Higher Order Squeezing in Stimulated Mode in. Seven Wave Mixing

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1 Higher Order Squeezing in Stimulated Mode in Seven Wave Mixing Savita Gill* Department of pplied Science, University Institute of Engineering and Technology, Kurukshetra 36 9, Haryana, Indi STRT Higher order squeezing in stimulated modein seven-wave mixing optical processeshas been studied.it is found to be dependent on coupling constant g and phase values of the field amplitude with photon number of the fundamental as well as harmonic mode under short time approximation. Keywords:Higher order squeezing,onclassicality, Multiwave mixing.. ITRODUTIO Squeezed states of electromagnetic field correspond to a non-classical state [, ] in which reduction of quantum fluctuation below the coherent state level takes place. large number of methods have been proposed in literature to generate and detect squeezed states theoretically and experimentally [3-0]. Due to low noise property of squeezed states potential applications of squeezed light have been reported in recent past in the processing of quantum information, for example, for quantum teleportation [-3], quantum cryptography [4] and quantum information networking [5]. In the present work, we have reported the generation of higher order squeezing state in stimulated mode in seven-wave mixing optical process.. HIGHER ORDER SQUEEZIG Higher order squeezing is defined in various ways. Hong and Mandel [6, 7] and Hillery [] have introduced the notion of higher order squeezing of quantized electromagnetic field as generalization of normal squeezing.mplitude-cubed squeezing is defined in terms of operators Z and Z as 3 3 i 3 3 and Z Z Where Z and Z are the real and imaginary parts of the cube of field amplitude, respectively. and i t slowly varying operators defined by ae and a e it. The operators Z and Z obey the commutation relation () are 77 P a g e

2 Z, Z i / 4 (9 9 6) () This leads to the uncertainty relation Z / Z (3) where is the usual number operator. mplitude-cubed squeezing is said to exist in Z variable if ( Z ) / Or the squeezing f is (4) f = ( Z ) / (5) 3. SEVE-WVEMIXIGPROESS multiwave mixing process can be viewed in the optics as a process involving multi photon interaction. In this process, the interaction is looked upon as a process which involves the absorption of two pump photons, each having frequency ω and emission of two probe photons of frequency ω, and signal photons of frequency ω 3 where ω = ω +ω 3 The Hamiltonian for this process is given as follows (ћ=) H a a b b c c g a b c a b c in which g is a coupling constant. (6) = aexp (iω t), = b exp (iω t) and = c exp (iω 3 t) are the slowly varying operators at frequencies ω, ω and ω 3, a (a ), b (b ) and c (c ) are the usual annihilation (creation) operators, respectively. The Heisenberg equation of motion for fundamental mode is given as d i H, dt t (7) y using the short-time approximation technique, we expand t () by using Taylor s series expansion and retaining the terms up to g t as t igt g t (8) Where, and. Using Equations (8) number of photons in mode may be expressed as 78 P a g e

3 t t t g t 4 (9) 3 3 t t t g t 4 4 (0) 3. STIMULTED THIRD ORDER MPLITUDE SQUEEZIG The real quadrature component for third order squeezing in fundamental mode isdefined as 3 3 Y t t t Initially, we consider the quantum state of the field amplitude as a product of coherent state for the fundamental mode and harmonic mode for and vacuum state for mode i.e. 0 () Using Equations (8) and () the third-order amplitude of the fundamental mode is expressed as t g t () 3 3 Y t t t g t Using Equations () and (3), we get the expectation values as 6 4 Y t g t ( ) 4 (4) and Y t g t ( ) 4 6 (3) Therefore (5) 79 P a g e

4 Y t g t ( ) Using Equations (9), (0) and (6) a straightforward but strenuous calculation yields (6) Y t 9 t 9 t gt (cos 6 ) The right hand side of Equation (7) is negative, indicating that squeezing occurs in cube of field amplitude in the fundamental mode in seven wave mixing. 4. RESULT (7) The results show the presence of squeezing in third order of field amplitude in seven wave mixing in stimulated mode.taking gt 4 0 and 0 for maximum squeezing, the variations of Y S is shown in Figure. Degree of squeezing is shown as a function of with. It is clear from Figure that squeezing increase nonlinearly and. Thus we can conclude that the degree of squeezing directly depends upon the photon number of the fundamental mode as well as on the harmonic mode. 4 9 Figure.. Dependence of stimulated third order amplitudesqueezing in 7wmxon. 80 P a g e

5 5. OLUSIO It is shown that the selective phase values of field amplitude of fundamental mode lead to higher order squeezing up to third order in seven-wave mixing process.gain, from Equation (7) we can conclude that the degree of higher order squeezing present in the system can be tuned by varying the values of initial phase of the coherent state ( ), number of photons present in the radiation field prior to the interaction ( interaction time (t). ) and the REFEREES.M. Hillery, mplitude-square squeezing of the electromagnetic field, Phys. Rev., 36,987, Orlowski, lassical entropy of quantum states of light, Phys. Rev.., 48, 993, D. F Walls andg. J Milburch, Quantum Optics, Springer erlin Heidelberg., 008; Savita, S. Rani and. Singh, Squeezing and sub-poissonian effect in eighth harmonic generation, Journal of information systems and communication, 3, 0, Savita, S Rani and Singh, Higher Order mplitude Squeezing in Fourth and Fifth Harmonic Generation, Indian Journal of Physics, 86, 0, D. K Giri and P. S Gupta, The squeezing of radiation in four-wave mixing processes, J. Opt. : Quantum Semiclass. Opt.,6, 004, J Perinaand J Krepelka, Stimulated Raman scattering of squeezed light with pump depletion, Journal of modern optics, 38(), 99, D.ntonosyan, G. Yu, Kryunchkyan,Multi-mode squeezing in micro structured non linear media, Physics of particles and uclei Letters,6(7), 009, J Perina, O Haderka, Sibilia, M ertolottiand M Scalora, Squeezed-light generation in a nonlinear planar waveguide with a periodic corrugation, Phys. Rev., 76(3), 007, , 0. Predojevic, ZZhai,J.M aballeroand M.W Mitchell,Rubidium resonant squeezed light from a diode pumped optical parametric oscillator,phys. Rev., 78(6), 008, Takei, T oki,s Koike, Ken-ichiro Yoshino, K Waki,H Yonezawa,T Hiraoka, J Mizno, M Takeoka, M an, Frsawa,Experimental demonstration of quantum teleportation of a squeezed light, Phys. Rev., 7, 005, J alsamiglia, M spachs, R Munoz-Tapia ande agan, Phase covariant quantum benchmarks, Phys. Rev., 99, 009, YHidehiro,S.L raunstein, Furusawa, Experimental Demonstration of Quantum Teleportation of roadband Squeezing,Phys. Rev. Lett., 9, 007, M hristandl, R Koenig and R Renner, Postselection Technique for Quantum hannels with pplications to Quantum ryptography, Phys. Rev. Lett.,0, 009, P a g e

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