Sqeezing Squeezing operator Experimental realization of squeezing V

① Sqeezing ② Squeezing operator ③ Experimental realization of squeezing

V- Quadrature and squeezed states

1) Squeezing: basic idea position Heisenberg uncertainty principle momentum • Coherent state • Squeezed state Noise distribution symmetric in phase space or Noise distribution not symmetric in phase space Ellipse Circle • complex amplitude • complex squeezing parameter (position in phase space) ( degree of squeezing, direction of squeezing)

2) The squeezing operator Displacement operator 2 photons processes • • Ideal squeezed state Squeezed vacuum ? Some properties of the squeezing operator Hermitian conjugate operation Transformation of annihilation and creation operators ?

Is a minimum uncertainty state ? State is displaced in the complex plane if

• Average number of photon in the squeezed state # of photons in the coherent state # of photons in the squeezed vacuum • Challenge problem: Find the number state expansion of the squeezed vacuum state ? ? What is the photon statistics of a squeezed coherent state? • Another definition of the squeezed state Bogoliubov transformation Bosons is an eigenstate of Squeezed state is a coherent state for the operator coherent displacement of the squeezed vacuum and can thus be obtained by a and

• A different squeezed state First squeeze then displace First displace then squeeze Both are minimum uncertainty states these states are different! If you first displace by then squeeze with

3) Generation of squeezed states • Squeezed light can be generated in nonlinear optical crystals. Non linear interaction with the medium non linearity (optical fiber) (Li. Nb. O 3 or lithium triborate (LBO)) four-wave-mixing (2 pumps now) nonlinear optical Kerr effect Parametric amplification interaction between three distinct light waves (with different frequencies) 1) Pump 2) Signal 3) Idler The Kerr effect transforms a coherent state from a pump laser into a squeezed state Pump photons are converted into signal and idler photons Degenerate parametric amplification 30 years of squeezed light generation Arxiv 1511. 03250 Photon in the pump Nonlinear interaction one c-photon two a-photons If the pump intensity is large: classical field vacuum input can generate a squeezed vacuum PRL 100 (3), 033602 (2008) In phase space, higher amplitude regions induce an increased phase shift Significant pump powers required Phonon-photon coupling