Abstract

Long-term stable entanglement is a crucial aspect in the implementation of reliable quantum information processes. However, long-term continuous variable entanglement generation, especially in type-II non-degenerate optical parametric amplifier, has yet to be reported on. Here, we derive the relationship between entanglement and temperature fluctuations in the crystal of a type-II non-degenerate optical parametric amplifier, and propose a novel method for long-term stable entanglement generation by locking the temperature of the crystal. In the experiment, we obtain a 5.4 dB entanglement lasting two hours. The method holds promise in the generation of a truly usable above 10 dB entanglement and brings us closer to continuous-variable quantum information processing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  40. H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8(4), 333–338 (2014).
    [Crossref]

2018 (1)

P. C. Humphreys, N. Kalb, J. P. Morits, R. N. Schouten, R. F. Vermeulen, D. J. Twitchen, M. Markham, and R. Hanson, “Deterministic delivery of remote entanglement on a quantum network,” Nature 558(7709), 268–273 (2018).
[Crossref]

2017 (2)

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through epr entanglement,” Nat. Phys. 13(8), 776–780 (2017).
[Crossref]

W. Yang, S. Shi, Y. Wang, W. Ma, Y. Zheng, and K. Peng, “Detection of stably bright squeezed light with the quantum noise reduction of 12.6 db by mutually compensating the phase fluctuations,” Opt. Lett. 42(21), 4553–4556 (2017).
[Crossref]

2015 (1)

2014 (1)

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8(4), 333–338 (2014).
[Crossref]

2013 (3)

X. Su, S. Hao, X. Deng, L. Ma, M. Wang, X. Jia, C. Xie, and K. Peng, “Gate sequence for continuous variable one-way quantum computation,” Nat. Commun. 4(1), 2828 (2013).
[Crossref]

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

F. Feng, S. wen Bi, B. zhu Lu, and M. hua Kang, “Long-term stable bright amplitude-squeezed state of light at 1064 nm for quantum imaging,” Optik (Munich, Ger.) 124(11), 1070–1073 (2013).
[Crossref]

2012 (2)

A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Classical Quantum Gravity 29(7), 075001 (2012).
[Crossref]

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3(1), 1083 (2012).
[Crossref]

2011 (2)

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong einstein-podolsky-rosen entanglement from a single squeezed light source,” Phys. Rev. A 83(5), 052329 (2011).
[Crossref]

M. Vainio and L. Halonen, “Stable operation of a cw optical parametric oscillator near the signal–idler degeneracy,” Opt. Lett. 36(4), 475–477 (2011).
[Crossref]

2010 (1)

2009 (1)

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[Crossref]

2008 (2)

R. Schnabel, “Gravitational wave detectors: Squeezing up the sensitivity,” Nat. Phys. 4(6), 440–441 (2008).
[Crossref]

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

2006 (2)

N. C. Menicucci, P. Van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97(11), 110501 (2006).
[Crossref]

K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Nonlinear phase matching locking via optical readout,” Opt. Express 14(23), 11256–11264 (2006).
[Crossref]

2005 (3)

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]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power-and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref]

G.-f. Zhang, S.-s. Li, and J.-q. Liang, “Thermal entanglement in spin-1 biparticle system,” Opt. Commun. 245(1-6), 457–463 (2005).
[Crossref]

2004 (2)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306(5700), 1330–1336 (2004).
[Crossref]

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431(7007), 430–433 (2004).
[Crossref]

2002 (1)

K. McKenzie, D. A. Shaddock, D. E. McClelland, B. C. Buchler, and P. K. Lam, “Experimental demonstration of a squeezing-enhanced power-recycled michelson interferometer for gravitational wave detection,” Phys. Rev. Lett. 88(23), 231102 (2002).
[Crossref]

2001 (2)

B. Julsgaard, A. Kozhekin, and E. S. Polzik, “Experimental long-lived entanglement of two macroscopic objects,” Nature 413(6854), 400–403 (2001).
[Crossref]

E. D. Black, “An introduction to pound–drever–hall laser frequency stabilization,” Am. J. Phys. 69(1), 79–87 (2001).
[Crossref]

2000 (1)

Y. T. Liu and K. S. Thorne, “Thermoelastic noise and homogeneous thermal noise in finite sized gravitational-wave test masses,” Phys. Rev. D 62(12), 122002 (2000).
[Crossref]

1999 (1)

V. Braginsky, M. Gorodetsky, and S. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,” Phys. Lett. A 264(1), 1–10 (1999).
[Crossref]

1998 (1)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref]

1997 (1)

R. Bruckmeier, H. Hansen, and S. Schiller, “Repeated quantum nondemolition measurements of continuous optical waves,” Phys. Rev. Lett. 79(8), 1463–1466 (1997).
[Crossref]

1996 (1)

1995 (1)

A. Henderson, M. Padgett, F. Colville, J. Zhang, and M. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119(1-2), 256–264 (1995).
[Crossref]

1993 (1)

1990 (2)

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and W. Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2(2), 159–187 (1990).
[Crossref]

M. Innocenzi, H. Yura, C. Fincher, and R. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[Crossref]

1986 (1)

A. E. Siegman, “Lasers university science books,” Mill Val. CA 37, 169 (1986).

1983 (1)

R. Drever, J. L. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31(2), 97–105 (1983).
[Crossref]

Adhikari, R.

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4(6), 472–476 (2008).
[Crossref]

Andersen, U. L.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3(1), 1083 (2012).
[Crossref]

Aoki, T.

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431(7007), 430–433 (2004).
[Crossref]

Aolita, L.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

Assad, S. M.

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8(4), 333–338 (2014).
[Crossref]

Ã-zisik, M. N.

M. N. Ã-zisik, M. N. Özísík, and M. N. Özíşík, Heat conduction (John Wiley, 1993).

Ballato, J.

M. C. Gupta and J. Ballato, The handbook of photonics (Taylor & Francis, New York, 2018).

Black, E. D.

E. D. Black, “An introduction to pound–drever–hall laser frequency stabilization,” Am. J. Phys. 69(1), 79–87 (2001).
[Crossref]

Braginsky, V.

V. Braginsky, M. Gorodetsky, and S. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,” Phys. Lett. A 264(1), 1–10 (1999).
[Crossref]

Braunstein, S. L.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref]

Bruckmeier, R.

R. Bruckmeier, H. Hansen, and S. Schiller, “Repeated quantum nondemolition measurements of continuous optical waves,” Phys. Rev. Lett. 79(8), 1463–1466 (1997).
[Crossref]

K. Schneider, R. Bruckmeier, H. Hansen, S. Schiller, and J. Mlynek, “Bright squeezed-light generation by a continuous-wave semimonolithic parametric amplifier,” Opt. Lett. 21(17), 1396–1398 (1996).
[Crossref]

Buchler, B. C.

K. McKenzie, D. A. Shaddock, D. E. McClelland, B. C. Buchler, and P. K. Lam, “Experimental demonstration of a squeezing-enhanced power-recycled michelson interferometer for gravitational wave detection,” Phys. Rev. Lett. 88(23), 231102 (2002).
[Crossref]

Cerf, N. J.

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[Crossref]

Chelkowski, S.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power-and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref]

Chen, Y.

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through epr entanglement,” Nat. Phys. 13(8), 776–780 (2017).
[Crossref]

Chrzanowski, H. M.

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8(4), 333–338 (2014).
[Crossref]

Colville, F.

A. Henderson, M. Padgett, F. Colville, J. Zhang, and M. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119(1-2), 256–264 (1995).
[Crossref]

D’ambrosio, V.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

Danzmann, K.

A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Classical Quantum Gravity 29(7), 075001 (2012).
[Crossref]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power-and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref]

Debuisschert, T.

Del Re, L.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
[Crossref]

Deng, X.

X. Su, S. Hao, X. Deng, L. Ma, M. Wang, X. Jia, C. Xie, and K. Peng, “Gate sequence for continuous variable one-way quantum computation,” Nat. Commun. 4(1), 2828 (2013).
[Crossref]

Drever, R.

R. Drever, J. L. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31(2), 97–105 (1983).
[Crossref]

Duhme, J.

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong einstein-podolsky-rosen entanglement from a single squeezed light source,” Phys. Rev. A 83(5), 052329 (2011).
[Crossref]

Dunn, M.

A. Henderson, M. Padgett, F. Colville, J. Zhang, and M. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119(1-2), 256–264 (1995).
[Crossref]

Eberle, T.

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong einstein-podolsky-rosen entanglement from a single squeezed light source,” Phys. Rev. A 83(5), 052329 (2011).
[Crossref]

Evans, M.

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through epr entanglement,” Nat. Phys. 13(8), 776–780 (2017).
[Crossref]

Fabre, C.

T. Debuisschert, A. Sizmann, E. Giacobino, and C. Fabre, “Type-ii continuous-wave optical parametric oscillators: oscillation and frequency-tuning characteristics,” J. Opt. Soc. Am. B 10(9), 1668–1680 (1993).
[Crossref]

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and W. Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2(2), 159–187 (1990).
[Crossref]

Feng, F.

F. Feng, S. wen Bi, B. zhu Lu, and M. hua Kang, “Long-term stable bright amplitude-squeezed state of light at 1064 nm for quantum imaging,” Optik (Munich, Ger.) 124(11), 1070–1073 (2013).
[Crossref]

Fields, R.

M. Innocenzi, H. Yura, C. Fincher, and R. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[Crossref]

Filip, R.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3(1), 1083 (2012).
[Crossref]

Fincher, C.

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V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(1), 2432 (2013).
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Nat. Photonics (1)

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8(4), 333–338 (2014).
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Nat. Phys. (3)

Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, “Proposal for gravitational-wave detection beyond the standard quantum limit through epr entanglement,” Nat. Phys. 13(8), 776–780 (2017).
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Nature (3)

P. C. Humphreys, N. Kalb, J. P. Morits, R. N. Schouten, R. F. Vermeulen, D. J. Twitchen, M. Markham, and R. Hanson, “Deterministic delivery of remote entanglement on a quantum network,” Nature 558(7709), 268–273 (2018).
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B. Julsgaard, A. Kozhekin, and E. S. Polzik, “Experimental long-lived entanglement of two macroscopic objects,” Nature 413(6854), 400–403 (2001).
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H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431(7007), 430–433 (2004).
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Opt. Commun. (2)

G.-f. Zhang, S.-s. Li, and J.-q. Liang, “Thermal entanglement in spin-1 biparticle system,” Opt. Commun. 245(1-6), 457–463 (2005).
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Opt. Express (3)

Opt. Lett. (3)

Optik (Munich, Ger.) (1)

F. Feng, S. wen Bi, B. zhu Lu, and M. hua Kang, “Long-term stable bright amplitude-squeezed state of light at 1064 nm for quantum imaging,” Optik (Munich, Ger.) 124(11), 1070–1073 (2013).
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Phys. Lett. A (1)

V. Braginsky, M. Gorodetsky, and S. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,” Phys. Lett. A 264(1), 1–10 (1999).
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Phys. Rev. A (2)

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).
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Phys. Rev. D (1)

Y. T. Liu and K. S. Thorne, “Thermoelastic noise and homogeneous thermal noise in finite sized gravitational-wave test masses,” Phys. Rev. D 62(12), 122002 (2000).
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Phys. Rev. Lett. (5)

N. C. Menicucci, P. Van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97(11), 110501 (2006).
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K. McKenzie, D. A. Shaddock, D. E. McClelland, B. C. Buchler, and P. K. Lam, “Experimental demonstration of a squeezing-enhanced power-recycled michelson interferometer for gravitational wave detection,” Phys. Rev. Lett. 88(23), 231102 (2002).
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Quantum Opt. (1)

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and W. Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2(2), 159–187 (1990).
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Science (2)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306(5700), 1330–1336 (2004).
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M. C. Gupta and J. Ballato, The handbook of photonics (Taylor & Francis, New York, 2018).

D. F. Walls and G. J. Milburn, Quantum optics (Springer, 2007).

M. N. Ã-zisik, M. N. Özísík, and M. N. Özíşík, Heat conduction (John Wiley, 1993).

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Figures (7)

Fig. 1.
Fig. 1. Entanglement as a function of crystal temperature fluctuation. The solid curve, dashed curve and dash-dotted curve indicate that the entanglement is 10 dB, 5.4 dB and 3 dB respectively when there is no crystal temperature fluctuation. The parameter values used are: $\lambda = 1080 nm$, $n = 1.7$, ${L_c} = 10 mm$, $\gamma = 6.0 \times {10^7}{s^{ - 1}}$, $\frac {{d{n_s}}}{{dT}} = 1.6 \times {10^{ - 5}}{K^{ - 1}}$, $\frac {{d{n_i}}}{{dT}} = 1.3 \times {10^{ - 5}}{K^{ - 1}}$, ${b_s} = 0.6 \times {10^{ - 6}}{K^{ - 1}}$, ${b_i} = 9 \times {10^{ - 6}}{K^{ - 1}}$, and $\sigma = 0.8$
Fig. 2.
Fig. 2. Schematic of the experimental setup. RF: Radio frequency source; PM: Phase modulator; PID: Proportional integral derivative controller; VCO: Voltage controlled oscillator; AOM: Acousto-optic modulator; PD: Photoelectric detector; TFL: temperature feedback loop; SA: spectrum analyzer; BHD: balanced homodyne detector; HWP: Half wave plate.
Fig. 3.
Fig. 3. Transmitted power of the idler field and crystal temperature locking error signal as a function of temperature fluctuation obtained from theory and experiments: (a) and (b) transmission of the idler field, (c) and (d) associated crystal temperature locking error signal. Parameters values used are: $t_1=0.1 \%$, $t_2=5.4 \%$, absorption coefficient of KTP: 0.8 %/cm, thermal conductivity of KTP: 0.13 W/cm*K, spot size of control field: 40 $\mu m$, spot size of idler field: 56 $\mu m$. For other parameter settings, see Fig. 1.
Fig. 4.
Fig. 4. Parametric gain behavior as a function of time, normalized by the resonant power without parametric gain.
Fig. 5.
Fig. 5. Comparison of stability performance for entanglement without and with the crystal temperature locking. (a) amplitude-sum squeezing. (b) phase-difference squeezing. The measurement parameters of spectrum analyzer: RBW: 100 kHz, VBW: 100 Hz. Analysis frequency: 3 MHz.
Fig. 6.
Fig. 6. Measured transfer function of the TFL. (a) Magnitude and (b) Phase of the transfer function.
Fig. 7.
Fig. 7. Long-term entanglement recorded continuously for 2 hours. (a) amplitude-sum squeezing, (b) phase-difference squeezing. The measurement parameters of spectrum analyzer: RBW: 100 kHz, VBW: 100 Hz. Analysis frequency: 3 MHz.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

a ^ ˙ s = γ a ^ s + χ a p a ^ i + 2 γ a ^ s i n
a ^ ˙ i = γ ( 1 i Δ ) a ^ i + χ a p a ^ s + 2 γ a ^ i i n .
| δ X ^ i o u t + δ X ^ s o u t | 2 = | δ Y ^ i o u t δ Y ^ s o u t | 2 = 1 4 σ ( σ 1 ) 2 Δ 2 + ( σ 1 ) 2
Δ = 2 π υ F S R Δ L λ γ
Δ L = n L c [ ( 1 n ( d n i d T d n s d T ) + ( b i b s ) ) ] δ T
Δ = 2 π υ F S R 1 λ γ n L c [ ( 1 n ( d n i d T d n s d T ) + ( b i b s ) ) ] δ T
Γ ( Δ ) = 2 t 1 2 τ t 2 2 τ / 2 t 1 2 τ t 2 2 τ ( t 1 + t 2 2 τ + ( t 1 + t 2 2 τ + i Δ )
Υ ( Δ ) = ( t 1 τ t 1 + t 2 2 τ i Δ ) / ( t 1 τ t 1 + t 2 2 τ i Δ ) ( t 1 + t 2 2 τ + ( t 1 + t 2 2 τ + i Δ )
V Im ( Υ ( Δ ) Υ ( Δ + ω n ) Υ ( Δ ) Υ ( Δ ω n ) )

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