Magnetic coupling of a Bose-Einstein condensate to a nanomechanical resonator

In this project we study magnetic coupling between the spin of a Bose-Einstein condensate (BEC) and a nanomechanical resonator with a magnetic tip. An advantage of the coupling to an internal degree of freedom of the atoms is that it allows for higher eigenfrequencies of the resonator (~0.1-100 MHz) and that more sophisticated preparation and readout techniques are available for the atomic internal state than for the motional state. The magnetic coupling between the spin of the atoms in the BEC and the cantilever oscillations is mediated by a single-domain ferromagnet on the cantilever tip, see Figure 1.

Figure 1: Schematic setup. Atom chip with a BEC of ⁸⁷Rb atoms (red: BEC wave function) at micrometer distance from a nanomechanical resonator. The free-standing structure (dark blue) is supported at one end to form a cantilever-type resonator that performs out-of-plane mechanical oscillations. The single-domain ferromagnet (purple) on the resonator tip creates a magnetic field with a strong gradient. It transduces the cantilever oscillations into an oscillatory magnetic field at the atoms' location. This field couples to the spin of the atoms, leading to observable spin flips.
Figure 2: SEM micrograph of a chip prototype for the experiment.

In a theoretical paper (Phys. Rev. Lett. 99, 140403 (2007), see our publications) we have investigated the coupled BEC-nanoresonator system. Oscillations of the cantilever lead to spin-flip transitions of the magnetically trapped atoms, e.g. to untrapped states. This is similar to an atom laser experiment, with the mechanical resonator inducing the radio-frequency magnetic field for output coupling. By either probing the spin state populations or detecting the loss of atoms from the trap, the BEC could be used as a sensitive probe for the mechanical motion of the cantilever, which should allow a time-resolved detection of the thermal amplitude fluctuations.

At low cantilever temperatures, as realized in recent experiments with cryogenic or laser cooling, back-action 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 BECs.

In this regime, the BEC can be used as a sensitive probe, as a coolant, or a coherent actuator for the nanomechanical resonator. The coupling could be used to transfer nonclassical states of the BEC, which consists of a few thousand atoms, to the mechanical system, which consists of several billions of atoms. Due to the dissipative coupling of the resonator to its environment, interesting questions of decoherence arise and could be studied with this system.

The core of the experiment will be an atom chip which comprises gold wires for a magnetic trap, free-standing nanomechanical resonators, and single-domain ferromagnetic structures (Figure 2). We fabricate this structure in the cleanroom of the nanophysics group of Prof. J.P. Kotthaus at LMU Munich using various lithography, deposition and etching techniques. The experiment is a collaboration between our group (MPQ and LMU Munich), Jakob Reichel (ENS Paris), and Daniel König from the nanophysics group of Prof. J.P. Kotthaus (also at LMU Munich).