1. Quantum optomechanics: possible applications to
Investigation of Planck-scale physics
P. Mataloni
Quantum Optics Group, Dipartimento di Fisica
Sapienza Università di Roma, 00185, Italy
INO – CNR, Firenze, Italy
ENEA Frascati,

2. Quantum Optomechanics: to generate, control and manipulate quantum states of a mechanical system by Quantum Optics.
The optical mode and the mechanical mode interact via momentum transfer (i.e. radiation pressure) within an optical cavity.
Nonlinear interaction occur when the
light is confined in a cavity modified
by the mechanical motion.
Implemented by direct change of cavity length.
Current optical technology based on high quality optomechanical
devices makes possible experiments in this field. 2

3. Model of optomechanical setup
Pump laser field with large amplitude |ac|>>1 and frequency wL
ac , ac+: optical field
bc , bc+: mechanical motion 3

4. Mechanical resonatorsb) c)
a) Fabry-Perot cavity
b) microtoroid structure
c) optomechanical crystal

5. Interaction Hamiltonian
1st term: Energy transfer between laser field and joint excitation of optical and mechanical mode.
Allows to generate correlated/anticorrelated modes and also entanglement between optical and mechanical fields.
2nd term: Energy transfer between the two modes. Equivalent to a quantum optical beam splitter interaction.
May allow cooling of the optomechanical mode. Interaction tuned by choosing the right detuning D.

6. Mechanical mode is in a thermal mixed state
Optical mode is in a pure state
T < 50 mK needed for a mechanical mode bandwidth = 1 MHz

7. Quantization of spacetime may result in a modification of the Heisenberg uncertainty relation due to quantum gravitational effects. Deformation of the commutator [x, p]  xp – px leads to a generalized uncertainty relation:

8. The Idea
Use quantum optics to test quantum gravitational effects by probing the canonical commutation of the centre-of-mass mode of a mechanical oscillator.
Probe the commutator of a quantum oscillator with mass close to the Planck mass by a sequence of interactions with a strong optical field in an optomechanical setting, which uses radiation pressure inside an optical cavity.
Need to perform a high-sensitivity measurement of the uncertainty relation

9. 1) Displacement Operator
Xm , Pm: quadrature operators

10. 2) Choose a sequence of four optomechanical interactions to displace the mechanical state around a loop in phase-space
Note: Xm , Pm don’t commute any change in the optical field depends on the commutator [Xm , Pm]. Moreover:
Coherent states |a> with photon
number Np>>1:
A deformed commutator affects the optical field by introducing an additional displacement in phase space.
Measured with optical imprecision:

11. 3) How to realize the displacement operator?
Within a single oscillation a 4-pulse interaction U(q) = eiq is implemented
in a sequence which allows Xm and Pm to be interchanged after a quarter of the oscillator period.
After the four-pulse interaction the optical field can be analysed by an interferometric measurement (homodyne technique) yielding the phase
information of the light with very high precision.

12. 4) How to implement the four pulse interaction?
Mean value and variance of the mechanical state after a short input pulse
<< T = 2p/wm:
PL: measurement outcome
W: momentum transfer
Divide in 4 quarters the oscillation period
Look at the momentum in the 1st quarter, then at the position in the 2nd one, then viceversa in the 3rd and 4th quarters.
Four operations performed within one oscillation period

13. 5) Experimental scheme

14. 6) some number…..
(1)
determines the resolution db0, dm0, dg0 .
sout: quantum noise of the output pulse
The inaccuracy
(2)
(3)

15. 7) Micromechanical mirror
Works with a flat suspended mirror.
Cavity length = 4l
l = 1064 nm
Effective mass m = 10 ng

16. The quantum opto-mechanics experiment in Italy
- Univ. of Camerino (P- Tombesi, G. Di Giuseppe, D. Vitali)
- Univ. Di Firenze (G. Tino) coll. with Roma Sapienza (G. A. Camelia)

17. Univ. Firenze (F. Marin, F. Cataliotti): towards quantum effects in the mechanical interaction of light with macroscopic objects
Supported by LENS (UniFI), INFN (CSN5, SQUALO)

18. World record for Q and Finesse in oscillating micro-mirrors
Mass = 2x10-7 Kg
Freq. = 85 KHz
Q = 2.6 x 106
Finesse = 6 x 104
T = 5 K
World record for Q and Finesse in oscillating micro-mirrors
Unpublished-Confidential
Also required: Q > 10
6 T < 100mK
SiN membrane are being studied
for mass ~ Kg
Also required Q > 106 , T < 100 mK

19. Thank you!