Optomechanical coupling of ultracold atoms and a membrane
Laser light can exert a force on material objects through radiation pressure and through the optical dipole force. In the very active field of optomechanics, such light forces are exploited for cooling and control of the vibrations of mechanical oscillators, with possible applications in precision force sensing and studies of quantum physics at macroscopic scales. This has many similarities with the field of ultracold atoms, where radiation pressure forces are routinely used for laser cooling and optical dipole forces are used for trapping and quantum manipulation of atomic motion, most notably in optical lattices.
It has been proposed that light forces could also be used to couple the motion of atoms in a trap to the vibrations of a single mode of a mechanical oscillator. In the resulting hybrid optomechanical system the atoms could be used to read out the motion of the oscillator, to engineer its dissipation, and ultimately to perform quantum information tasks such as coherently exchanging the quantum state of the two systems. Manipulation of the oscillator on the quantum level would represent the ultimate control over the system. Such experiments could also shed new light on the boundary between quantum and classical mechanics.
In our experiment we couple the motion of a mechanical membrane oscillator to the motion of ultracold atoms in an optical lattice. Atoms provide both the continuous degree of freedom of collective atomic motion as well as a discrete set of internal levels that can be reduced to a two-level system.
Figure 1 (left): SEM micrograph of a SiN membrane oscillator. Figure 2 (right): Schematic coupling mechanism: A laserbeam is retro-reflected on a membrane oscillator and creates a standing wave.
The standing wave acts as a red-detuned optical lattice potential for the atoms. Membrane oscillations and center-of-mass oscillations of the atoms are coupled through the lattice laser light. Laser cooling of the atoms in the lattice potential extracts energy from the coupled atom-membrane system resulting in sympathetic cooling of the membrane mode.
Our membrane oscillators (Fig. 1) are made of SiN, have dimensions of 500 μm x 500 μm x 50 nm, and a fundamental eigenfrequency of 250 kHz. These membranes have outstanding mechanical quality factors Q > 1x106 at room temperature. The optical lattice potential is formed by retro-reflection of a laser beam from the membrane surface, as depicted in Fig. 2. Movements of the membrane will move the standing wave, such that the membrane oscillations are directly transferred to an oscillation of the trapping potential of the atoms. If the membrane oscillation frequency is resonant with the trap frequency of the atoms along the lattice direction, resonant excitation of the collective c.o.m. mode of the atoms leads to an energy transfer from the membrane to the atom cloud. On the other hand, the excited atoms imprint a signature of their motion onto the light-field which is then felt by the membrane: As the atoms are displaced from their equilibrium position, they experience a restoring force. This restoring force arises from a coherent redistribution of photons between the two k-vector components that make up the lattice. This translates into power modulation of the counter-propagating laser beams, and consequently, a modulated radiation pressure force on the membrane. As the oscillating membrane excites the atoms to collective motion, there is a fixed phase relation between atomic and membrane oscillation. The resulting radiation pressure modulation at the membrane will have the right phase lag to damp the membrane oscillation. If the atoms are simultaneously laser-cooled, this will result in cooling of the membrane mode.
We have demonstrated experimentally the both the coupling from the membrane to the atoms and the backaction of the atoms to the membrane. Figure 3 shows the resonant heating of the atoms in the trap along the axial (i.e., lattice) direction when the membrane is driven at it's eigenfrequency. P denotes the power of the lattice beam that is adjusted to adjust the trap frequency of the atoms and eventually match the trap frequency to the membrane frequency. The resonant power is around 70 mW.
Figure 3. Effect of membrane vibrations on the atoms. Top: temperature increase of the atoms along the lattice and in the radial direction for a driven membrane with respect to reference measurements for an undriven membrane. Bottom: dependence of lattice atom number on the lattice beam power, for driven and undriven membrane.
The backaction of the laser-cooled atomic ensemble onto the membrane vibrations is observed in membrane ringdown measurements. The atoms act as an additional dissipation channel for the membrane mode that results in faster damping of the membrane amplitude. In the measurement, the atoms are continuously cooled in the lattice while the membrane rigndown is recorded. We perform alternating experiments with and without atoms in the lattice and determine the respective membrane decay rates Γ and γ. The difference in these decay rates is shown in Figure 4 for various lattice powers (i.e., trap frequencies of the atoms).
Figure 4. Backaction of laser-cooled atoms onto the membrane. Top: measured additional membrane dissipation rate due to coupling to atoms as a function of the lattice power P. Solid line: theory for a thermal ensemble in the lattice. Bottom: lattice atom number in the experiment.
In order to study the dependence of the membrane dissipation on atom number, the system was prepared on resonance and the atom number N in the lattice was varied. We observe a linear dependence of Δ γ on N, as shown in Figure 5. The linear scaling is in full agreenment with the theory [2]. For detailed information about the experimental results, please see Ref. [1]. A completely quantum theory of our system is described in Ref. [2].
Figure 4 Measured additional membrane dissipation Δ γ as a function of atom number for resonant coupling (P=76 mW). The blue line is a linear fit. The observed dependence agrees well with theory. Inset: histogram of measurements of Γ for N=2.3E6(red) and N=0 (blue).
Our observation of backaction of the atoms onto the membrane and the predictions of [2] agree remarkably well, suggesting that the theory can be used for extrapolation to optimized parameters. In the theoretical proposal [1] it has been estimated that this damping can be made strong enough to sympathetically cool the membrane mode to its ground state. This requires that the membrane is placed in a cryostat and that a large number of atoms is cooled to the ground state of the lattice potential by Raman sideband laser cooling.
Reference and collaboration
[1] S. Camerer, M. Korppi, A. Jöckel, D. Hunger, T. W. Hänsch, and P. Treutlein,
Realization of an optomechanical interface between ultracold atoms and a membrane,
Phys. Rev. Lett. 107, 223001 (2011), see our list of publications.
[2] K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, and T. W. Hänsch, Phys. Rev. A 82, 021803 (2010), see our list of publications.
This paper is the result of a collaboration with the theory group of P. Zoller (Universität Innsbruck).