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Interference effects in cavity optomechanics with hybridized membranes

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Radiation pressure forces in cavity optomechanics allow for efficient cooling of motion, the manipulation of photonic and phononic quantum states, as well as generation of optomechanical entanglement. The standard mechanism relies on the cavity photons directly modifying the state of the mechanical resonator. Hybrid cavity optomechanics provides an alternative approach by coupling mechanical objects to quantum emitters, either directly or indirectly via the common interaction with a cavity field mode. In these systems, the interference between forces from the cavity field and the emitters can give rise to novel optomechanical phenomena. We analyze two such hybrid optomechanical systems where a vibrating membrane is doped by quantum emitters or patterned with a photonic crystal structure. In particular, we demonstrate that, in the former system, a three-body interaction between the cavity field, emitters, and mechanical motion can be used to improve cooling of the mechanical motion. Second, we show that, when a photonic crystal structure in the membrane strongly modifies the membrane reflectivity, the cavity linewidth can be significantly reduced and the system can reach the sideband resolved regime.

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Interference effects in cavity optomechanics with hybridized membranes

  1. 1. Interference effects in cavity optomechanics with hybridized membranes Ondřej Černotík,1,* Aurélien Dantan,2 and Claudiu Genes1 1Max Planck Institute for the Science of Light, Erlangen, Germany 2Department of Physics and Astronomy, Aarhus University, Denmark *Now at Department of Optics, Palacký University Olomouc, Czechia APS March Meeting, Boston, March 6, 2019
  2. 2. Ondrej Cernotík (MPL Erlangen & UP Olomouc): Interference effects in cavity optomechanics with hybridized membranesˇˇ Optomechanical systems are useful for many applications in quantum technologies. 2 M. Aspelmeyer et al., RMP 86, 1391 (2014) Basic Hamiltonian: H = !cc† c + !mb† b + g0c† c(b + b† ) Linearization: H = cc† c + !mb† b + g(c + c† )(b + b† ), g = g0↵ Red-detuned drive: State swap, cooling c = !c !L = !m Hint = g(c† b + b† c) Blue-detuned drive: Squeezing, entanglement c = !m Hint = g(cb + c† b† ) Resonant drive: Position readout c = 0 Hint = g(c + c† )(b + b† ) ˆa ˆx !L !c !m
  3. 3. Ondrej Cernotík (MPL Erlangen & UP Olomouc): Interference effects in cavity optomechanics with hybridized membranesˇˇ Further experiments are possible with hybrid systems. 3 Atoms A. Jöckel et al., Nature Nano 10, 55 (2015) Color centers O. Arcizet et al., Nature Physics 7, 879 (2011) Bose–Einstein condensates P. Treutlein et al., PRL 99, 140403 (2007) Superconducting systems OC et al., PRA 94, 012340 (2016)ˇ
  4. 4. Ondrej Cernotík (MPL Erlangen & UP Olomouc): Interference effects in cavity optomechanics with hybridized membranesˇˇ We focus on membranes doped with two-level systems or patterned with gratings. 4 OC et al., Quantum Science and Technology 4, 024002 (2019) ˇ H = !cc† c + !mb† b + g0c† c(b + b† ) + !aa† a + [ + µ0(b + b† )](a† c + c† a) H = cc† c + !mb† b + (˜g⇤ c + ˜gc† )(b + b† ) + aa† a + (a† c + c† a) + µ(a + a† )(b + b† ) ˜g = g0↵ i µ + i a , µ = µ0↵ Basic Hamiltonian: Linearization:
  5. 5. Ondrej Cernotík (MPL Erlangen & UP Olomouc): Interference effects in cavity optomechanics with hybridized membranesˇˇ Interference in light–matter interactions leads to a Fano resonance in the cavity spectrum. 5 ˙q = !mp, ˙p = !mq mp + ⇠ F F = ˜g⇤ c + ˜gc† + µ(a + a† ) OC et al., Quantum Science and Technology 4, 024002 (2019) ˇ cavity noise dopant noise total noise this work no radiation pressure, A. Dantan et al., PRA 90, 033820 (2014) g = 0 atoms in the cavity, C. Genes et al., PRA 80, 061803 (2009) µ = 0 Bad cavity regime
  6. 6. Ondrej Cernotík (MPL Erlangen & UP Olomouc): Interference effects in cavity optomechanics with hybridized membranesˇˇ Frequency Transmission standard cavity hybrid cavity With strong coupling, the membrane can be used as an end mirror. 6 ˙c = (i!c + )c (i + p L )d + p 2Lbin + p 2Rcin ˙d = (i!d + )d (i + p L )c + p 2 bin bout = bin p 2Lc p 2 d cout = cin p 2Rc OC et al., arXiv:1902.10400ˇ
  7. 7. Ondrej Cernotík (MPL Erlangen & UP Olomouc): Interference effects in cavity optomechanics with hybridized membranesˇˇ The Fano resonance suppresses Stokes scattering in cooling. 7 OC et al., arXiv:1902.10400ˇ pum p anti-Stokes Stokes sam e reflectivity sam e linew idth hybrid cavity ¯n = 100 ¯n = 10
  8. 8. Ondrej Cernotík (MPL Erlangen & UP Olomouc): Interference effects in cavity optomechanics with hybridized membranesˇˇ Many systems can be used to achieve these effects. 8 Photonic crystal membranes R. Norte et al., PRL 116, 147202 (2016) Atoms trapped along waveguides D.E. Chang et al., NJP 14, 063003 (2012) Excitons in semiconductors G. Scuri et al., PRL 120, 037402 (2018) P. Back et al., PRL 120, 037401 (2018) E. Shahmoon et al., arXiv:1810.01052 Trapped atom arrays
  9. 9. Ondrej Cernotík (MPL Erlangen & UP Olomouc): Interference effects in cavity optomechanics with hybridized membranesˇˇ Functionalized membranes can be used for novel applications in optomechanics and cavity QED. 9 cavity mechanics dopant cavity mechanics dopant (a) (b) (c) • Fano resonance for improved cooling OC et al., QST 4, 024002 (2019) OC et al., arXiv:1902.10400 • Applicable to various systems OC et al., arXiv:1920.10400ˇ ˇ ˇ

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