Resonant coupling of a Bose-Einstein condensate to a micromechanical resonator via atom-surface forces

Quantum optics and solid-state physics presently show strong convergence. On the one hand, quantum optical systems, most notably neutral atoms in optical lattices, have been used to experimentally investigate concepts of solid-state physics such as Bloch oscillations and Fermi surfaces. On the other hand, micro- and nanostructured solid-state systems beautifully demonstrate concepts known from quantum optics, such as laser cooling of mechanical oscillators and cavity quantum electrodynamics with superconducting circuits.

An exciting possibility beyond this successful conceptual interaction is to physically couple a quantum optical system to a solid-state system. Micro- and nanostructured mechanical oscillators are promising in this context because of the impressive improvements in cooling and read out of mechanical motion that were achieved recently. A long term motivation of coupling mechanical oscillators to atomic systems is the realization of hybrid quantum systems, where strong coupling enables the creation of atom-oscillator entanglement, quantum state transfer and quantum control of mechanical force sensors.

A key ingredient of such a system is a controlled interaction mechanism. As a first experimental step in this direction, we study the coupling of atomic Bose-Einstein condensates to a micromechanical resonator via atom-surface forces (see our paper [1]). The most fundamental force acting on neutral atoms close to a surface is the attractive Casimir-Polder force. It arises from the change of vacuum fluctuations close to a reflecting surface which leads to a distance-dependent Lamb shift of the atomic ground state. An advantage of using the Casimir-Polder force for the coupling to mechanical oscillators is that no functionalization of the oscillator with magnets, electrodes or mirrors is necessary. It could thus be used to couple atoms to nanoscale oscillators such as carbon nanotubes. Surface forces can even be stronger than the Casimir-Polder force. Additional potentials can arise from adsorbates, magnetic contamination, electric stray charges or patch potentials.

Figure 1: a) Schematic setup: Micro-cantilever mounted on an atom chip with gold wires. A ⁸⁷Rb BEC can be trapped and positioned near the cantilever with magnetic fields from wire currents. Cantilever vibrations can be excited with a piezo and independently probed with a readout laser. b) Photograph of the atom chip (scale bar: 1 mm). c) Combined magnetic and surface potential. The surface potential reduces the trap depth to U₀. Cantilever oscillations modulate the potential, thereby coupling to atomic motion.

In our experiment, we use a Bose-Einstein condensate of ⁸⁷Rb atoms as a sensitive local probe, having the unique property that all degrees of freedom are controlled on the quantum level. Benefitting from the small spatial extent (< 300 nm) and high positioning reproducibility (< 6 nm) in a magnetic microtrap, we place the BEC at about one micrometer distance from the surface of a micromechanical cantilever (see Fig. 1) and use it as a probe for cantilever oscillations. At such small distance, the magnetic trapping potential is substantially modified by the surface potential. The main effect of the potential is to reduce the potential depth U₀ (see Fig. 1c). In addition, it shifts the trap frequency and the trap minimum position. When the cantilever oscillates, the potential depth, the trap position and curvature are modulated at the cantilever frequency ω_m. We find that this excites atomic motion, which can be detected most simply via atom loss across the barrier U₀ (see Fig. 2).

Figure 2: BECs are positioned close to the cantilever (typically 1.5μm distance) for a duration a few ms during which they couple to cantilever vibrations. The cantilever is driven with a piezo at frequecy ω_p. The number of atoms remaining in the trap shows a sharp resonance as a function of driving frequency, corresponding to the mechanical resonance of the cantilever. In this way we can read out mechanical oscillations with the atoms down to 10 nm amplitude.

The coupling depends strongly on the trap parameters and shows resonant behaviour if ω_m matches the frequency of a collective mechanical mode of the BEC. This can be used to control the interaction efficiently.

While being far away from the sensitivity necessary to detect quantum oscillations for the large cantilever used in our experiment, the coupling mechanism could be powerful for nanoscale oscillators which have large ground state amplitudes. A 15 μm long single-wall carbon nanotube has a room-temperature thermal amplitude of 4 μm and a quantum-mechanical ground state amplitude of 0.2 nm. It is interesting to investigate whether a BEC-nanotube system coupled via surface forces allows one to reach the strong coupling regime.

Reference and collaboration

[1] D. Hunger et al., Phys. Rev. Lett. 104, 143002 (2010), see our list of publications. The paper is the result of a collaboration with the groups of J. P. Kotthaus (LMU Munich) and J. Reichel (ENS Paris).