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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 16 — Jul. 30, 2012
  • pp: 18173–18179
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Low-frequency phase measurement with high-frequency squeezing

Zehui Zhai and Jiangrui Gao  »View Author Affiliations


Optics Express, Vol. 20, Issue 16, pp. 18173-18179 (2012)
http://dx.doi.org/10.1364/OE.20.018173


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Abstract

Squeezed-state enhanced audio-frequency signal measurement is crucial for some special applications, such as gravitational wave detection. But generation of squeezed state of light at such frequency is more difficult than that at megahertz-frequency. In this paper we propose an experimental scheme to measure low-frequency phase signal with high-frequency squeezing. To utilize the high-frequency sidebands of the squeezed light, a two-frequency intense laser is applied in the interferometry instead of a single-frequency laser as usual. This technique is in the reach of modern quantum optics technology.

© 2012 OSA

Introduction

The concept of radiation field squeezing [1

1. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

] has attracted much interest since its application to gravitational wave detection was proposed [2

2. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D Part. Fields 23(8), 1693–1708 (1981). [CrossRef]

]. This sort of radiation field was first generated with a four-wave mixing process by Slusher et al [3

3. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985). [CrossRef] [PubMed]

] and improved with an optical parametric oscillator (OPO) by Wu et al [4

4. L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57(20), 2520–2523 (1986). [CrossRef] [PubMed]

]. It has been useful in various quantum-enhanced measurement schemes, such as squeezed-light magnetometry [5

5. F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, “Squeezed-light optical magnetometry,” Phys. Rev. Lett. 105(5), 053601 (2010). [CrossRef] [PubMed]

], displacement measurement [6

6. N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maître, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett. 88(20), 203601 (2002). [CrossRef] [PubMed]

], spectroscopy [7

7. E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68(20), 3020–3023 (1992). [CrossRef] [PubMed]

], polarization measurement [8

8. P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light-enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987). [CrossRef] [PubMed]

], phase measurement [9

9. M. Xiao, L.-A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987). [CrossRef] [PubMed]

], and so on. Squeezed states of light are also vital ingredients for continuous-variable quantum communication and quantum computation [10

10. S. L. Braunstein and A. K. Pati, eds., Quantum Information with Continuous Variables (Kluwer Academic, 2003).

]. In some applications, such as gravitational wave detection, it is appealing to measure low-frequency signals with a squeezed light state [11

11. R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1(8), 121 (2010). [CrossRef]

]. Low-frequency squeezing has attracted much interest in recent years as terrestrial gravitational wave detectors (GW-detectors) are approaching their shot noise limit, which has been successfully overcome with squeezing at audio frequencies very recently [12

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Campsie, J. Cannizzo, K. Cannon, J. Cao, C. D. Capano, S. Caride, S. Caudill, M. Cavagliá, C. Cepeda, T. Chalermsongsak, E. Chalkley, P. Charlton, S. Chelkowski, Y. Chen, N. Christensen, H. Cho, S. S. Y. Chua, S. Chung, C. T. Y. Chung, G. Ciani, F. Clara, D. E. Clark, J. Clark, J. H. Clayton, R. Conte, D. Cook, T. R. Corbitt, M. Cordier, N. Cornish, A. Corsi, C. A. Costa, M. Coughlin, P. Couvares, D. M. Coward, D. C. Coyne, J. D. E. Creighton, T. D. Creighton, A. M. Cruise, A. Cumming, L. Cunningham, R. M. Cutler, K. Dahl, S. L. Danilishin, R. Dannenberg, K. Danzmann, B. Daudert, H. Daveloza, G. Davies, E. J. Daw, T. Dayanga, D. DeBra, J. Degallaix, T. Dent, V. Dergachev, R. DeRosa, R. DeSalvo, S. Dhurandhar, J. DiGuglielmo, I. Di Palma, M. Díaz, F. Donovan, K. L. Dooley, S. Dorsher, R. W. P. Drever, J. C. Driggers, Z. Du, J.-C. Dumas, S. Dwyer, T. Eberle, M. Edgar, M. Edwards, A. Effler, P. Ehrens, R. Engel, T. Etzel, K. Evans, M. Evans, T. Evans, M. Factourovich, S. Fairhurst, Y. 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J. Howell, B. Hughey, T. Huynh-Dinh, S. Husa, S. H. Huttner, D. R. Ingram, R. Inta, T. Isogai, A. Ivanov, K. Izumi, M. Jacobson, H. Jang, W. W. Johnson, D. I. Jones, G. Jones, R. Jones, L. Ju, P. Kalmus, V. Kalogera, I. Kamaretsos, S. Kandhasamy, G. Kang, J. B. Kanner, E. Katsavounidis, W. Katzman, H. Kaufer, K. Kawabe, S. Kawamura, F. Kawazoe, W. Kells, D. G. Keppel, Z. Keresztes, A. Khalaidovski, F. Y. Khalili, E. A. Khazanov, B. Kim, C. Kim, D. Kim, H. Kim, K. Kim, N. Kim, Y.-M. Kim, P. J. King, M. Kinsey, D. L. Kinzel, J. S. Kissel, S. Klimenko, K. Kokeyama, V. Kondrashov, R. Kopparapu, S. Koranda, W. Z. Korth, D. Kozak, V. Kringel, S. Krishnamurthy, B. Krishnan, G. Kuehn, R. Kumar, P. Kwee, P. K. Lam, M. Landry, M. Lang, B. Lantz, N. Lastzka, C. Lawrie, A. Lazzarini, P. Leaci, C. H. Lee, H. M. Lee, N. Leindecker, J. R. Leong, I. Leonor, J. Li, P. E. Lindquist, N. A. Lockerbie, D. Lodhia, M. Lormand, J. Luan, M. Lubinski, H. Lück, A. P. Lundgren, E. Macdonald, B. Machenschalk, M. MacInnis, D. M. Macleod, M. Mageswaran, K. Mailand, I. Mandel, V. Mandic, A. Marandi, S. Márka, Z. Márka, A. Markosyan, E. Maros, I. W. Martin, R. M. Martin, J. N. Marx, K. Mason, F. Matichard, L. Matone, R. A. Matzner, N. Mavalvala, G. Mazzolo, R. McCarthy, D. E. McClelland, S. C. McGuire, G. McIntyre, J. McIver, D. J. A. McKechan, G. D. Meadors, M. Mehmet, T. Meier, A. Melatos, A. C. Melissinos, G. Mendell, D. Menendez, R. A. Mercer, S. Meshkov, C. Messenger, M. S. Meyer, H. Miao, J. Miller, V. P. Mitrofanov, G. Mitselmakher, R. Mittleman, O. Miyakawa, B. Moe, P. Moesta, S. D. Mohanty, D. Moraru, G. Moreno, T. Mori, K. Mossavi, C. M. Mow-Lowry, C. L. Mueller, G. Mueller, S. Mukherjee, A. Mullavey, H. Müller-Ebhardt, J. Munch, D. Murphy, P. G. Murray, A. Mytidis, T. Nash, R. Nawrodt, V. Necula, J. Nelson, G. Newton, A. Nishizawa, D. Nolting, L. Nuttall, J. O’Dell, B. O’Reilly, R. O’Shaughnessy, E. Ochsner, E. Oelker, J. J. Oh, S. H. Oh, G. H. Ogin, R. G. Oldenburg, C. Osthelder, C. 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Savage, R. Schilling, S. Schlamminger, R. Schnabel, R. M. S. Schofield, B. Schulz, B. F. Schutz, P. Schwinberg, J. Scott, S. M. Scott, A. C. Searle, F. Seifert, D. Sellers, A. S. Sengupta, A. Sergeev, D. A. Shaddock, M. Shaltev, B. Shapiro, P. Shawhan, D. H. Shoemaker, A. Sibley, X. Siemens, D. Sigg, A. Singer, L. Singer, A. M. Sintes, G. Skelton, B. J. J. Slagmolen, J. Slutsky, R. J. E. Smith, J. R. Smith, M. R. Smith, N. D. Smith, K. Somiya, B. Sorazu, J. Soto, F. C. Speirits, A. J. Stein, E. Steinert, J. Steinlechner, S. Steinlechner, S. Steplewski, M. Stefszky, A. Stochino, R. Stone, K. A. Strain, S. Strigin, A. S. Stroeer, A. L. Stuver, T. Z. Summerscales, M. Sung, S. Susmithan, P. J. Sutton, D. Talukder, D. B. Tanner, S. P. Tarabrin, J. R. Taylor, R. Taylor, P. Thomas, K. A. Thorne, K. S. Thorne, E. Thrane, A. Thüring, C. Titsler, K. V. Tokmakov, C. Torres, C. I. Torrie, G. Traylor, M. Trias, K. Tseng, D. Ugolini, K. Urbanek, H. Vahlbruch, M. Vallisneri, A. A. van Veggel, S. Vass, R. Vaulin, A. Vecchio, J. Veitch, P. J. Veitch, C. Veltkamp, A. E. Villar, S. Vitale, C. Vorvick, S. P. Vyatchanin, A. Wade, S. J. Waldman, L. Wallace, Y. Wan, A. Wanner, X. Wang, Z. Wang, R. L. Ward, P. Wei, M. Weinert, A. J. Weinstein, R. Weiss, L. Wen, S. Wen, P. Wessels, M. West, T. Westphal, K. Wette, J. T. Whelan, S. E. Whitcomb, D. White, B. F. Whiting, C. Wilkinson, P. A. Willems, H. R. Williams, L. Williams, B. Willke, L. Winkelmann, W. Winkler, C. C. Wipf, H. Wittel, A. G. Wiseman, G. Woan, R. Wooley, J. Worden, J. Yablon, I. Yakushin, K. Yamamoto, H. Yamamoto, H. Yang, D. Yeaton-Massey, S. Yoshida, P. Yu, M. Zanolin, L. Zhang, W. Zhang, Z. Zhang, C. Zhao, N. Zotov, M. E. Zucker, and J. ZweizigJ. AbadieB. P. AbbottR. AbbottT. D. AbbottM. AbernathyC. AdamsR. AdhikariC. AffeldtB. AllenG. S. AllenE. Amador CeronD. AmariuteiR. S. AminS. B. AndersonW. G. AndersonK. AraiM. A. ArainM. C. ArayaS. M. AstonD. AtkinsonP. AufmuthC. AulbertB. E. AylottS. BabakP. BakerS. BallmerD. 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PankowM. A. PapaP. AjithP. PatelM. PedrazaP. PeirisL. PekowskyS. PennC. PeraltaA. PerrecaM. PhelpsM. PickenpackI. M. PintoM. PitkinH. J. PletschM. V. PlissiJ. PöldF. PostiglioneV. PredoiL. R. PriceM. PrijateljM. PrincipeS. PriviteraR. PrixL. ProkhorovO. PunckenV. QuetschkeF. J. RaabH. RadkinsP. RaffaiM. RakhmanovC. R. RametB. RankinsS. R. P. MohapatraV. RaymondK. RedwineC. M. ReedT. ReedS. ReidD. H. ReitzeR. RiesenK. RilesN. A. RobertsonC. RobinsonE. L. RobinsonS. RoddyC. RodriguezM. RodruckJ. RollinsJ. D. RomanoJ. H. RomieC. RöverS. RowanA. RüdigerK. RyanH. RyllP. SainathanM. SakoskyF. SalemiA. SamblowskiL. SammutL. Sancho de la JordanaV. SandbergS. SankarV. SannibaleL. SantamaríaI. Santiago-PrietoG. SantostasiB. S. SathyaprakashS. SatoP. R. SaulsonR. L. SavageR. SchillingS. SchlammingerR. SchnabelR. M. S. SchofieldB. SchulzB. F. SchutzP. SchwinbergJ. ScottS. M. ScottA. C. SearleF. SeifertD. SellersA. S. SenguptaA. SergeevD. A. ShaddockM. ShaltevB. ShapiroP. ShawhanD. H. ShoemakerA. 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WinklerC. C. WipfH. WittelA. G. WisemanG. WoanR. WooleyJ. WordenJ. YablonI. YakushinK. YamamotoH. YamamotoH. YangD. Yeaton-MasseyS. YoshidaP. YuM. ZanolinL. ZhangW. ZhangZ. ZhangC. ZhaoN. ZotovM. E. ZuckerJ. ZweizigThe LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7(12), 962–965 (2011). [CrossRef]

,13

13. H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gr¨af, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010). [CrossRef]

]. This experiment further enhanced confidence and passion in applying squeezed state to large scale GW-detectors. Actually great progress of generating this kind of squeezing has been made in recent years [14

14. W. P. Bowen, R. Schnabel, N. Treps, H.-A. Bachor, and P. K. Lam, “Recovery of continuous wave squeezing at low frequencies,” J. Opt. B Quantum Semiclassical Opt. 4(6), 421–424 (2002). [CrossRef]

20

20. H. Vahlbruch, S. Chelkowski, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys. 9(10), 371–378 (2007). [CrossRef]

]. It’s found that coherently controlling the phases of the experimental set-up while not to introduce extra noise is one of the keys to generate low-frequency squeezing [16

16. J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A 70(4), 042315 (2004). [CrossRef]

20

20. H. Vahlbruch, S. Chelkowski, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys. 9(10), 371–378 (2007). [CrossRef]

]. In 2007, an unprecedented experiment of generating squeezed vacuum states with a noise power 6.5 dB below vacuum noise within the entire detection bandwidth of ground-based GW-detectors (10 Hz - 10 kHz) was demonstrated by using a sophisticated control scheme [20

20. H. Vahlbruch, S. Chelkowski, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys. 9(10), 371–378 (2007). [CrossRef]

]. An alternative way to conquer this difficulty is to use two-frequency laser and broadband squeezing at higher frequency, which has been primarily used in many quantum optics laboratories, to enhance the signal-to-noise ratio (SNR) of an interferometer for lower-frequency phase measurement. When the carriers with frequencies other than central frequency of squeezed state appear in the interferometer, high-frequency squeezing sidebands will come into play. J. Gea-Banacloche and G. Leuchs [21

21. J. Gea-Banacloche and G. Leuchs, “Squeezed states for interferometric gravitational-wave detectors,” J. Mod. Opt. 34(6-7), 793–811 (1987). [CrossRef]

] theoretically showed that, in Michelson interferometers stabilized with phase modulation technique, broadband squeezing is needed. Almost at the same time, Yurke et al [22

22. B. Yurke, P. Grangier, and R. E. Slusher, “Squeezed-state enhanced two-frequency interferometry,” J. Opt. Soc. Am. B 4(10), 1677–1682 (1987). [CrossRef]

] proposed a squeezed-state enhanced two-frequency interferometer to perform sub-shot-noise measurement of low-frequency signals by reading the photocurrent at frequency 2νs(frequency interval of the two-frequency laser), well away from the low-frequency technical noise. In this study, we read low-frequency signals directly and calculate the SNR. This technique can be straightforwardly extended to the other squeezing-enhanced measurement schemes mentioned above.

Theoretical model

The physics of this scheme can be explained as follows. Instead of using a single-frequency intense laser at frequency ω0 in the interferometry, we use an intense laser with the carrier frequencies ω0Ω and ω0+Ω, with which the entangled upper and lower sidebands of vacuum squeezing interfere. Therefore, the low-frequency signal, which generates sidebands near the carrier fields, can be detected with sub-shot noise resolution, thanks to the entangled sidebands of squeezing. The terms with phase signals at frequencies w12Ω and w1+2Ω coupled to the SNR at frequency w1 in Eq. (11) originate from the beating between one of the carriers and the sidebands at w12Ω and w1+2Ω of the other carrier. It’s interesting to note that in Eq. (11) the signal appears at frequency w1 and w1±2Ω while the noise at frequency w1±Ω. This difference can be attributed to the fact that, in Mach-Zehnder interferometer, signal sidebands are generated around carrier fields while noise sidebands come from the injected squeezing.

Conclusion

We have calculated the utility of high-frequency squeezed-state enhanced two-frequency interferometry for low-frequency phase measurement. By means of a two-frequency laser interferometer, the higher-frequency sidebands of the squeezed state can be used to enhance the lower-frequency phase measurement. A proof-of-principle experiment is in the reach of modern quantum optics technology and is in progress in our laboratory. Moreover, this scheme is also useful for many other squeezing-enhanced measurement schemes, and also provides a method to generate low-frequency squeezing with high-frequency squeezing.

Acknowledgments

Zehui Zhai thanks Dabo Guo for helpful discussion. This work was supported in part by the National Science Foundation of China under Grant No. 11174189, No.60708010 and No.60978008, by the National Basic Research Program of China under Grant No.2010CB923102, and by the Open project of State Key Laboratory of Quantum Optics and Quantum Optics Devices under Grant No.200902.

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SibleyX. SiemensD. SiggA. SingerL. SingerA. M. SintesG. SkeltonB. J. J. SlagmolenJ. SlutskyR. J. E. SmithJ. R. SmithM. R. SmithN. D. SmithK. SomiyaB. SorazuJ. SotoF. C. SpeiritsA. J. SteinE. SteinertJ. SteinlechnerS. SteinlechnerS. SteplewskiM. StefszkyA. StochinoR. StoneK. A. StrainS. StriginA. S. StroeerA. L. StuverT. Z. SummerscalesM. SungS. SusmithanP. J. SuttonD. TalukderD. B. TannerS. P. TarabrinJ. R. TaylorR. TaylorP. ThomasK. A. ThorneK. S. ThorneE. ThraneA. ThüringC. TitslerK. V. TokmakovC. TorresC. I. TorrieG. TraylorM. TriasK. TsengD. UgoliniK. UrbanekH. VahlbruchM. VallisneriA. A. van VeggelS. VassR. VaulinA. VecchioJ. VeitchP. J. VeitchC. VeltkampA. E. VillarS. VitaleC. VorvickS. P. VyatchaninA. WadeS. J. WaldmanL. WallaceY. WanA. WannerX. WangZ. WangR. L. WardP. WeiM. WeinertA. J. WeinsteinR. WeissL. WenS. WenP. WesselsM. WestT. WestphalK. WetteJ. T. WhelanS. E. WhitcombD. WhiteB. F. WhitingC. WilkinsonP. A. WillemsH. R. WilliamsL. WilliamsB. WillkeL. WinkelmannW. WinklerC. C. WipfH. WittelA. G. WisemanG. WoanR. WooleyJ. WordenJ. YablonI. YakushinK. YamamotoH. YamamotoH. YangD. Yeaton-MasseyS. YoshidaP. YuM. ZanolinL. ZhangW. ZhangZ. ZhangC. ZhaoN. ZotovM. E. ZuckerJ. ZweizigThe LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7(12), 962–965 (2011). [CrossRef]

13.

H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gr¨af, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Gravity 27(8), 084027 (2010). [CrossRef]

14.

W. P. Bowen, R. Schnabel, N. Treps, H.-A. Bachor, and P. K. Lam, “Recovery of continuous wave squeezing at low frequencies,” J. Opt. B Quantum Semiclassical Opt. 4(6), 421–424 (2002). [CrossRef]

15.

R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun. 240(1-3), 185–190 (2004). [CrossRef]

16.

J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A 70(4), 042315 (2004). [CrossRef]

17.

K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 72(4), 043819 (2005). [CrossRef]

18.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Coherent control of vacuum squeezing in the gravitational-wave detection band,” Phys. Rev. Lett. 97(1), 011101 (2006). [CrossRef] [PubMed]

19.

K. Goda, E. E. Mikhailov, O. Miyakawa, S. Saraf, S. Vass, A. Weinstein, and N. Mavalvala, “Generation of a stable low-frequency squeezed vacuum field with periodically poled KTiOPO4 at 1064 nm,” Opt. Lett. 33(2), 92–94 (2008). [CrossRef] [PubMed]

20.

H. Vahlbruch, S. Chelkowski, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys. 9(10), 371–378 (2007). [CrossRef]

21.

J. Gea-Banacloche and G. Leuchs, “Squeezed states for interferometric gravitational-wave detectors,” J. Mod. Opt. 34(6-7), 793–811 (1987). [CrossRef]

22.

B. Yurke, P. Grangier, and R. E. Slusher, “Squeezed-state enhanced two-frequency interferometry,” J. Opt. Soc. Am. B 4(10), 1677–1682 (1987). [CrossRef]

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(270.0270) Quantum optics : Quantum optics
(270.6570) Quantum optics : Squeezed states

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: November 21, 2011
Revised Manuscript: December 18, 2011
Manuscript Accepted: January 27, 2012
Published: July 23, 2012

Citation
Zehui Zhai and Jiangrui Gao, "Low-frequency phase measurement with high-frequency squeezing," Opt. Express 20, 18173-18179 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-18173


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J. Howell, B. Hughey, T. Huynh-Dinh, S. Husa, S. H. Huttner, D. R. Ingram, R. Inta, T. Isogai, A. Ivanov, K. Izumi, M. Jacobson, H. Jang, W. W. Johnson, D. I. Jones, G. Jones, R. Jones, L. Ju, P. Kalmus, V. Kalogera, I. Kamaretsos, S. Kandhasamy, G. Kang, J. B. Kanner, E. Katsavounidis, W. Katzman, H. Kaufer, K. Kawabe, S. Kawamura, F. Kawazoe, W. Kells, D. G. Keppel, Z. Keresztes, A. Khalaidovski, F. Y. Khalili, E. A. Khazanov, B. Kim, C. Kim, D. Kim, H. Kim, K. Kim, N. Kim, Y.-M. Kim, P. J. King, M. Kinsey, D. L. Kinzel, J. S. Kissel, S. Klimenko, K. Kokeyama, V. Kondrashov, R. Kopparapu, S. Koranda, W. Z. Korth, D. Kozak, V. Kringel, S. Krishnamurthy, B. Krishnan, G. Kuehn, R. Kumar, P. Kwee, P. K. Lam, M. Landry, M. Lang, B. Lantz, N. Lastzka, C. Lawrie, A. Lazzarini, P. Leaci, C. H. Lee, H. M. Lee, N. Leindecker, J. R. Leong, I. Leonor, J. Li, P. E. Lindquist, N. A. Lockerbie, D. Lodhia, M. Lormand, J. Luan, M. Lubinski, H. Lück, A. P. Lundgren, E. Macdonald, B. Machenschalk, M. MacInnis, D. M. Macleod, M. Mageswaran, K. Mailand, I. Mandel, V. Mandic, A. Marandi, S. Márka, Z. Márka, A. Markosyan, E. Maros, I. W. Martin, R. M. Martin, J. N. Marx, K. Mason, F. Matichard, L. Matone, R. A. Matzner, N. Mavalvala, G. Mazzolo, R. McCarthy, D. E. McClelland, S. C. McGuire, G. McIntyre, J. McIver, D. J. A. McKechan, G. D. Meadors, M. Mehmet, T. Meier, A. Melatos, A. C. Melissinos, G. Mendell, D. Menendez, R. A. Mercer, S. Meshkov, C. Messenger, M. S. Meyer, H. Miao, J. Miller, V. P. Mitrofanov, G. Mitselmakher, R. Mittleman, O. Miyakawa, B. Moe, P. Moesta, S. D. Mohanty, D. Moraru, G. Moreno, T. Mori, K. Mossavi, C. M. Mow-Lowry, C. L. Mueller, G. Mueller, S. Mukherjee, A. Mullavey, H. Müller-Ebhardt, J. Munch, D. Murphy, P. G. Murray, A. Mytidis, T. Nash, R. Nawrodt, V. Necula, J. Nelson, G. Newton, A. Nishizawa, D. Nolting, L. Nuttall, J. O’Dell, B. O’Reilly, R. O’Shaughnessy, E. Ochsner, E. Oelker, J. J. Oh, S. H. Oh, G. H. Ogin, R. G. Oldenburg, C. Osthelder, C. D. Ott, D. J. Ottaway, R. S. Ottens, H. Overmier, B. J. Owen, A. Page, Y. Pan, C. Pankow, M. A. Papa, P. Ajith, P. Patel, M. Pedraza, P. Peiris, L. Pekowsky, S. Penn, C. Peralta, A. Perreca, M. Phelps, M. Pickenpack, I. M. Pinto, M. Pitkin, H. J. Pletsch, M. V. Plissi, J. Pöld, F. Postiglione, V. Predoi, L. R. Price, M. Prijatelj, M. Principe, S. Privitera, R. Prix, L. Prokhorov, O. Puncken, V. Quetschke, F. J. Raab, H. Radkins, P. Raffai, M. Rakhmanov, C. R. Ramet, B. Rankins, S. R. P. Mohapatra, V. Raymond, K. Redwine, C. M. Reed, T. Reed, S. Reid, D. H. Reitze, R. Riesen, K. Riles, N. A. Robertson, C. Robinson, E. L. Robinson, S. Roddy, C. Rodriguez, M. Rodruck, J. Rollins, J. D. Romano, J. H. Romie, C. Röver, S. Rowan, A. Rüdiger, K. Ryan, H. Ryll, P. Sainathan, M. Sakosky, F. Salemi, A. Samblowski, L. Sammut, L. Sancho de la Jordana, V. Sandberg, S. Sankar, V. Sannibale, L. Santamaría, I. Santiago-Prieto, G. Santostasi, B. S. Sathyaprakash, S. Sato, P. R. Saulson, R. L. 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Vass, R. Vaulin, A. Vecchio, J. Veitch, P. J. Veitch, C. Veltkamp, A. E. Villar, S. Vitale, C. Vorvick, S. P. Vyatchanin, A. Wade, S. J. Waldman, L. Wallace, Y. Wan, A. Wanner, X. Wang, Z. Wang, R. L. Ward, P. Wei, M. Weinert, A. J. Weinstein, R. Weiss, L. Wen, S. Wen, P. Wessels, M. West, T. Westphal, K. Wette, J. T. Whelan, S. E. Whitcomb, D. White, B. F. Whiting, C. Wilkinson, P. A. Willems, H. R. Williams, L. Williams, B. Willke, L. Winkelmann, W. Winkler, C. C. Wipf, H. Wittel, A. G. Wiseman, G. Woan, R. Wooley, J. Worden, J. Yablon, I. Yakushin, K. Yamamoto, H. Yamamoto, H. Yang, D. Yeaton-Massey, S. Yoshida, P. Yu, M. Zanolin, L. Zhang, W. Zhang, Z. Zhang, C. Zhao, N. Zotov, M. E. Zucker, J. Zweizig, and The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys.7(12), 962–965 (2011). [CrossRef]
  13. H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gr¨af, K. Danzmann, and R. Schnabel, “The GEO 600 squeezed light source,” Class. Quantum Gravity27(8), 084027 (2010). [CrossRef]
  14. W. P. Bowen, R. Schnabel, N. Treps, H.-A. Bachor, and P. K. Lam, “Recovery of continuous wave squeezing at low frequencies,” J. Opt. B Quantum Semiclassical Opt.4(6), 421–424 (2002). [CrossRef]
  15. R. Schnabel, H. Vahlbruch, A. Franzen, S. Chelkowski, N. Grosse, H.-A. Bachor, W. P. Bowen, P. K. Lam, and K. Danzmann, “Squeezed light at sideband frequencies below 100 kHz from a single OPA,” Opt. Commun.240(1-3), 185–190 (2004). [CrossRef]
  16. J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, “Compact source of Einstein-Podolsky-Rosen entanglement and squeezing at very low noise frequencies,” Phys. Rev. A70(4), 042315 (2004). [CrossRef]
  17. K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A72(4), 043819 (2005). [CrossRef]
  18. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Coherent control of vacuum squeezing in the gravitational-wave detection band,” Phys. Rev. Lett.97(1), 011101 (2006). [CrossRef] [PubMed]
  19. K. Goda, E. E. Mikhailov, O. Miyakawa, S. Saraf, S. Vass, A. Weinstein, and N. Mavalvala, “Generation of a stable low-frequency squeezed vacuum field with periodically poled KTiOPO4 at 1064 nm,” Opt. Lett.33(2), 92–94 (2008). [CrossRef] [PubMed]
  20. H. Vahlbruch, S. Chelkowski, K. Danzmann, and R. Schnabel, “Quantum engineering of squeezed states for quantum communication and metrology,” New J. Phys.9(10), 371–378 (2007). [CrossRef]
  21. J. Gea-Banacloche and G. Leuchs, “Squeezed states for interferometric gravitational-wave detectors,” J. Mod. Opt.34(6-7), 793–811 (1987). [CrossRef]
  22. B. Yurke, P. Grangier, and R. E. Slusher, “Squeezed-state enhanced two-frequency interferometry,” J. Opt. Soc. Am. B4(10), 1677–1682 (1987). [CrossRef]