1. A quantum optical beam n Classically an optical beam can have well defined amplitude AND phase simultaneously. n Quantum mechanics however imposes an uncertainty principle. –The deterministic classical beam is blurred out by quantum noise. Uncertainty principle:

2. Coherent state Squeezed state n V + =V - =1 n Ideal output of a low- noise laser n Same quantum noise as vacuum n V + or V - < 1 n Very fragile in the presence of loss

3. n Laser outputs are typically very noisy at low frequency. n Measure squeezing of the beat of the carrier with frequencies outside this noise bandwidth. Sideband squeezing

4. Coherent Production of squeezing n Produce squeezing in a below threshold optical parametric amplifier (OPA)

5. Coherent Production of squeezing n Produce squeezing in a below threshold optical parametric amplifier (OPA) Amplitude squeezed

6. Coherent Production of squeezing n Produce squeezing in a below threshold optical parametric amplifier (OPA) Amplitude squeezed Phase squeezed

7. Comparison of OPAs and OPOs n OPAs are seeded with a bright beam whereas OPOs are vacuum seeded. n Advantages of OPAs: –Can lock the length of the resonator. –Bright squeezed output that can be controlled in downstream applications. n Advantage of OPOs: –No classical noise coupled from the laser into the squeezed beam.

9. n In our two OPAs this noise is correlated and can be cancelled by optical or electronic means. Recovering buried squeezing

11. The Poincaré sphere

12. Commutation relations of Stokes operators

13. The Poincaré sphere Commutation relations of Stokes operators Uncertainty relations of Stokes operators

14. The Poincaré sphere Commutation relations of Stokes operators Uncertainty relations of Stokes operators

15. Polarisation squeezing n A Stokes parameter is squeezed if its variance is below the shot-noise of a coherent beam of equal power.

16. Polarisation state of a coherent beam

17. Polarisation state of a coherent beam Polarisation state of an amplitude squeezed beam one Stokes parameter squeezed

18. Polarisation state of a coherent beam Polarisation state of an amplitude squeezed beam one Stokes parameter squeezed Polarisation state of a squeezed beam combined with a coherent beam one Stokes parameter squeezed [P.Grangier et al., Phys.Rev.Lett, 59, 2153 (1987)]

19. Polarisation state of a coherent beam Polarisation state of an amplitude squeezed beam one Stokes parameter squeezed Polarisation state of a squeezed beam combined with a coherent beam one Stokes parameter squeezed [P.Grangier et al., Phys.Rev.Lett, 59, 2153 (1987)] Polarisation state of two phase squeezed beams combined one Stokes parameter squeezed

20. Polarisation state of a coherent beam Polarisation state of an amplitude squeezed beam one Stokes parameter squeezed Polarisation state of a squeezed beam combined with a coherent beam one Stokes parameter squeezed [P.Grangier et al., Phys.Rev.Lett, 59, 2153 (1987)] Polarisation state of two phase squeezed beams combined one Stokes parameter squeezed Polarisation state of two amplitude squeezed beams combined two Stokes parameters squeezed [W. Bowen et. al. http://xxx.lanl.gov/abs/quant-ph/0110129 (2001)]

23. Summary n We have produced two reliable strongly quadrature squeezed sources. n We produce new quantum polarisation states and investigate their properties. n We cancel the classical noise of our input laser beam to produce squeezing at low frequencies. n We have produced EPR entanglement and are presently characterising it.