Interference effects in doped cavity optomechanics
Radiation pressure forces in cavity optomechanics allow for efficient cooling of vibrational modes of macroscopic mechanical resonators, the manipulation of their 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. While many approaches exist, they typically share a simple effective description in terms of a single force acting on the mechanical resonator. More generally, one can study the interplay between various forces acting on the mechanical resonator in such hybrid mechanical devices. This interplay can lead to interference effects that may, for instance, improve cooling of the mechanical motion or lead to generation of entanglement between various parts of the hybrid device. Here, we provide such an example of a hybrid optomechanical system where an ensemble of quantum emitters is embedded into the mechanical resonator formed by a vibrating membrane. The interference between the radiation pressure force and the mechanically modulated Tavis--Cummings interaction leads to enhanced cooling dynamics in regimes in which neither force is efficient by itself. Our results pave the way towards engineering novel optomechanical interactions in hybrid optomechanical systems.
Interference effects in doped cavity optomechanics
Radiation pressure forces in cavity optomechanics allow for efficient cooling of vibrational modes of macroscopic mechanical resonators, the manipulation of their 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. While many approaches exist, they typically share a simple effective description in terms of a single force acting on the mechanical resonator. More generally, one can study the interplay between various forces acting on the mechanical resonator in such hybrid mechanical devices. This interplay can lead to interference effects that may, for instance, improve cooling of the mechanical motion or lead to generation of entanglement between various parts of the hybrid device. Here, we provide such an example of a hybrid optomechanical system where an ensemble of quantum emitters is embedded into the mechanical resonator formed by a vibrating membrane. The interference between the radiation pressure force and the mechanically modulated Tavis--Cummings interaction leads to enhanced cooling dynamics in regimes in which neither force is efficient by itself. Our results pave the way towards engineering novel optomechanical interactions in hybrid optomechanical systems.
![Interference effects in doped cavity optomechanics
1
Max Planck Institute for the Science of Light, Erlangen, Germany
2
Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark
Ondřej Černotík,1
Claudiu Genes,1
and Aurélien Dantan2
[1] C. Genes et al., Phys. Rev. A 80, 061803 (2009).
[2] A. Dantan et al., Phys. Rev. A 90, 033820 (2014).
[3] C. Fabre et al., Phys. Rev. A 49, 1337 (1994).
[4] J. Qian et al., Phys. Rev. Lett. 109, 253601 (2012).
CoolingMotivation
Cavity optomechanics assisted by two-level quantum emitters offers an
interesting alternative to standard radiation pressure interaction.
Stokes or anti-Stokes scattering can be suppressed even in the bad-
cavity regime owing to modified cavity response [1].
Interference between radiation pressure and Jaynes–Cummings
interaction gives rise to new effects, regimes, and applications.
Ground state cooling with atoms and cavity on resonance
Cooling via polaritons
optimal atomic detuning
Doped membrane
Constituents: cavity field, mechanical oscillator, and an ensemble of
two-level emitters
Radiation pressure interaction
Position-dependent Tavis–Cummings coupling [2]
Cavity drive
Cavity optomechanics
Radiation pressure interaction
Linearization around a classical amplitude,
Stokes and anti-Stokes scattering
Linearized dynamics
Free evolution in the rotating frame ( )
Linearized interaction ( , )
Decay: (cavity), (atoms), (mechanics)
Other effects
Lower instability threshold with interference
Ponderomotive squeezing [3]
Mechanical limit cycles [4]
Interference cooling
Sideband cooling
-5 -2.5 0 1 2.5 5
Cavity detuning c/ m
101
103
105
Finaloccupation
Requires a good cavity,
20 10 0 10 20
Cavity detuning c/ m
100
101
102
103
Finaloccupation
With atoms
No atoms
10 2
10 1
100
101
102
Atom-cavity coupling / m
100
101
102
103
Finaloccupation
100 80 60 40 20 0 20 40
Cavity detuning c/ m
10 1
100
101
102
103
Finaloccupation
All effects
Radiation pressure, = = 0
Dressed cavity, = 0 [1]
Dopant only, g = 0 [2]
Bad cavity dressed by good atoms [1]
Works with poor
sideband ratio
50 0 50
Cavity detuning c/ m
3
2
1
0
1
2
3
Atomicdetuninga/m
Final occupation (log scale)
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 10000 20000 30000 40000 50000 60000 70000 80000
Intracavity photon number |c|2
0.0
0.5
1.0
1.5
2.0
Inputintensity(/m)2
1e7
All effects
Radiation pressure, = 0 = 0
Dressed cavity, 0 = 0
Dopant only, g0 = 0
All effects
Radiation pressure
0.8 0.9 1.0 1.1 1.2
0.5
1
5
10
Frequency ω/ωm
Quadraturevariance
(unitsofshotnoise)
Email: ondrej.cernotik@mpl.mpg.de](https://image.slidesharecdn.com/02poster-191113144213/75/interference-effects-in-doped-cavity-optomechanics-1-2048.jpg?cb=1674628071)
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Interference effects in doped cavity optomechanics
- 1. Interference effects in doped cavity optomechanics 1 Max Planck Institute for the Science of Light, Erlangen, Germany 2 Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark Ondřej Černotík,1 Claudiu Genes,1 and Aurélien Dantan2 [1] C. Genes et al., Phys. Rev. A 80, 061803 (2009). [2] A. Dantan et al., Phys. Rev. A 90, 033820 (2014). [3] C. Fabre et al., Phys. Rev. A 49, 1337 (1994). [4] J. Qian et al., Phys. Rev. Lett. 109, 253601 (2012). CoolingMotivation Cavity optomechanics assisted by two-level quantum emitters offers an interesting alternative to standard radiation pressure interaction. Stokes or anti-Stokes scattering can be suppressed even in the bad- cavity regime owing to modified cavity response [1]. Interference between radiation pressure and Jaynes–Cummings interaction gives rise to new effects, regimes, and applications. Ground state cooling with atoms and cavity on resonance Cooling via polaritons optimal atomic detuning Doped membrane Constituents: cavity field, mechanical oscillator, and an ensemble of two-level emitters Radiation pressure interaction Position-dependent Tavis–Cummings coupling [2] Cavity drive Cavity optomechanics Radiation pressure interaction Linearization around a classical amplitude, Stokes and anti-Stokes scattering Linearized dynamics Free evolution in the rotating frame ( ) Linearized interaction ( , ) Decay: (cavity), (atoms), (mechanics) Other effects Lower instability threshold with interference Ponderomotive squeezing [3] Mechanical limit cycles [4] Interference cooling Sideband cooling -5 -2.5 0 1 2.5 5 Cavity detuning c/ m 101 103 105 Finaloccupation Requires a good cavity, 20 10 0 10 20 Cavity detuning c/ m 100 101 102 103 Finaloccupation With atoms No atoms 10 2 10 1 100 101 102 Atom-cavity coupling / m 100 101 102 103 Finaloccupation 100 80 60 40 20 0 20 40 Cavity detuning c/ m 10 1 100 101 102 103 Finaloccupation All effects Radiation pressure, = = 0 Dressed cavity, = 0 [1] Dopant only, g = 0 [2] Bad cavity dressed by good atoms [1] Works with poor sideband ratio 50 0 50 Cavity detuning c/ m 3 2 1 0 1 2 3 Atomicdetuninga/m Final occupation (log scale) 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0 10000 20000 30000 40000 50000 60000 70000 80000 Intracavity photon number |c|2 0.0 0.5 1.0 1.5 2.0 Inputintensity(/m)2 1e7 All effects Radiation pressure, = 0 = 0 Dressed cavity, 0 = 0 Dopant only, g0 = 0 All effects Radiation pressure 0.8 0.9 1.0 1.1 1.2 0.5 1 5 10 Frequency ω/ωm Quadraturevariance (unitsofshotnoise) Email: ondrej.cernotik@mpl.mpg.de