## Abstract

We report on efficient generation of continuous-wave squeezed light and second harmonics with a periodically poled MgO:LiNbO_{3} (PPMgLN) crystal which enables us to utilize the large nonlinear optical coefficient *d*_{33}. We achieved the squeezing level of −7.60±0.15dB at 860 nm by utilizing a subthreshold optical parametric oscillator with a PPMgLN crystal. We also generated 400 mW of second harmonics at 430 nm from 570 mW of fundamental waves with 70% of conversion efficiency by using a PPMgLN crystal inside an external cavity.

©2010 Optical Society of America

## 1. Introduction

One of the attractive applications of squeezed light is quantum information processing for continuous variables [1]. Quadrature squeezed vacuum states are applied to realize quantum teleportation which is a fundamental protocol in quantum information processing [2]. The fidelity of such protocols is limited directly by the squeezing level [3]. So it is important to generate highly squeezed light to achieve better performance.

A typical method to generate highly squeezed light is utilization of a subthreshold optical parametric oscillator (OPO) which includes a nonlinear optical medium. The oscillation threshold of pump power *P _{th}* and the escape efficiency

*ρ*are important factors to exhibit characteristic features of the OPO and described as

respectively, where *E _{NL}* is the effective nonlinearity of optical medium,

*L*is the intracavity loss, and

*T*is the transmittance of output coupler. It is important to reduce the

*P*and improve the

_{th}*ρ*for generating highly squeezed light.

Over the past few decades a considerable number of the experiments have been performed to generate highly squeezed light as shown in Table 1. Polzik, *et al.* achieved −6.0±0.3dB of squeezing at 852 nm with a bow-tie configuration of the OPO including a KNbO_{3} (KN) crystal as the nonlinear medium [4]. A major factor of degradation of the observed squeezing level was intracavity losses caused by blue light induced infrared absorption (BLIIRA) in the KN crystal. Suzuki, *et al.* and Takeno, *et al.* achieved −7.2±0.14dB [3] and −9.01±0.14dB [5] of squeezing at 860 nm respectively with periodically poled KTiOPO4 (PPKTP) crystals which have rather low losses without BLIIRA. Recently Mehmet, *et al.* succeeded in measuring −11.5 ± 0.1dB of squeezing at 1064 nm [6]. They utilized a monolithic OPO of a MgO-7mol%-doped LiNbO_{3} (MgLN) single crystal in order to reduce intracavity losses caused by extra optical components. Note that the MgLN crystal had little losses caused by pump induced absorption at this wavelength [6].

From this passage, they placed more considerable emphasis on reduction of intracavity losses to improve the escape efficiency of OPO and thus to obtain higher squeezing level. On the other hand, they have not so attended to improve the nonlinearity of optical media. As the result, rather low nonlinear optical coefficient led to increase of the oscillation threshold.

In this work, we focus on utilization of the largest nonlinear optical coefficient *d*
_{33} of MgLN crystal to improve the effective nonlinearity *E _{NL}* for generating highly squeezed light at 860 nm. The high

*E*reduces the

_{NL}*P*directly from the relation of Eq. (1) and allows us to use high transmittance of output coupler to improve the

_{th}*ρ*. So the high nonlinearity is essentially important to generate highly squeezed light. The high nonlinearity is also important to generate second harmonic wave as a pump beam of the OPO. To achieve the high nonlinearity with MgLN crystal at 860 nm, it is necessary to fabricate a periodically poled structure with 3.4

*µ*m period. However, it has been a difficult task to fabricate a periodically poled structure in the bulk crystal with such a short period.

In earlier studies a periodically poled undoped LiNbO_{3} (PPLN) was utilized for generating various kinds of squeezed light at longer wavelength [7, 8]. With regard to generation of squeezed vacuum state, Feng, *et al.* achieved −2.4 ± 0.1dB of squeezing at 1560 nm by utilizing a subthreshold OPO with a PPLN crystal [9]. Yoshino, *et al.* achieved −1.7dB at 946 nm by utilizing a PPLN waveguide [10]. In both cases, the squeezing levels were limited by losses which were induced by pump light.

For simultaneous acquisition of the high nonlinearity and low loss with pump light at 860 nm, we fabricated periodically poled MgO-5mol%-doped LiNbO_{3} (PPMgLN) bulk crystals with 3.4 *µ*m period by temperature-elevated field-poling technique [11] as shown in Fig. 1. As the result the effective nonlinearity of 0.043 (W^{−1}) was realized. We achieved −7.60 ± 0.15dB of squeezing at 860 nm by utilizing a subthreshold OPO with the PPMgLN crystal. We also generated second harmonic waves at 430 nm with conversion efficiency of 70% with the PPMgLN crystal inside an external cavity.

## 2. Experimental setup

A schematic of experimental setup is shown in Fig. 2. We use a continuous-wave Ti:Sapphire laser at 860 nm as the fundamental source. The optical system mainly consists of three cavities with bow-tie configurations, an OPO, an optical frequency doubler to generate a pump beam of the OPO, and a mode cleaner for spatially filtering a local oscillator (LO) beam to make the same spatial mode as the OPO output, where the LO beam is used for homodyne measurement. The 860 nm beam is phase-modulated at 9.1 MHz by an electro-optic modulator (EOM) in order to lock the cavities at the resonance by conventional FM sideband locking technique [12]. Both cavities of the OPO and the frequency doubler have two spherical mirrors and two flat mirrors, where the radius of curvature of the spherical mirrors is 50 mm. One of the flat mirrors has partial transmittance (PT) at 860 nm and is used as a coupling mirror. 9.5 mm and 8 mm-long PPMgLN crystals whose temperature is controlled around 50°C are placed between the two spherical mirrors of the OPO and the frequency doubler, respectively. The round trip length of the cavities is about 500 mm which yields the beam waist size of 21 *µ*m in radius at the crystal center.

## 3. Characterization of PPMgLN crystal

Firstly we characterized the effective nonlinearity *E _{NL}* of the PPMgLN crystal and the intracavity loss

*L*of the OPO. These are necessary for evaluating the

*P*and

_{th}*ρ*of the OPO by using Eqs. (1) and (2). The

*E*is defined as

_{NL}*P*

_{2ω}/

*P*

^{2}

*(W*

_{ω}^{−1}) where

*P*and

_{ω}*P*

_{2ω}are the power of fundamental wave and second harmonic respectively with single pass frequency doubling. We obtained the

*E*of 0.043 (W

_{NL}^{−1}) which is two times larger than the previously reported ones for KNbO

_{3}and PPKTP under the similar focusing condition [3, 4] and one-order higher than that of MgLM [6] as shown in Table 1. This is caused by the high nonlinearity of the PPMgLN crystal. Theoretical estimation of the effective nonlinear optical coefficient,

*d*= (2/

_{eff}*π*)

*d*

_{33}, from the observed

*E*by using the well-known theory of Boyd and Kleinman [13] yields 15 (pm/V) which reasonably agrees with the previously reported value [14]. A slight difference might be caused by imperfection of the periodically poled structure. By utilizing high nonlinearity of the PPMgLN crystal we also constructed the frequency doubler with a coupling mirror whose transmittance is 0.10. We achieved the second harmonic power of 400 mW from fundamental wave power of 570 mW which corresponds to the conversion efficiency of 70% as shown in Fig. 3.

_{NL}Next we evaluated the intracavity loss *L* of the OPO by injecting a weak coherent beam from the output coupler. The analysis shows the loss without a pump beam is 0.011, which is rather high compared to the previously reported crystals and might be caused by imperfection of the periodically poled structure. The intracavity loss increases up to 0.022 at the pump power of 350 mW probably due to BLIIRA and/or photo-refractive effect. The experimental results can be expressed as a following equation

where *L*
_{0} is a passive loss without the pump beam and *a* is a coefficient of pump induced losses and they are calculated as *L*
_{0} = 0.0124 and *a* = 0.0246 (W^{−1}), respectively.

A detailed analysis of the passive loss *L*
_{0} is following. Losses caused by imperfection of an antireflective coating of crystal surfaces and highly reflective mirrors are 0.002 and 0.0005, respectively. Absorption or scattering losses in the MgLN bulk crystal are 0.0015. Residual 0.007 losses are induced by periodically poling which is confirmed by direct comparison between with and without periodically poling.

We calculated the *P _{th}* of the OPO from the parametric gain when a weak coherent light (probe beam) was introduced from the highly reflective (HR) mirror of the OPO. At that time the resonance of the OPO was locked by using a counter-propagating lock beam. When we used the output coupler with transmittance of 0.113, the

*P*was estimated as 110 mW which was much lower than the previous works regardless of the large intracavity losses. This is again because of the high nonlinearity of the PPMgLN crystal. High nonlinearity allows us to use high transmittance of output coupler to improve the

_{th}*ρ*. On the other hand, too much high transmittance causes increase of the

*P*. So we have to chose the transmittance in order to maximize the

_{th}*ρ*for generating highly squeezed light under the condition that the

*P*does not exceed the available pump power.

_{th}For optimizing *T* we need to revise the expression of *P _{th}* and

*ρ*when the intracavity loss increases as the pump power. The

*P*depends on the loss

_{th}*L*, which is described as

*L*(

*P*) =

_{th}*L*

_{0}+

*aP*by using Eq. (3). By substituting

_{th}*L*(

*P*) for

_{th}*L*in the Eq. (1), the

*P*can be derived by a self-consistent analysis and given by

_{th}We can rewrite the *ρ* of Eq. (2) as

where *L*
_{0} + *aP _{th}x*

^{2}is an alternative expression of the

*L*by using normalized pump parameter $x=\sqrt{\frac{{P}_{2\omega}}{{P}_{\mathrm{th}}}}$ . We calculate the value of

*P*and ρ by using current experimental parameters

_{th}*E*,

_{NL}*L*

_{0}, and

*a*in Eqs. (4) and (5). The results are shown in Fig. 4(a) and 4(b) as a function of

*T*. At lower

*x*[Fig. 4(b)(i)–(ii)], the

*ρ*improves monotonically by using a higher

*T*. However, at higher

*x*[Fig. 4(b)(iii)], the

*ρ*starts to degrade due to the increase of intracavity losses caused by high pump power. As a result there is an optimum transmittance

*T*which maximizes the

_{opt}*ρ*at

*x*= 1. Theoretical formula of

*T*can be derived under the condition of

_{opt}*dρ*/

*dT*= 0 at

*x*= 1 and expressed as

The current experimental parameters result in 0.27 as the *T _{opt}*. We decided to use 0.21 of

*T*which gives us nearly optimum value of the

*ρ*of 0.91 in Fig. 4(b) (iii). Although the observed

*P*increased up to 377mW with

_{th}*T*= 0.21 as shown in Fig. 4(a), it was still below the maximum power from our frequency doubler. Another advantage of using higher

*T*is broadening of a cavity bandwidth of the OPO which enables us to obtain higher squeezing level even at 2 MHz without degradation caused by detuning, where the noise level of our laser is almost shot-noise level at 2 MHz.

## 4. Squeezing experiment and discussions

Figure 5 shows typical results of the squeezing experiment at pump power of 200 mW. The noise level is measured with a spectrum analyzer in zero-span mode with the resolution bandwidth of 30 kHz and the video bandwidth of 300 Hz. The shot-noise level is 26 dB above the circuit noise of the homodyne detector. The observed squeezing level is −7.60±0.15dB and antisqueezing level is +13.97±0.10dB, respectively.

We continued above experiment at several pump powers and the results are summarized in Fig. 6. The squeezing level saturates at the higher pump power. To explain this result we calculated theoretical values of the squeezing and antisqueezing by using the same analysis described in references [3, 5]. The noise levels *R*
_{±} for the antisqueezed (+) and squeezed (−) quadrature can be modeled as

where *α* is homodyne detection efficiency and *f* is a detuning factor. In the current setup, *α* = 0.968 and *f* = 0.165. Taking account of phase fluctuation *$\tilde{\theta}$* of the LO for homodyne measurement, the theoretical squeezing and antisqueezing levels are modified as

In Fig. 6, theoretical curves with the intracavity losses expressed as Eq. (3) and the phase fluctuation of 1.5° agree well with the observed values. So it is concluded that the squeezing level is limited by the intracavity losses and the phase fluctuation of the LO at the moment.

Although we had a problem with large intracavity losses at the moment, we achieved high nonlinearity of optical medium by utilizing the largest nonlinear optical coefficient *d*
_{33} of MgLN crystal. With the PPMgLN crystal the oscillation threshold *P _{th}* was improved to less than half compared with the MgLN monolithic OPO [6] even with the higher transmittance of output coupler of

*T*= 0.21, as shown in Table 1. The high nonlinearity allows us to use higher

*T*which is essentially important to improve the escape efficiency

*ρ*. If we could reduce the intracavity losses to 0.0038 which is the same as that of the OPO with PPKTP [5] by improving a periodically poled structure and using better coatings, the

*ρ*would be 0.982 with

*T*= 0.21 and the squeezing level of −10 dB would be expected. If we could reduce the intracavity losses to 0.001, the

*ρ*would be 0.995 with

*T*= 0.21, where 0.001 of intracavity losses is the same as that of the MgLN monolithic OPO [6]. Moreover, if we could suppress the phase fluctuation to negligibly small as reported in Ref. [6], the squeezing level of −13 dB would be expected.

## 5. Conclusion

In conclusion, high nonlinearity was realized by fabricating a periodically poled MgO:LiNbO_{3} crystal for utilizing the large nonlinear optical coefficient *d*
_{33}. We achieved the squeezing level of −7.60±0.15dB and antisqueezing level of +13.97±0.10dB respectively with the PPMgLN crystal. We also generated 400 mW of second harmonic waves at 430 nm with 70% of conversion efficiency by using the PPMgLN crystal. To achieve higher squeezing levels we need to reduce the intracavity losses by improving a periodically poled structure and coatings, and to suppress the phase fluctuation in future work.

## Acknowledgments

This work is partly supported by SCF, GIA, G-COE, PFN, and FIRST commissioned by the MEXT, RFOST, and SCOPE of the MIC.

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