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Hindawi Publishing CorporationInternational Journal of OpticsVolume 2011, Article ID 629605, 9 pagesdoi:10.1155/2011/629605

Research Article

Higher-Order Amplitude Squeezing in Six-Wave Mixing Process

Sunil Rani,1 Jawahar Lal,2 and Nafa Singh3

1 Department of Applied Physics, Shri Krishan Institute of Engineering & Technology, Kurukshetra 136118, India2 Department of Physics, Markanda National College, Shahbad, Kurukshetra 136118, India3 Department of Physics, Kurukshetra University, Kurukshetra 136119, India

Correspondence should be addressed to Sunil Rani, [email protected]

Received 28 April 2010; Accepted 11 April 2011

Academic Editor: A. Cartaxo

Copyright © 2011 Sunil Rani et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We investigate theoretically the generation of squeezed states in spontaneous and stimulated six-wave mixing process quantummechanically. It has been found that squeezing occurs in field amplitude, amplitude-squared, amplitude-cubed, and fourth powerof field amplitude of fundamental mode in the process. It is found to be dependent on coupling parameter “g” (characteristics ofhigher-order susceptibility tensor) and phase values of the field amplitude under short-time approximation. Six-wave mixing is aprocess which involves absorption of three pump photons and emission of two probe photons of the same frequency and a signalphoton of different frequency. It is shown that squeezing is greater in a stimulated interaction than the corresponding squeezing inspontaneous process. The degree of squeezing depends upon the photon number in first and higher orders of field amplitude. Westudy the statistical behaviour of quantum field in the fundamental mode and found it to be sub-Poissonian in nature. The signal-to-noise ratio has been studied in different orders. It is found that signal-to-noise ratio is higher in lower orders. This study whensupplemented with experimental observations offers possibility of improving performance of many optical devices and opticalcommunication networks.

1. Introduction

Over the past three decades, particular attention has beenfocused on theoretical investigations and experimentalobservations in generation of squeezed light, for improv-ing the performance of many optical devices and opticalcommunication networks. The concept of squeezed light isconcerned with reduction of quantum fluctuations in oneof the quadrature, at the expense of increased fluctuationsin the other quadrature. In general, the two importantnonclassical effects, squeezing and antibunching (or Sub-Poissonian photon statistics), are not interrelated; that is,some states exist that exhibit the first but not the second andvice versa. However, squeezing can be detected using simplephoton counting in higher-order sub-Poissonian statistics.

A lot of work has appeared in the literature on thetheoretical and experimental investigations on generationof squeezed states of electromagnetic field. Mandel [1]found squeezed state of the second harmonic when abeam of light propagates through a nonlinear crystal. Later,Hillery [2] defined amplitude-squared squeezing and showed

that amplitude-squared squeezed states can be of use inreducing noise in the output of certain nonlinear opticaldevices. Hong and Mandel [3, 4] introduced the notionof Nth-order squeezing as a generalization of the second-order squeezing. Zhan [5] proposed the generation ofamplitude-cubed squeezing in the fundamental mode insecond and third harmonic generation. Jawahar and Jaiswal[6] extended the results obtained by Zhan for amplitude-cubed squeezing in the fundamental mode during secondand third harmonic generations to kth order. The significantexperimental observations include gravity wave detection[7–10], in optical communication [11], in nanodisplace-ment measurement [12], and in optical storage [13], andinterferometer enhancement [14, 15]. The experimentaldetections and applications confirm the importance of thetheoretical investigations into various optical processes suchas four- and six-wave mixing [16–20], eight-wave mixing[21], higher-order harmonic generation [22–25], parametricamplification [26], Raman [27] and hyper-Raman processes[28], and so forth. Higher-order sub-Poissonian statisticshave been studied by a number of authors such as those in

2 International Journal of Optics

[29–31]. The conversion of higher-order squeezed light intononclassical light with high sub-Poissonian statistics and itsexperimental detection has been discussed in [31–33].

Recently, Giri and Gupta [19] have investigated the sque-ezing effects in six-wave mixing process. In this paper, wepropose a different model for the same interaction process.Also, this paper shows one of the distinguished examples ofnonlinear processes when light exhibits both squeezing andsub-Poissonian photon statistics at the same time. Squeezingin field amplitude, amplitude-squared, amplitude-cubed,and in fourth-order amplitude has been studied in funda-mental mode for the proposed model. The photon statisticsand dependence of squeezing on photon number have alsobeen investigated.

2. Definition of Squeezing and Higher-OrderSqueezing

Squeezing is a purely quantum mechanical phenomenonwhich cannot be explained on the basis of classical physics.The coherent states do not exhibit nonclassical effects, but asuperposition of coherent states can exhibit normal squeez-ing, higher-order squeezing, and sub-Poissonian photonstatistics. A coherent state changes to a superposition ofcoherent states when it interacts with a non linear medium.Squeezed states of an electromagnetic field are the states withreduced noise below the vacuum limit in one of the canonicalconjugate quadratures. Normal squeezing is defined in termsof the operators

X1 = 12(A + A†

), X2 = 12i

(A− A†

), (1)

where X1 and X2 are the real and imaginary parts of thefield amplitude, respectively. A and A† are slowly varyingoperators defined by

A = aeiωt, A† = a†e−iωt. (2)The operators X1 and X2 obey the commutation relation

[X1,X2] = i2 (3)

which leads to the uncertainty relation (� = 1)

ΔX1ΔX2 ≥ 14 . (4)

A quantum state is squeezed in Xi variable if

ΔXi <12

for i = 1 or 2. (5)

Amplitude-squared squeezing is defined in terms of opera-tors Y1 and Y2 as

Y1 = 12[A2 + A†2

], Y2 = 12i

[A2 − A†2

]. (6)

The operators Y1 and Y2 obey the commutation relation[Y1,Y2] = i(2N + 1), where N is the usual number operatorwhich leads to the uncertainty relation

ΔY1ΔY2 ≥〈(

N +12

). (7)

Amplitude-squared squeezing is said to exist in Yi variable if

(ΔYi)2 <

〈(N +

12

)for i = 1 or 2. (8)

Amplitude-cubed squeezing is defined in terms of theoperators

Z1 = 12(A3 + A†

3)

, Z2 = 12i(A3 − A†3

). (9)

The operators Z1 and Z2 obey the commutation relation

[Z1,Z2] = i2(9N2 + 9N + 6

). (10)

Relation (10) leads to the uncertainty relation

ΔZ1ΔZ2 ≥ 14(9N2 + 9N + 6

). (11)

Amplitude-cubed squeezing exists when

(ΔZi)2 <

14

〈(9N2 + 9N + 6

)〉for i = 1 or 2. (12)

Real and imaginary parts of fourth-order amplitude are givenas

F1 = 12(A4 + A†4

), F2 = 12i

(A4 − A†4

). (13)

The operators F1 and F2 obey the commutation relation

[F1,F2] = i2(16N3 + 24N2 + 56N + 24

)(14)

and satisfy the uncertainty relation (� = 1)

ΔF1ΔF2 ≥ 14〈(

16N3 + 24N2 + 56N + 24)〉. (15)

Fourth-order squeezing exists when

(ΔFi)2 <

14

〈(16N3 + 24N2 + 56N + 24

)〉for i = 1 or 2.

(16)

3. Squeezing in Fundamental Mode inSix-Wave Mixing Process

The model considers the process involving absorption ofthree pump photons of frequency ω1 each, going from state|1〉 to state |2〉 and emission of two probe photons from state|2〉 to state |3〉 with frequency ω2 each. The atomic systemreturns to its original state by emitting one signal photon offrequency ω3 from state |3〉 to |1〉. The process is shown inFigure 1.

The Hamiltonian for this process is as follows (� = 1)

H = ω1a†a + ω2b†b + ω3c†c + g(a3b†2c† + a†3b2c

), (17)

in which g is a coupling constant. A = aeiω1t, B = beiω2t , andC = ceiω3t , respectively, are the slowly varying operators forthe three modes at ω1, ω2, and ω3. a(a†), b(b†), c(c†) are the

International Journal of Optics 3

ω1

ω1

ω1ω3

2ω2

|1⟩

|2⟩

|3⟩

Figure 1: Six-wave interaction model.

usual annihilation (creation) operators associated with therelation 3ω1 = 2ω2 + ω3.

The Heisenberg equation of motion for mode A is

Ȧ = ∂A∂t

+ i[H ,A]. (18)

Using (17) in (18), we obtain

Ȧ = −3igA†2B2C. (19)

Similarly, we obtained the relations for Ḃ and Ċ as

Ḃ = −2igA3B†C†,

Ċ = −igA3B†2.(20)

Expanding A(t) using Taylor’s series expansion by assumingthe short-time interaction of waves with the medium andretaining the terms up to |gt|2, we obtain

A(t) = A− 3igtA†2B2C + 32g2t2

×(

6A†A2B†2B2C†C + 6AB†2B2C†C

− 4A†2A3B†BC†C

− 2A†2A3C†C − A†2A3B†2B2C†C

− 4A†2A3B†BC†C − 2A†2A3).

(21)

The real quadrature component for squeezing of fieldamplitude in fundamental mode A is given as

X1A(t) = 12[A(t) +A†(t)

]. (22)

For spontaneous interaction, we consider the quantum stateas a product of coherent state for the fundamental mode Aand the vacuum state for the modes B and C, that is,

∣∣ψ〉 = |α〉A|0〉B|0〉C , (23)

where α is the complex field amplitude of the fundamentalmode. Using (21)–(23), we obtain the expectation values as〈ψ∣∣X21A(t)

∣∣ψ〉

= 14

[α2 + α∗2 + 2|α|2 + 1

−6g2t2(α2|α|4 +α2|α|2 +α∗2|α|4 +α∗2|α|2 +2|α|6

)],

(24)

〈ψ|X1A(t)|ψ

〉2

= 14

[α2 + α∗2 + 2|α|2 − 6g2t2

(α2|α|4 + α∗2|α|4 + 2|α|6

)].

(25)

Therefore,

[ΔX1A(t)]2 = 〈X21A(t)

〉− 〈X1A(t)〉2

= 14

[1− 6g2t2

(α2|α|2 + α∗2|α|2

)],

(26)

[ΔX1A(t)]2 − 1

4= −3g2t2|α|4 cos 2θ, (27)

where θ is the phase angle, with α = |α|eiθ and α∗ = |α|e−iθ .The right-hand side of the expression (27) is negative,

indicating that squeezing will occur in the first-order ampli-tude in the fundamental mode in six-wave mixing process forwhich cos 2θ > 0 for spontaneous interaction.

In parallel to the spontaneous interaction, the stimulatedemission is caused due to the coupling of the atom to theother states of the field. Therefore, the study of squeezing instimulated interaction in six-wave mixing process requiresinitial quantum state as a product of coherent states formodes 1, 2 and vacuum state for 3, that is,

∣∣ψ〉 = |α〉A∣∣β〉B|0〉C. (28)

Retaining the terms up to g2t 2, we obtain

〈ψ|X1A(t)|ψ

〉2

= 14

[α2 + α∗2 + 2|α|2 − 3g2t2

(α2|α|4 + α∗2|α|4 + 2|α|6

)

×(∣∣β

∣∣4 + 4∣∣β∣∣2 + 2

)],

〈ψ∣∣X21A(t)

∣∣ψ〉

= 14

[α2 + α∗2 + 2|α|2 + 1− 3g2t2

×(α2|α|4 + α2|α|2 + α∗2|α|4 + α∗2|α|2 + 2|α|6

)

×(∣∣β

∣∣4 + 4∣∣β∣∣2 + 2

)].

(29)

Therefore,

[ΔX1A(t)]2 − 1

4= −3

2g2t2|α|4

(∣∣β∣∣4 + 4

∣∣β∣∣2 + 2

)cos 2θ,

(30)


which is negative, indicating that squeezing will occur forthose values of θ for which cos 2θ > 0, in the funda-mental mode in stimulated interaction under short-timeapproximation. The effect of the stimulated interaction isrepresented by the factor (|β|4 + 4|β|2 + 2).

Using (21) and (23), the second-order amplitude isexpressed as

A2(t) = A2 − 6igt(A†2A + A†

)B2C − 3g2t2

×(A†2A4 + A†A3

)(B†2B2 + 4B†B + 2

).

(31)

For second-order squeezing, the real quadrature componentfor the fundamental mode is expressed as

Y1A(t) = 12[A2(t) + A†2(t)

]. (32)

Using (23) and (31) in (32), we get the expectation values inspontaneous six-wave mixing process as

〈ψ|Y1A(t)|ψ

〉2

= 14

[α4 + α∗4 + 2|α|4 − 12g2t2

×(α4|α|4 + α4|α|2 + α∗4|α|4 + α∗4|α|2 + 2|α|8

+2|α|6)]

,

(33)

〈ψ∣∣Y 21A(t)

∣∣ψ〉

= 14

[α4 + α∗4 + 2|α|4 + 4|α|2 + 2− 12g2t2

×(α4|α|4 + 3α4|α|2 + 2α4 + α∗4|α|4 + 3α∗4|α|2

+2α∗4 + 2|α|8 + 4|α|6)].

(34)

Therefore,

[ΔY1A(t)]2

= 〈Y 21A(t)〉− 〈Y1A(t)〉2

= 14

[4|α|2 +2−24g2t2

(α4|α|2 +α4 +α∗4|α|2 +α∗4 +|α|6

)].

(35)

The number of photons in mode A may be expressed as

N1A(t) = A†(t)A(t)

= A†A + 3igt(A3B†2C† − A†3B2C

)

− 3g2t2A†3A3(B†2B2 + 4B†B + 2

)

+ 9g2t2(A†2A2 + 4A†A + 2

)B†4B4C†C.

(36)

Thus, using condition (23), we get〈N1A(t) +

12

=[|α|2 + 1

2− 6g2t2|α|6

]. (37)

Subtracting (37) from (35), we get

[ΔY1A(t)]2 −

〈N1A(t) +

12

= −12g2t2

(|α|6 + |α|4

)cos 4θ.

(38)

Using initial condition (28), we obtain squeezing for thestimulated process as

[ΔY1A(t)]2 −

〈N1A(t) +

12

= −6g2t2

(|α|6 + |α|4

)

×(∣∣β

∣∣4 + 4∣∣β∣∣2 + 2

)cos 4θ.

(39)

The right-hand sides of (38) and (39) are negative for allvalues of θ for which cos 4θ > 0 and thus shows the existenceof squeezing in the second order of the field amplitude inspontaneous and stimulated interaction under short-timeapproximation.

Using (21), cubed-amplitude is expressed as

A3(t) = A3 − 3igt(

3A†2A2 + 6A†A + 2)B2C

− 18g2t2(A†4A + 3A†3

)B4C2 − 3

2g2t2

×(

3A†2A5 + 6A†A4 + 2A3)(B†2B2 + 4B†B + 2

),

(40)

and the real quadrature component for third-order squeez-ing in the fundamental mode is expressed as

Z1A(t)

= 12

[A3(t) + A†3(t)

]

= 12

[A3 + A†3 − 3igt

(A†2A2 + 6A†A + 2

)B2C

+ 3igt(A†2A2 + 6A†A + 2

)B†2C†

−18g2t2(A†4A+3A†3

)B4C2

−18g2t2(A†A4 +3A3

)B†4C†2 − 3

2g2t2

×(

3A†5A2 +6A†4A+2A†3 +3A†2A5 +6A†A4 +2A3)].

(41)

Using (23) and (41), we get the expectation values for sponta-neous interaction as

〈ψ|Z1A(t)|ψ

〉2

= 14

[α6 + α∗6 + 2|α|6 − 6g2t2

×(

3|α|4 + 6|α|2 + 2)(α6 + α∗6 + 2|α|6

)],

(42)


〈ψ∣∣Z21A(t)

∣∣ψ〉

= 14

[α6 + α∗6 + 2|α|6 + 9|α|4 + 18|α|2 + 6

− 6g2t2(

3|α|4 + 15|α|2 + 20)(α6 + α∗6

)

+6|α|10 + 30|α|8 + 40|α|6].

(43)


[ΔZ1A(t)]2 = 1

4

[9|α|4 + 18|α|2 + 6− 54g2t2

×(|α|2 + 2

)(α6 + α∗6

)+ 2|α|8 + 4|α|6

].

(44)

Using (23) and (36), we have

14

〈9N21A(t) + 9N1A(t) + 6

〉

= 14

[9|α|4 + 18|α|2 + 6− 108g2t2

(|α|8 + 2|α|6

)].

(45)


[ΔZ1A(t)]2 − 1

4

〈9N21A(t) + 9N1A(t) + 6

〉

= −27g2t2(|α|8 + 2|α|6

)cos 6θ.

(46)

Using (28), we obtain the stimulated process as

[ΔZ1A(t)]2 − 1

4

〈9N21A(t) + 9N1A(t) + 6

〉

= −272g2t2

(|α|8 + 2|α|6

)(∣∣β∣∣4 + 4

∣∣β∣∣2 + 2

)cos 6θ.

(47)

The right-hand sides of (46) and (47) are negative, for allvalues of θ for which cos 6θ > 0, indicating the existence ofsqueezing in cubed amplitude in the fundamental mode inthe spontaneous and stimulated processes.

For fourth-order squeezing, amplitude is expressed as

A4(t) = A4 − 12igt(A†2A3 + 3A†A2 + 2A

)B2C − 6g2t2

×(A†2A6 + 3A†A5 + 2A4

)(B†2B2 + 4B†B + 2

).

(48)

The real quadrature component for fourth-order squeezingin fundamental mode is given as

F1A(t) = 12[A4(t) +A†4(t)

]. (49)

Using (23) and (48) in (49), we get the expectation values as

〈ψ|F1A(t)|ψ

〉2 = 14

[α8 + α∗8 + 2|α|8 − 24g2t2

×{(|α|4 + 3|α|2 + 2

)(α8 + α∗8

)

+2|α|12 + 6|α|10 + 4|α|8}]

,

(50)

〈ψ∣∣F21A(t)

∣∣ψ〉 = 14

[α8 + α∗8 + 2|α|8 + 16|α|6 + 72|α|4

+ 96|α|2 + 24− 24g2t2

×{(|α|4 + 7|α|2 + 14

)(α8 + α∗8

)

+2|α|12 + 18|α|10 +64|α|8 +68|α|6}].

(51)

Therefore, subtracting (50) from (51), we obtain

[ΔF1A(t)]2 = 1

4

[16|α|6 + 72|α|4 + 96|α|2 + 24− 24g2t2

×{(

4|α|2 + 12)(α8 + α∗8

)+ 12|α|10

+ 60|α|8 + 68|α|6}].

(52)

Using (23) and (36), we have

14

〈16N31A(t) + 24N

21A(t) + 56NA + 24

〉

= 14

[16|α|6 + 72|α|4 + 96|α|2 + 24

−24g2t2(

12|α|10 + 60|α|8 + 68|α|6)].

(53)


[ΔF1A(t)]2 − 1

4

〈16N31A(t) + 24N

21A(t) + 56NA + 24

〉

= −48g2t2(|α|10 + 3|α|8

)cos 8θ.

(54)

Using (28), we obtain the stimulated process as

[ΔF1A(t)]2 − 1

4

〈16N31A + 24N

21A(t) + 56N1A(t) + 24

〉

= −24g2t2(|α|10 + 3|α|8

)(∣∣β∣∣4 + 4

∣∣β∣∣2 + 2

)cos 8θ.

(55)

The right-hand sides of (54) and (55) are negative,for all values of θ for which cos 8θ > 0, indicating theexistence of squeezing in fourth-order field amplitude inthe fundamental mode in the spontaneous and stimulatedprocesses, respectively.

Using (23) and (36), the statistics of fundamental modein six-wave mixing is found to be sub-Poissonian, given as

〈ΔN1A〉2 − 〈N1A〉 = −12g2t2|α|6. (56)


0 10 20 30 40 50

−0.8

−0.6

−0.4

−0.2

0

S x

|α|2

(a)

0 10 20 30 40 500

|α|2

S x

−150

−100

−50

|β|2 = 4|β|2 = 9

(b)

Figure 2: Dependence of first-order squeezing (a) sX with |α|2 in spontaneous and (b) s′X with |α|2 and |β|2 in stimulated six-wave mixingprocess.

00

10 20 30 40 50

|α|2

−200

−150

−100

−50

Sy

(a)

|β|2 = 4|β|2 = 9

00 10 20 30 40 50

|α|2

−10000

−8000

−6000

−4000

−2000

S y

(b)

Figure 3: Dependence of amplitude-squared squeezing (a) sy with |α|2 in spontaneous and (b) s′y with |α|2 and |β|2 in stimulated six-wavemixing process.

4. Signal-to-Noise Ratio

Signal-to-noise ratio is defined as ratio of the magnitude ofthe signal to the magnitude of the noise. With the approxi-mations θ = 0 and |gt|2 � 1, the maximum signal-to-noiseratio (in decibels) in field amplitude and higher orders isgiven in the following.

Using (25) and (26), signal-to-noise ratio in field ampli-tude is defined as

SNR1 = 20∗ log10〈X1A(t)〉2

[ΔX1A(t)]2 = 20∗ log10

(2|α|2

). (57)

Using (33) and (35), SNR in amplitude-squared squeezing isgiven as

SNR2 = 20∗ log10

(2|α|4 + |α|2

)(

3|α|2 + 2) . (58)

Using (42) and (44), SNR in amplitude-cubed squeezing isexpressed as

SNR3 = 20∗ log10

(3|α|4 + 6|α|2 + 2

)(

9|α|2 + 18) . (59)


0 10 20 30 40 50

|α|2

S z

−2

−1.5

−1

−0.5

0

×104

(a)

0 10 20 30 40 50

|α|2

|β|2 = 4|β|2 = 9

S z

0

×105−15

−10

−5

(b)

Figure 4: Dependence of amplitude-cubed squeezing (a) Sz with|α|2 in spontaneous and (b) S′z with |α|2 and |β|2 in stimulated six-wave mixing process.

Using (50) and (52), SNR in fourth-order squeezing is expre-ssed as

SNR4 = 20∗ log10

(|α|6 + 3|α|4 + 2|α|2

)(

5|α|4 + 21|α|2 + 17) . (60)

5. Results

The results show the presence of squeezing in field ampli-tude, amplitude-squared, amplitude-cubed, and fourth-order field amplitude of fundamental mode in six-wave mix-ing process. To study squeezing, we denote the right-handsides of relations (27), (38),(46), and (54) by Sx, Sy , Sz, and S ffor spontaneous and right-hand sides of relations (30), (39),(47), and (55) by S′x, S′y , S′z, and S

′f for stimulated interaction

for field amplitude, amplitude-squared, amplitude-cubed,

0 10 20 30 40 50

|α|2

Sf

−2

−1.5

−1

−0.5

0

×106

(a)

0 10 20 30 40 50

|α|2

S f

0

×107−10

−8

−6

−4

−2

|β|2 = 4|β|2 = 9

(b)

Figure 5: Dependence of fourth-order field amplitude squeezing(a) S f with |α|2 in spontaneous and (b) S′f with |α|2 and |β|2 instimulated six-wave mixing process.

−60

−40

−20

0

20

40

SNR

(dB

)

SNR1SNR2

SNR3SNR4

0 10 20 30 40 50

|α|2

Figure 6: Signal-to-noise ratio for different order squeezing.


and for fourth-order field amplitude, respectively. Taking|gt|2 = 10−4 and θ = 0, the variations of Sx, Sy , Sz, and S fwith photon number |α|2 for spontaneous interaction and ofS′x, S′y , S′z, and S

′f with |α|2and |β|2for stimulated interaction

are shown from Figures 2, 3, 4, and 5.A comparison between results of spontaneous and

stimulated processes shows the occurrence of multiplicationfactor (|β|4 + 4|β|2 + 2). It implies that squeezing in thefundamental mode in stimulated interaction is greater thancorresponding squeezing in spontaneous interaction. It isalso seen that maximum squeezing occurs when θ = 0. Thesignal-to-noise ratio is found to be higher in lower orders asshown in Figure 6.

6. Conclusion

Figures 2, 3, 4, and 5 show that squeezing increases nonlin-early with |α|2, which is directly dependent upon the numberof photons. The squeezing in any order during stimulatedinteraction (Figures 5(b), 4(b), 3(b), and 2(b)) is higherthan the squeezing in corresponding order in spontaneous(Figures 5, 4, 3, and 2) interaction by a factor (|β|4+4|β|2+2).The squeezing is higher in higher orders in both processes.Thus, the higher-order squeezing associated with higherorder nonlinear optical processes makes it possible to achievesignificant noise reduction.

It has also been found that the fundamental mode of fieldamplitude shows sub-Poissonian behavior as shown in rela-tion (56). The signal-to-noise ratio is higher in lower orderssqueezed states as reported earlier for Raman process [34].

References

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[2] M. Hillery, “Squeezing of the square of the field amplitude insecond harmonic generation,” Optics Communications, vol. 62,no. 2, pp. 135–138, 1987.

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