Abstract

Mechanical resonators are gradually becoming available as new quantum systems. Quantum optics in combination with optomechanical interactions (quantum optomechanics) provides a particularly helpful toolbox for generating and controlling mechanical quantum states. We highlight some of the current challenges in the field by discussing two of our recent experiments.

© 2010 Optical Society of America

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2010 (7)

A. Cho, “Faintest thrum heralds quantum machines,” Science 327, 516–518 (2010).
[CrossRef] [PubMed]

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[CrossRef] [PubMed]

O. Romero-Isart, M. L. Juan, R. Quidant, and J. Ignacio Cirac, “Towards quantum superposition of living organisms,” New J. Phys. 12, 033015 (2010).
[CrossRef]

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. U.S.A. 107, 1005–1010 (2010).
[CrossRef] [PubMed]

P. F. Barker and M. N. Schneider, “Cavity cooling of a trapped nanoparticle,” Phys. Rev. A 81, 023826 (2010).
[CrossRef]

T. Rocheleau, T. Ndukum, C. Macklin, J. B. Hertzberg, A. A. Clerk, and K. C. Schwab, “Preparation and detection of a mechanical resonator near the ground state of motion,” Nature 463, 72–75 (2010).
[CrossRef]

M. Wallquist, K. Hammerer, P. Zoller, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, J. Ye, and H. J. Kimble, “Single-atom cavity QED and opto-micromechanics,” Phys. Rev. A 81, 023816 (2010).
[CrossRef]

2009 (24)

M. Arndt, M. Aspelmeyer, and A. Zeilinger, “How to extend quantum experiments,” Fortschritt der Physik , 57, 1153–1162 (2009).
[CrossRef]

K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble, “Strong coupling of a mechanical oscillator and a single atom,” Phys. Rev. Lett. 103, 063005 (2009).
[CrossRef] [PubMed]

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P. Rabl, S. J. Kolkowitz, F. H. Koppens, J. G. E. Harris, P. Zoller, and M. D. Lukin, “A quantum spin transducer based on nano electro-mechancial resonator arrays,” arXiv:0908.0316v1 [quant-ph].

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic representation of an optomechanical system. The cavity mode is an optical harmonic oscillator (described by creation and annihilation operators a and a of the optical field) that is coupled to a mechanical harmonic oscillator (described by creation and annihilation operators b and b of the mechanical motion), e.g., via the mechanical modulation of the cavity length. (b) Recent examples of mechanical resonator designs in a Fabry–Pérot cavity [66], a microtoroid structure [59], and an optomechanical crystal [23]. (c) The choice of detuning Δ of the driving laser frequency ω pump with respect to the cavity resonance frequency ω cavity allows to engineer the optomechanical interaction and provides access to the toolbox of two-mode quantum optics. Red detuning (blue detuning) gives rise to a beamsplitter (two-mode squeezing) interaction, which is of relevance, e.g., for optical cooling or quantum state transfer (for the generation of optomechanical entanglement). Resonant driving ( Δ = 0 ) allows for example for quantum nondemolition measurements.

Fig. 2
Fig. 2

Mechanical laser cooling (a) Sketch of the setup that was used to perform resolved sideband cooling of a micromechanical resonator in a cryogenic Fabry–Pérot cavity (from [66]). The cavity is pumped by two laser fields at orthogonal polarizations, derived from an ultralow phase-noise laser source (at 1064 nm ). A weak, resonant beam (red) is used to lock the laser to the cavity resonance frequency ω c . Its phase quadrature is modulated by the mechanical motion, which can be read out via homodyne detection of the reflected resonant pump field. This allows, e.g., to infer the effective temperature of the mechanical mode from the noise-power spectrum of the cavity-field phase quadrature. A second, stronger beam is red detuned by the mechanical resonator frequency ( Δ = ω m ) and is used to cool the center of mass motion of this resonator mode. The cooling process [inset in (b)] takes place because the rate ( A ) at which photons are scattered into the anti-Stokes sideband at the cavity resonance under extraction of a phonon is dominant compared to heating by scattering into the off-resonant Stokes sideband ( A + ) . (b) The plot shows the calibrated effective mechanical mode temperature T eff versus the observed mechanical damping Γ eff for various power and detuning values of the cooling beam. No deviations from the theoretically expected power-law dependence (red solid line) can be observed, which demonstrates the absence of residual heating effects. In this experiment the fundamental mode of the micromechanical resonator has been cooled down to a mean occupation of n = 32 phonons, only limited by the unavoidable thermal coupling of the resonator to its environment. (c) Cross section of the He 4 cryostat to precool the optomechanical system. The optical access is provided through a thermal radiation shield. The bulk input coupler is mounted inside the cryostat. The chip (green), with the mechanical resonator ( ω m 2 π 950 KHz , Q 30000 ) is cooled to 5 K . It can be aligned with respect to the second mirror forming the Fabry–Pérot cavity ( F = 3900 ) with a bandwidth of 2 π 770 kHz , allowing operation in the moderately resolved sideband regime.

Fig. 3
Fig. 3

Micromechanics in the strong coupling regime. When the optomechanical coupling rate overcomes the intrinsic decoherence rates, here the cavity decay rate and the mechanical damping rate, the optical mode becomes “dressed” by the mechanical mode. The new dynamics can be described by a set of “normal modes” of a truly hybrid optomechanical system. (a) Shown are the measured normal mode frequencies of the optomechanical system as a function of cavity detuning (from [82]). The normal mode frequencies are obtained from fits to the emission spectra of the driven optomechanical cavity, which are measured via sideband homodyne detection of the cooling beam. For far off-resonant driving, the normal modes approach the limiting case of two uncoupled—one optical and one mechanical—systems (indicated by the dashed lines). At resonance and for sufficiently strong driving, the normal mode spectrum is split and results in an avoided level crossing. (b) and (c) compare a strongly driven optomechanical resonator to a strongly driven two-level system. In the absence of coupling both energy spectra comprise equidistant levels of energy N ω m with degeneracy N and 2, respectively. In the coupled case the degeneracy is lifted. In (b), for a cavity in a coherent state with a mean numbers of n c photons ( n c 1 ) , each level splits up into an N-multiplett of dressed states | m , n that are separated by g = g 0 n c ( m + n = N , where m, n are the normal mode excitations). Emission of a cavity photon is accompanied only by transitions between dressed states | m , n and | m 1 , n or | m , n 1 . Accordingly, emitted photons have to lie at sideband frequencies ω L + ω ± , where ω ± are the frequencies of the normal modes. This gives rise to a doublet structure in the sideband spectrum (bottom) with a splitting. As depicted in (c), the same considerations lead to the four different allowed transitions in the case of a strongly coupled two-level system giving rise to the well-known Mollow-triplet in the atom resonance fluorescence. The analogy even holds for strong coupling in the single photon regime (yellow part) where for a two-level system vacuum Rabi splitting is observed—a phenomenon that is predicted for the optomechanical case with a splitting of g 0 2 ω m .

Equations (1)

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H int = g X c X m = g ( a c b m + a c + b m + ) + g ( a c b m + + a c + b m )

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