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arXiv:quant-ph/0703199 · Physical Review Letters

Bose-Einstein Condensate Coupled to a Nanomechanical Resonator on an Atom Chip

Philipp Treutlein, David Hunger, Stephan Camerer, Theodor W. Hänsch, Jakob Reichel

Published Oct 3, 2007• 207 citations
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Abstract

We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever quality factors, the strong coupling regime can be reached, either with single atoms or collectively with Bose-Einstein condensates. We discuss an implementation on an atom chip.

DOI
10.1103/physrevlett.99.140403

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We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever quality factors, the strong coupling regime can be reached, either with single atoms or collectively with Bose-Einstein condensates. We discuss an implementation on an atom chip.
This work investigates different coupling mechanisms between ultracold atoms and mechanical oscillators. In a first experiment, atom-surface force is used to couple the vibrations of a mechanical cantilever to the motion of a Bose-Einstein condensate in a magnetic microtrap on a chip. The atoms are trapped at sub-micrometer distance from the cantilever surface. Coupling is used to read out the cantilever vibrations with the atoms. Coupling via surface forces could be employed to couple atoms to molecular-scale oscillators such as carbon nanotubes. In a second experiment, coupling via a 1D optical lattice that is formed by a laser beam retroreflected from the cantilever tip. The optical lattice serves as a transfer rod which couples vibrations of the cantilever to the atoms and vice versa.
In this thesis I present experiments investigating controlled coupling between mechanical oscillators and ultracold atoms. I report on three different coupling mechanisms. In a first experiment, the surface potential experienced by atoms close to the mechanical oscillator is employed to couple the oscillator motion to the center of mass (COM) motion of a trapped Bose-Einstein condensate (BEC). The magnetic trapping potential is modified by the surface potential arising from the oscillator surface which results in a reduced trap depth. Vibration of the oscillator leads to a modulation of the trap frequency and the minimum of the trapping potential. Observing the loss of atoms from the BEC allows us to read out the amplitude of the mechanical oscillator with the atoms. In a second experiment, we study the coupling of a mechanical membrane oscillator and thermal atoms trapped in a 1D optical lattice. The membrane is the end mirror of the lattice, and oscillation of the membrane couples to the COM mode of the atomic ensemble. Conversely, the center of mass motion of the atomic ensemble redistributes photons between the two running waves forming the 1D optical lattice, effectively modulating their power, and hence the radiation pressure acting onto the membrane. We observe the action of the oscillating membrane onto the atoms by detecting the resulting temperature increase of the atomic ensemble in absorption imaging. To observe the backaction of the atoms onto the mechanical oscillator, the mechanical damping is measured in experiments with and without atoms in the lattice, and we measure higher damping in the presence of atoms in agreement with the theoretical predictions. These experiments are the first demonstration of backaction of an atomic system onto a mechanical oscillator. We investigate a third coupling mechanism, where the motion of a mechanical oscillator is coupled to the collective spin of a BEC. The tip of a mechanical oscillator is functionalized with a magnet, which transduces the oscillators' motion into oscillations of the magnetic field. This drives spin-flip transitions of trapped atoms to untrapped motional states. The coupling strength is not limited by the square root of the mass ratio of atoms and oscillator as in the other coupling schemes discussed in this thesis. We investigate this coupling scheme theoretically, and discuss the realization of a nanometer-sized mechanical oscillator with a magnetic island. I report on the status of the fabrication, and propose a simplified fabrication method.
We propose a scheme to probe quantum coherence in the state of a nanocantilever based on its magnetic coupling (mediated by a magnetic tip) with a spinor Bose Einstein condensate (BEC). By mapping the BEC into a rotor, its coupling with the cantilever results in a gyroscopic motion whose properties depend on the state of the cantilever: the dynamics of one of the components of the rotor angular momentum turns out to be strictly related to the presence of quantum coherence in the state of the cantilever. We also suggest a detection scheme relying on Faraday rotation, which produces only a very small back-action on the BEC and is thus suitable for a continuous detection of the cantilever's dynamics.
Magnetic resonance in an ensemble of laser-cooled trapped Rb atoms is excited using a microcantilever with a magnetic tip. The cantilever is mounted on a multilayer chip designed to capture, cool, and magnetically transport cold atoms. The coupling is observed by measuring the loss from a magnetic trap as the oscillating cantilever induces Zeeman-state transitions in the atoms. Interfacing cold atoms with mechanical devices could enable probing and manipulating atomic spins with nanometer spatial resolution and single-spin sensitivity, leading to new capabilities in quantum computation, quantum simulation, and precision sensing.
We propose the possibility of a phonon laser by coupling a Bose–Einstein condensate to a nanomechanical cantilever with a magnetic tip. Due to the magnetic coupling, atomic spin flips induce cantilever motion, which can be used to produce a phonon laser. The system is described by the equivalent of the Jaynes–Cummings Hamiltonian. By controlling the number of atoms and the population inversion, one can obtain either a continuous wave or transient lasing. The two-body atom–atom interaction is also shown to coherently manipulate the lasing process. We also show that in the strong coupling limit, the same system can undergo a Dicke–Hepp–Lieb superradiant phase transition. Exotic phase diagrams can be obtained by tuning the two body atom–atom interaction.