beyond-RWA regime.
We present the first experimental demonstration of a multiple radio-frequency dressed potential for the configurable magnetic confinement of ultracold atoms. We load cold 87Rb^{87}\mathrm{Rb}87Rb atoms into a double-well potential with an adjustable barrier height, formed by three radio-frequencies applied to atoms in a static quadrupole magnetic field. Our multiple radio-frequency approach gives precise control over the double-well characteristics, including the depth of individual wells and the height of the barrier, and enables reliable transfer of atoms between the available trapping geometries. We characterize the multiple radio-frequency dressed system using radio-frequency spectroscopy, finding good agreement with the eigenvalues numerically calculated using Floquet theory. This method creates trapping potentials that can be reconfigured by changing the amplitudes, polarizations, and frequencies of the applied dressing fields and easily extended with additional dressing frequencies.
We study the hyperfine spectrum of atoms of 87Rb^{87}\mathrm{Rb}87Rb dressed by a radio-frequency field and present experimental results in three different situations: freely falling atoms, atoms trapped in an optical dipole trap, and atoms in an adiabatic radio-frequency dressed shell trap. In all cases, we observe several resonant sidebands spaced (in frequency) at intervals equal to the dressing frequency, corresponding to transitions enabled by the dressing field. We theoretically explain the main features of the microwave spectrum using a semiclassical model in the low-field limit and the rotating-wave approximation for alkali-metal-like species, in general, and 87Rb^{87}\mathrm{Rb}87Rb atoms, in particular. As a proof of concept, we demonstrate how the spectral signal of a dressed atomic ensemble enables an accurate determination of the dressing configuration and the probing microwave field.