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Bulletin of the American Physical Society

Self-energy of a Cold Atom Interacting with an Elastic Membrane

Sanghita Sengupta, Weishuang Linda Xu, Dennis P. Clougherty

Published Mar 3, 2015• 0 citations
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We demonstrate the generation of a cold-atom ensemble within a sub-millimeter diameter hole in a transparent membrane, a so-called "membrane MOT". With a sub-Doppler cooling process, the atoms trapped by the membrane MOT are cooled down to 10 [Formula: see text]K. The atom number inside the unbridged/bridged membrane hole is about [Formula: see text] to [Formula: see text], and the [Formula: see text]-diameter of the MOT cloud is about 180 [Formula: see text]m for a 400 [Formula: see text]m-diameter membrane hole. Such a membrane device can, in principle, efficiently load cold atoms into the evanescent-field optical trap generated by the suspended membrane waveguide for strong atom-light interaction and provide the capability of sufficient heat dissipation at the waveguide. This represents a key step toward the photonic atom trap integrated platform (ATIP).

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Hybrid systems combining mechanical oscillators and ultracold atoms provide novel \nopportunities for cooling, detection and quantum control of mechanical motion with \napplications in precision sensing, quantum-level signal transduction and for fundamental \ntests of quantum mechanics. \nIn this thesis I present experiments performed with a hybrid atom-membrane \nsystem, in which the vibrations of a Si_3N_4 membrane in an optical cavity are coupled \nto the motion of laser-cooled atoms in an optical lattice. The interactions are \nmediated by the lattice light over a macroscopic distance and enhanced by the cavity. \nVia the coupling to the cold atoms, the fundamental vibrational mode of the \nmembrane at 2π x 276 kHz is cooled sympathetically from room temperature to \n0.4(2) K, even though the mass of the mechanical oscillator exceeds that of the \natomic ensemble by a factor of 4 x 10^10. In other systems, sympathetic cooling \nof molecules with cold atoms or ions has been limited to mass ratios of up to 90. \nPrevious theoretical work has shown that our coupling mechanism is able to cool the \nmembrane vibration into the ground state and to perform coherent state transfers \nbetween atomic and membrane motion. \nUnder certain experimental conditions, the atom-membrane system shows self-oscillations, \nwhich arise from an effective delay in the backaction of the atoms onto \nthe light. This retardation drives the system into limit-cycle oscillations if the coupling \nis large. I study the dependence of this instability on several system parameters \nand find that a larger atom number and a smaller atom-light detuning make the system \nless stable. Further, the stability of the coupled system in presence of a delay is \ninvestigated theoretically and a modified expression for the sympathetic cooling rate \nis derived. This model allows to fit the measured atom number dependence with a \ndelay of τ = 88(1) ns. Moreover, direct measurements of the atomic backaction onto \nthe lattice light are presented. These show phase lags exceeding 180° in parameter \nregimes where the instability is observed, proving that the retardation arises within \nthe atomic ensemble. Finally, I present the results of numerical simulations, which \nshow that collective atomic effects within the atomic ensemble in an asymmetric \nlattice are able to induce the observed phase lag in the atomic backaction.

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Quantum electrodynamics (QED) provides a highly accurate description of phenomena involving the interaction of atoms with light. We argue that the quantum theory describing the interaction of cold atoms with a vibrating membrane---quantum acoustodynamics (QAD)---shares many issues and features with QED. Specifically, the adsorption of an atom on a vibrating membrane can be viewed as the counterpart to QED radiative electron capture. A calculation of the adsorption rate to lowest order in the atom-phonon coupling is finite; however, higher-order contributions suffer from an infrared problem mimicking the case of radiative capture in QED. Terms in the perturbation series for the adsorption rate diverge as a result of massless particles in the model (flexural phonons of the membrane in QAD and photons in QED). We treat this infrared problem in QAD explicitly to obtain finite results by regularizing with a low-frequency cutoff that corresponds to the inverse size of the membrane. Using a coherent-state basis for the soft-phonon final state, we then sum the dominant contributions to derive a new formula for the multiphonon adsorption rate of atoms on the membrane that gives results that are finite, nonperturbative in the atom-phonon coupling, and consistent with the Kinoshita-Lee-Nauenberg theorem. For micromembranes, we predict a reduction with increasing membrane size for the low-energy adsorption rate. We discuss the relevance of this to the adsorption of a cold gas of atomic hydrogen on suspended graphene.

arXiv:1611.09445•Physical Review A•May 12, 2017•5 citations
We demonstrate the generation of a cold-atom ensemble within a sub-millimeter diameter hole in a transparent membrane, a so-called "membrane MOT". With a sub-Doppler cooling process, the atoms trapped by the membrane MOT are cooled down to 10 [Formula: see text]K. The atom number inside the unbridged/bridged membrane hole is about [Formula: see text] to [Formula: see text], and the [Formula: see text]-diameter of the MOT cloud is about 180 [Formula: see text]m for a 400 [Formula: see text]m-diameter membrane hole. Such a membrane device can, in principle, efficiently load cold atoms into the evanescent-field optical trap generated by the suspended membrane waveguide for strong atom-light interaction and provide the capability of sufficient heat dissipation at the waveguide. This represents a key step toward the photonic atom trap integrated platform (ATIP).
Hybrid systems combining mechanical oscillators and ultracold atoms provide novel \nopportunities for cooling, detection and quantum control of mechanical motion with \napplications in precision sensing, quantum-level signal transduction and for fundamental \ntests of quantum mechanics. \nIn this thesis I present experiments performed with a hybrid atom-membrane \nsystem, in which the vibrations of a Si_3N_4 membrane in an optical cavity are coupled \nto the motion of laser-cooled atoms in an optical lattice. The interactions are \nmediated by the lattice light over a macroscopic distance and enhanced by the cavity. \nVia the coupling to the cold atoms, the fundamental vibrational mode of the \nmembrane at 2π x 276 kHz is cooled sympathetically from room temperature to \n0.4(2) K, even though the mass of the mechanical oscillator exceeds that of the \natomic ensemble by a factor of 4 x 10^10. In other systems, sympathetic cooling \nof molecules with cold atoms or ions has been limited to mass ratios of up to 90. \nPrevious theoretical work has shown that our coupling mechanism is able to cool the \nmembrane vibration into the ground state and to perform coherent state transfers \nbetween atomic and membrane motion. \nUnder certain experimental conditions, the atom-membrane system shows self-oscillations, \nwhich arise from an effective delay in the backaction of the atoms onto \nthe light. This retardation drives the system into limit-cycle oscillations if the coupling \nis large. I study the dependence of this instability on several system parameters \nand find that a larger atom number and a smaller atom-light detuning make the system \nless stable. Further, the stability of the coupled system in presence of a delay is \ninvestigated theoretically and a modified expression for the sympathetic cooling rate \nis derived. This model allows to fit the measured atom number dependence with a \ndelay of τ = 88(1) ns. Moreover, direct measurements of the atomic backaction onto \nthe lattice light are presented. These show phase lags exceeding 180° in parameter \nregimes where the instability is observed, proving that the retardation arises within \nthe atomic ensemble. Finally, I present the results of numerical simulations, which \nshow that collective atomic effects within the atomic ensemble in an asymmetric \nlattice are able to induce the observed phase lag in the atomic backaction.
Quantum electrodynamics (QED) provides a highly accurate description of phenomena involving the interaction of atoms with light. We argue that the quantum theory describing the interaction of cold atoms with a vibrating membrane---quantum acoustodynamics (QAD)---shares many issues and features with QED. Specifically, the adsorption of an atom on a vibrating membrane can be viewed as the counterpart to QED radiative electron capture. A calculation of the adsorption rate to lowest order in the atom-phonon coupling is finite; however, higher-order contributions suffer from an infrared problem mimicking the case of radiative capture in QED. Terms in the perturbation series for the adsorption rate diverge as a result of massless particles in the model (flexural phonons of the membrane in QAD and photons in QED). We treat this infrared problem in QAD explicitly to obtain finite results by regularizing with a low-frequency cutoff that corresponds to the inverse size of the membrane. Using a coherent-state basis for the soft-phonon final state, we then sum the dominant contributions to derive a new formula for the multiphonon adsorption rate of atoms on the membrane that gives results that are finite, nonperturbative in the atom-phonon coupling, and consistent with the Kinoshita-Lee-Nauenberg theorem. For micromembranes, we predict a reduction with increasing membrane size for the low-energy adsorption rate. We discuss the relevance of this to the adsorption of a cold gas of atomic hydrogen on suspended graphene.