Abstract

The continuous-variable (CV) quadratic phase gate is one of the most fundamental CV quantum gates for universal CV quantum computation, while its experimental realization still remains a challenge. Here we propose a novel and experimentally feasible scheme to realize optical CV quadratic phase gate via Faraday interaction in an atomic ensemble. The gate is performed by simply sending an optical beam three times through an atomic medium prepared in coherent spin state. The fidelity of the gate can ideally run up to one. We show that the scheme also works well as a device to generate optical polarization squeezing. Considering the noise effects due to atomic decoherence and light losses, we find that the observed fidelities of gate operation and the attainable degree of polarization squeezing are still quite high.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2013 (1)

R. Inoue, S.-I.-R. Tanaka, R. Namiki, T. Sagawa, Y. Takahashi, “Unconditional quantum-noise suppression via measurement-based quantum feedback,” Phys. Rev. Lett. 110, 163602 (2013).
[CrossRef] [PubMed]

2011 (1)

M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, Y.-Z. Zheng, “Continuous-variable controlled-z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
[CrossRef]

2010 (3)

C. M. Trail, P. S. Jessen, I. H. Deutsch, “Strongly enhanced spin squeezing via quantum control,” Phys. Rev. Lett. 105, 193602 (2010).
[CrossRef]

N. C. Menicucci, X. Ma, T. C. Ralph, “Arbitrarily large continuous-variable cluster states from a single quantum nondemolition gate,” Phys. Rev. Lett. 104, 250503 (2010).
[CrossRef] [PubMed]

K. Hammerer, A. S. Sørensen, E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[CrossRef]

2009 (5)

Y. Miwa, J.-i. Yoshikawa, P. van Loock, A. Furusawa, “Demonstration of a universal one-way quantum quadratic phase gate,” Phys. Rev. A 80, 050303 (2009).
[CrossRef]

J. Stasińska, C. Rodó, S. Paganelli, G. Birkl, A. Sanpera, “Manipulating mesoscopic multipartite entanglement with atom-light interfaces,” Phys. Rev. A 80, 062304 (2009).
[CrossRef]

T. Takano, M. Fuyama, R. Namiki, Y. Takahashi, “Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half,” Phys. Rev. Lett. 102, 033601 (2009).
[CrossRef] [PubMed]

M. Kubasik, M. Koschorreck, M. Napolitano, S. R. de Echaniz, H. Crepaz, J. Eschner, E. S. Polzik, M. W. Mitchell, “Polarization-based light-atom quantum interface with an all-optical trap,” Phys. Rev. A 79, 043815 (2009).
[CrossRef]

M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, P. van Loock, “Quantum computing with continuous-variable clusters,” Phys. Rev. A 79, 062318 (2009).
[CrossRef]

2008 (1)

T. Takano, M. Fuyama, R. Namiki, Y. Takahashi, “Continuous-variable quantum swapping gate between light and atoms,” Phys. Rev. A 78, 010307 (2008).
[CrossRef]

2007 (1)

J.-i. Yoshikawa, T. Hayashi, T. Akiyama, N. Takei, A. Huck, U. L. Andersen, A. Furusawa, “Demonstration of deterministic and high fidelity squeezing of quantum information,” Phys. Rev. A 76, 060301 (2007).
[CrossRef]

2006 (6)

J. Fiurášek, J. Sherson, T. Opatrný, E. S. Polzik, “Single-passage readout of atomic quantum memory,” Phys. Rev. A 73, 022331 (2006).
[CrossRef]

C. A. Muschik, K. Hammerer, E. S. Polzik, J. I. Cirac, “Efficient quantum memory and entanglement between light and an atomic ensemble using magnetic fields,” Phys. Rev. A 73, 062329 (2006).
[CrossRef]

J. F. Sherson, K. Mølmer, “Polarization squeezing by optical faraday rotation,” Phys. Rev. Lett. 97, 143602 (2006).
[CrossRef] [PubMed]

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

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, E. S. Polzik, “Quantum teleportation between light and matter,” Nature 443, 557–560 (2006).
[CrossRef] [PubMed]

M. Takeuchi, T. Takano, S. Ichihara, A. Yamaguchi, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Fast polarimetry system for the application to spin quantum non-demolition measurement,” Appl. Phys. B 83, 33–36 (2006).
[CrossRef]

2005 (5)

K. Hammerer, E. S. Polzik, J. I. Cirac, “Teleportation and spin squeezing utilizing multimode entanglement of light with atoms,” Phys. Rev. A 72, 052313 (2005).
[CrossRef]

M. Takeuchi, S. Ichihara, T. Takano, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin squeezing via one-axis twisting with coherent light,” Phys. Rev. Lett. 94, 023003 (2005).
[CrossRef] [PubMed]

S. L. Braunstein, P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

R. Filip, P. Marek, U. L. Andersen, “Measurement-induced continuous-variable quantum interactions,” Phys. Rev. A 71, 042308 (2005).
[CrossRef]

S. L. Braunstein, “Squeezing as an irreducible resource,” Phys. Rev. A 71, 055801 (2005).
[CrossRef]

2004 (4)

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432, 482–486 (2004).
[CrossRef] [PubMed]

E. Jeffrey, M. Brenner, P. Kwiat, “Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half,” Proc. SPIE 5161, 269–279 (2004).
[CrossRef]

K. Hammerer, K. Mølmer, E. S. Polzik, J. I. Cirac, “Light-matter quantum interface,” Phys. Rev. A 70, 044304 (2004).
[CrossRef]

L. B. Madsen, K. Mølmer, “Spin squeezing and precision probing with light and samples of atoms in the gaussian description,” Phys. Rev. A 70, 052324 (2004).
[CrossRef]

2000 (1)

L.-M. Duan, J. I. Cirac, P. Zoller, E. S. Polzik, “Quantum communication between atomic ensembles using coherent light,” Phys. Rev. Lett. 85, 5643–5646 (2000).
[CrossRef]

1999 (3)

Y. Takahashi, K. Honda, N. Tanaka, K. Toyoda, K. Ishikawa, T. Yabuzaki, “Quantum nondemolition measurement of spin via the paramagnetic faraday rotation,” Phys. Rev. A 60, 4974–4979 (1999).
[CrossRef]

A. Kuzmich, L. Mandel, J. Janis, Y. E. Young, R. Ejnisman, N. P. Bigelow, “Quantum nondemolition measurements of collective atomic spin,” Phys. Rev. A 60, 2346–2350 (1999).
[CrossRef]

S. Lloyd, S. L. Braunstein, “Quantum computation over continuous variables,” Phys. Rev. Lett. 82, 1784–1787 (1999).
[CrossRef]

1998 (2)

H. Scutaru, “Fidelity for displaced squeezed thermal states and the oscillator semigroup,” J. Phys. A 31, 3659–3663 (1998).
[CrossRef]

A. Kuzmich, N. P. Bigelow, L. Mandel, “Atomic quantum non-demolition measurements and squeezing,” Europhys. Lett. 42, 481–486 (1998).
[CrossRef]

1997 (2)

L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79, 325–328 (1997).
[CrossRef]

P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM J. Comput. 26, 1484–1509 (1997).
[CrossRef]

1996 (1)

M. G. Paris, “Displacement operator by beam splitter,” Physics Letters A 217, 78–80 (1996).
[CrossRef]

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[CrossRef] [PubMed]

1993 (3)

J. A. Levenson, I. Abram, T. Rivera, P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10, 2233–2238 (1993).
[CrossRef]

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[CrossRef] [PubMed]

J. P. Poizat, P. Grangier, “Experimental realization of a quantum optical tap,” Phys. Rev. Lett. 70, 271–274 (1993).
[CrossRef] [PubMed]

Abram, I.

J. A. Levenson, I. Abram, T. Rivera, P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10, 2233–2238 (1993).
[CrossRef]

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[CrossRef] [PubMed]

Akiyama, T.

J.-i. Yoshikawa, T. Hayashi, T. Akiyama, N. Takei, A. Huck, U. L. Andersen, A. Furusawa, “Demonstration of deterministic and high fidelity squeezing of quantum information,” Phys. Rev. A 76, 060301 (2007).
[CrossRef]

Andersen, U. L.

J.-i. Yoshikawa, T. Hayashi, T. Akiyama, N. Takei, A. Huck, U. L. Andersen, A. Furusawa, “Demonstration of deterministic and high fidelity squeezing of quantum information,” Phys. Rev. A 76, 060301 (2007).
[CrossRef]

R. Filip, P. Marek, U. L. Andersen, “Measurement-induced continuous-variable quantum interactions,” Phys. Rev. A 71, 042308 (2005).
[CrossRef]

Bernstein, H. J.

M. Reck, A. Zeilinger, H. J. Bernstein, P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[CrossRef] [PubMed]

Bertani, P.

M. Reck, A. Zeilinger, H. J. Bernstein, P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[CrossRef] [PubMed]

Bigelow, N. P.

A. Kuzmich, L. Mandel, J. Janis, Y. E. Young, R. Ejnisman, N. P. Bigelow, “Quantum nondemolition measurements of collective atomic spin,” Phys. Rev. A 60, 2346–2350 (1999).
[CrossRef]

A. Kuzmich, N. P. Bigelow, L. Mandel, “Atomic quantum non-demolition measurements and squeezing,” Europhys. Lett. 42, 481–486 (1998).
[CrossRef]

Birkl, G.

J. Stasińska, C. Rodó, S. Paganelli, G. Birkl, A. Sanpera, “Manipulating mesoscopic multipartite entanglement with atom-light interfaces,” Phys. Rev. A 80, 062304 (2009).
[CrossRef]

Braunstein, S. L.

S. L. Braunstein, “Squeezing as an irreducible resource,” Phys. Rev. A 71, 055801 (2005).
[CrossRef]

S. L. Braunstein, P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

S. Lloyd, S. L. Braunstein, “Quantum computation over continuous variables,” Phys. Rev. Lett. 82, 1784–1787 (1999).
[CrossRef]

Brenner, M.

E. Jeffrey, M. Brenner, P. Kwiat, “Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half,” Proc. SPIE 5161, 269–279 (2004).
[CrossRef]

Cirac, I.

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, E. S. Polzik, “Quantum teleportation between light and matter,” Nature 443, 557–560 (2006).
[CrossRef] [PubMed]

Cirac, J. I.

C. A. Muschik, K. Hammerer, E. S. Polzik, J. I. Cirac, “Efficient quantum memory and entanglement between light and an atomic ensemble using magnetic fields,” Phys. Rev. A 73, 062329 (2006).
[CrossRef]

K. Hammerer, E. S. Polzik, J. I. Cirac, “Teleportation and spin squeezing utilizing multimode entanglement of light with atoms,” Phys. Rev. A 72, 052313 (2005).
[CrossRef]

K. Hammerer, K. Mølmer, E. S. Polzik, J. I. Cirac, “Light-matter quantum interface,” Phys. Rev. A 70, 044304 (2004).
[CrossRef]

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432, 482–486 (2004).
[CrossRef] [PubMed]

L.-M. Duan, J. I. Cirac, P. Zoller, E. S. Polzik, “Quantum communication between atomic ensembles using coherent light,” Phys. Rev. Lett. 85, 5643–5646 (2000).
[CrossRef]

Crepaz, H.

M. Kubasik, M. Koschorreck, M. Napolitano, S. R. de Echaniz, H. Crepaz, J. Eschner, E. S. Polzik, M. W. Mitchell, “Polarization-based light-atom quantum interface with an all-optical trap,” Phys. Rev. A 79, 043815 (2009).
[CrossRef]

de Echaniz, S. R.

M. Kubasik, M. Koschorreck, M. Napolitano, S. R. de Echaniz, H. Crepaz, J. Eschner, E. S. Polzik, M. W. Mitchell, “Polarization-based light-atom quantum interface with an all-optical trap,” Phys. Rev. A 79, 043815 (2009).
[CrossRef]

Deutsch, I. H.

C. M. Trail, P. S. Jessen, I. H. Deutsch, “Strongly enhanced spin squeezing via quantum control,” Phys. Rev. Lett. 105, 193602 (2010).
[CrossRef]

Duan, L.-M.

L.-M. Duan, J. I. Cirac, P. Zoller, E. S. Polzik, “Quantum communication between atomic ensembles using coherent light,” Phys. Rev. Lett. 85, 5643–5646 (2000).
[CrossRef]

Ejnisman, R.

A. Kuzmich, L. Mandel, J. Janis, Y. E. Young, R. Ejnisman, N. P. Bigelow, “Quantum nondemolition measurements of collective atomic spin,” Phys. Rev. A 60, 2346–2350 (1999).
[CrossRef]

Eschner, J.

M. Kubasik, M. Koschorreck, M. Napolitano, S. R. de Echaniz, H. Crepaz, J. Eschner, E. S. Polzik, M. W. Mitchell, “Polarization-based light-atom quantum interface with an all-optical trap,” Phys. Rev. A 79, 043815 (2009).
[CrossRef]

Fayolle, P.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[CrossRef] [PubMed]

Filip, R.

R. Filip, P. Marek, U. L. Andersen, “Measurement-induced continuous-variable quantum interactions,” Phys. Rev. A 71, 042308 (2005).
[CrossRef]

Fiurasek, J.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432, 482–486 (2004).
[CrossRef] [PubMed]

Fiurášek, J.

J. Fiurášek, J. Sherson, T. Opatrný, E. S. Polzik, “Single-passage readout of atomic quantum memory,” Phys. Rev. A 73, 022331 (2006).
[CrossRef]

Furusawa, A.

Y. Miwa, J.-i. Yoshikawa, P. van Loock, A. Furusawa, “Demonstration of a universal one-way quantum quadratic phase gate,” Phys. Rev. A 80, 050303 (2009).
[CrossRef]

J.-i. Yoshikawa, T. Hayashi, T. Akiyama, N. Takei, A. Huck, U. L. Andersen, A. Furusawa, “Demonstration of deterministic and high fidelity squeezing of quantum information,” Phys. Rev. A 76, 060301 (2007).
[CrossRef]

Fuyama, M.

T. Takano, M. Fuyama, R. Namiki, Y. Takahashi, “Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half,” Phys. Rev. Lett. 102, 033601 (2009).
[CrossRef] [PubMed]

T. Takano, M. Fuyama, R. Namiki, Y. Takahashi, “Continuous-variable quantum swapping gate between light and atoms,” Phys. Rev. A 78, 010307 (2008).
[CrossRef]

Garreau, J. C.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[CrossRef] [PubMed]

Grangier, P.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
[CrossRef] [PubMed]

J. A. Levenson, I. Abram, T. Rivera, P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10, 2233–2238 (1993).
[CrossRef]

J. P. Poizat, P. Grangier, “Experimental realization of a quantum optical tap,” Phys. Rev. Lett. 70, 271–274 (1993).
[CrossRef] [PubMed]

Grover, L. K.

L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79, 325–328 (1997).
[CrossRef]

Gu, M.

M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, P. van Loock, “Quantum computing with continuous-variable clusters,” Phys. Rev. A 79, 062318 (2009).
[CrossRef]

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

Hammerer, K.

K. Hammerer, A. S. Sørensen, E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[CrossRef]

C. A. Muschik, K. Hammerer, E. S. Polzik, J. I. Cirac, “Efficient quantum memory and entanglement between light and an atomic ensemble using magnetic fields,” Phys. Rev. A 73, 062329 (2006).
[CrossRef]

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, E. S. Polzik, “Quantum teleportation between light and matter,” Nature 443, 557–560 (2006).
[CrossRef] [PubMed]

K. Hammerer, E. S. Polzik, J. I. Cirac, “Teleportation and spin squeezing utilizing multimode entanglement of light with atoms,” Phys. Rev. A 72, 052313 (2005).
[CrossRef]

K. Hammerer, K. Mølmer, E. S. Polzik, J. I. Cirac, “Light-matter quantum interface,” Phys. Rev. A 70, 044304 (2004).
[CrossRef]

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J.-i. Yoshikawa, T. Hayashi, T. Akiyama, N. Takei, A. Huck, U. L. Andersen, A. Furusawa, “Demonstration of deterministic and high fidelity squeezing of quantum information,” Phys. Rev. A 76, 060301 (2007).
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Y. Takahashi, K. Honda, N. Tanaka, K. Toyoda, K. Ishikawa, T. Yabuzaki, “Quantum nondemolition measurement of spin via the paramagnetic faraday rotation,” Phys. Rev. A 60, 4974–4979 (1999).
[CrossRef]

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J.-i. Yoshikawa, T. Hayashi, T. Akiyama, N. Takei, A. Huck, U. L. Andersen, A. Furusawa, “Demonstration of deterministic and high fidelity squeezing of quantum information,” Phys. Rev. A 76, 060301 (2007).
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M. Takeuchi, T. Takano, S. Ichihara, A. Yamaguchi, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Fast polarimetry system for the application to spin quantum non-demolition measurement,” Appl. Phys. B 83, 33–36 (2006).
[CrossRef]

M. Takeuchi, S. Ichihara, T. Takano, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin squeezing via one-axis twisting with coherent light,” Phys. Rev. Lett. 94, 023003 (2005).
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R. Inoue, S.-I.-R. Tanaka, R. Namiki, T. Sagawa, Y. Takahashi, “Unconditional quantum-noise suppression via measurement-based quantum feedback,” Phys. Rev. Lett. 110, 163602 (2013).
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Y. Takahashi, K. Honda, N. Tanaka, K. Toyoda, K. Ishikawa, T. Yabuzaki, “Quantum nondemolition measurement of spin via the paramagnetic faraday rotation,” Phys. Rev. A 60, 4974–4979 (1999).
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A. Kuzmich, L. Mandel, J. Janis, Y. E. Young, R. Ejnisman, N. P. Bigelow, “Quantum nondemolition measurements of collective atomic spin,” Phys. Rev. A 60, 2346–2350 (1999).
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C. M. Trail, P. S. Jessen, I. H. Deutsch, “Strongly enhanced spin squeezing via quantum control,” Phys. Rev. Lett. 105, 193602 (2010).
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M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, Y.-Z. Zheng, “Continuous-variable controlled-z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
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M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, Y.-Z. Zheng, “Continuous-variable controlled-z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
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J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, E. S. Polzik, “Quantum teleportation between light and matter,” Nature 443, 557–560 (2006).
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J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, E. S. Polzik, “Quantum teleportation between light and matter,” Nature 443, 557–560 (2006).
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M. Kubasik, M. Koschorreck, M. Napolitano, S. R. de Echaniz, H. Crepaz, J. Eschner, E. S. Polzik, M. W. Mitchell, “Polarization-based light-atom quantum interface with an all-optical trap,” Phys. Rev. A 79, 043815 (2009).
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M. Takeuchi, T. Takano, S. Ichihara, A. Yamaguchi, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Fast polarimetry system for the application to spin quantum non-demolition measurement,” Appl. Phys. B 83, 33–36 (2006).
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M. Takeuchi, S. Ichihara, T. Takano, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin squeezing via one-axis twisting with coherent light,” Phys. Rev. Lett. 94, 023003 (2005).
[CrossRef] [PubMed]

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A. Kuzmich, L. Mandel, J. Janis, Y. E. Young, R. Ejnisman, N. P. Bigelow, “Quantum nondemolition measurements of collective atomic spin,” Phys. Rev. A 60, 2346–2350 (1999).
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A. Kuzmich, N. P. Bigelow, L. Mandel, “Atomic quantum non-demolition measurements and squeezing,” Europhys. Lett. 42, 481–486 (1998).
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E. Jeffrey, M. Brenner, P. Kwiat, “Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half,” Proc. SPIE 5161, 269–279 (2004).
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J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
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N. C. Menicucci, X. Ma, T. C. Ralph, “Arbitrarily large continuous-variable cluster states from a single quantum nondemolition gate,” Phys. Rev. Lett. 104, 250503 (2010).
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L. B. Madsen, K. Mølmer, “Spin squeezing and precision probing with light and samples of atoms in the gaussian description,” Phys. Rev. A 70, 052324 (2004).
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A. Kuzmich, L. Mandel, J. Janis, Y. E. Young, R. Ejnisman, N. P. Bigelow, “Quantum nondemolition measurements of collective atomic spin,” Phys. Rev. A 60, 2346–2350 (1999).
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A. Kuzmich, N. P. Bigelow, L. Mandel, “Atomic quantum non-demolition measurements and squeezing,” Europhys. Lett. 42, 481–486 (1998).
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R. Filip, P. Marek, U. L. Andersen, “Measurement-induced continuous-variable quantum interactions,” Phys. Rev. A 71, 042308 (2005).
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N. C. Menicucci, X. Ma, T. C. Ralph, “Arbitrarily large continuous-variable cluster states from a single quantum nondemolition gate,” Phys. Rev. Lett. 104, 250503 (2010).
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M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, P. van Loock, “Quantum computing with continuous-variable clusters,” Phys. Rev. A 79, 062318 (2009).
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N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
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M. Kubasik, M. Koschorreck, M. Napolitano, S. R. de Echaniz, H. Crepaz, J. Eschner, E. S. Polzik, M. W. Mitchell, “Polarization-based light-atom quantum interface with an all-optical trap,” Phys. Rev. A 79, 043815 (2009).
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Y. Miwa, J.-i. Yoshikawa, P. van Loock, A. Furusawa, “Demonstration of a universal one-way quantum quadratic phase gate,” Phys. Rev. A 80, 050303 (2009).
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J. F. Sherson, K. Mølmer, “Polarization squeezing by optical faraday rotation,” Phys. Rev. Lett. 97, 143602 (2006).
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L. B. Madsen, K. Mølmer, “Spin squeezing and precision probing with light and samples of atoms in the gaussian description,” Phys. Rev. A 70, 052324 (2004).
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K. Hammerer, K. Mølmer, E. S. Polzik, J. I. Cirac, “Light-matter quantum interface,” Phys. Rev. A 70, 044304 (2004).
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C. A. Muschik, K. Hammerer, E. S. Polzik, J. I. Cirac, “Efficient quantum memory and entanglement between light and an atomic ensemble using magnetic fields,” Phys. Rev. A 73, 062329 (2006).
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R. Inoue, S.-I.-R. Tanaka, R. Namiki, T. Sagawa, Y. Takahashi, “Unconditional quantum-noise suppression via measurement-based quantum feedback,” Phys. Rev. Lett. 110, 163602 (2013).
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T. Takano, M. Fuyama, R. Namiki, Y. Takahashi, “Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half,” Phys. Rev. Lett. 102, 033601 (2009).
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T. Takano, M. Fuyama, R. Namiki, Y. Takahashi, “Continuous-variable quantum swapping gate between light and atoms,” Phys. Rev. A 78, 010307 (2008).
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M. Kubasik, M. Koschorreck, M. Napolitano, S. R. de Echaniz, H. Crepaz, J. Eschner, E. S. Polzik, M. W. Mitchell, “Polarization-based light-atom quantum interface with an all-optical trap,” Phys. Rev. A 79, 043815 (2009).
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N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
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J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, E. S. Polzik, “Quantum teleportation between light and matter,” Nature 443, 557–560 (2006).
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J. Fiurášek, J. Sherson, T. Opatrný, E. S. Polzik, “Single-passage readout of atomic quantum memory,” Phys. Rev. A 73, 022331 (2006).
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K. Hammerer, A. S. Sørensen, E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
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M. Kubasik, M. Koschorreck, M. Napolitano, S. R. de Echaniz, H. Crepaz, J. Eschner, E. S. Polzik, M. W. Mitchell, “Polarization-based light-atom quantum interface with an all-optical trap,” Phys. Rev. A 79, 043815 (2009).
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J. Fiurášek, J. Sherson, T. Opatrný, E. S. Polzik, “Single-passage readout of atomic quantum memory,” Phys. Rev. A 73, 022331 (2006).
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C. A. Muschik, K. Hammerer, E. S. Polzik, J. I. Cirac, “Efficient quantum memory and entanglement between light and an atomic ensemble using magnetic fields,” Phys. Rev. A 73, 062329 (2006).
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J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, E. S. Polzik, “Quantum teleportation between light and matter,” Nature 443, 557–560 (2006).
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K. Hammerer, E. S. Polzik, J. I. Cirac, “Teleportation and spin squeezing utilizing multimode entanglement of light with atoms,” Phys. Rev. A 72, 052313 (2005).
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K. Hammerer, K. Mølmer, E. S. Polzik, J. I. Cirac, “Light-matter quantum interface,” Phys. Rev. A 70, 044304 (2004).
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B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432, 482–486 (2004).
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L.-M. Duan, J. I. Cirac, P. Zoller, E. S. Polzik, “Quantum communication between atomic ensembles using coherent light,” Phys. Rev. Lett. 85, 5643–5646 (2000).
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N. C. Menicucci, X. Ma, T. C. Ralph, “Arbitrarily large continuous-variable cluster states from a single quantum nondemolition gate,” Phys. Rev. Lett. 104, 250503 (2010).
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M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, P. van Loock, “Quantum computing with continuous-variable clusters,” Phys. Rev. A 79, 062318 (2009).
[CrossRef]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
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J. A. Levenson, I. Abram, T. Rivera, P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10, 2233–2238 (1993).
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J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70, 267–270 (1993).
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J. Stasińska, C. Rodó, S. Paganelli, G. Birkl, A. Sanpera, “Manipulating mesoscopic multipartite entanglement with atom-light interfaces,” Phys. Rev. A 80, 062304 (2009).
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R. Inoue, S.-I.-R. Tanaka, R. Namiki, T. Sagawa, Y. Takahashi, “Unconditional quantum-noise suppression via measurement-based quantum feedback,” Phys. Rev. Lett. 110, 163602 (2013).
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J. Stasińska, C. Rodó, S. Paganelli, G. Birkl, A. Sanpera, “Manipulating mesoscopic multipartite entanglement with atom-light interfaces,” Phys. Rev. A 80, 062304 (2009).
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J. Fiurášek, J. Sherson, T. Opatrný, E. S. Polzik, “Single-passage readout of atomic quantum memory,” Phys. Rev. A 73, 022331 (2006).
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B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432, 482–486 (2004).
[CrossRef] [PubMed]

Sherson, J. F.

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, E. S. Polzik, “Quantum teleportation between light and matter,” Nature 443, 557–560 (2006).
[CrossRef] [PubMed]

J. F. Sherson, K. Mølmer, “Polarization squeezing by optical faraday rotation,” Phys. Rev. Lett. 97, 143602 (2006).
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K. Hammerer, A. S. Sørensen, E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[CrossRef]

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J. Stasińska, C. Rodó, S. Paganelli, G. Birkl, A. Sanpera, “Manipulating mesoscopic multipartite entanglement with atom-light interfaces,” Phys. Rev. A 80, 062304 (2009).
[CrossRef]

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R. Inoue, S.-I.-R. Tanaka, R. Namiki, T. Sagawa, Y. Takahashi, “Unconditional quantum-noise suppression via measurement-based quantum feedback,” Phys. Rev. Lett. 110, 163602 (2013).
[CrossRef] [PubMed]

T. Takano, M. Fuyama, R. Namiki, Y. Takahashi, “Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half,” Phys. Rev. Lett. 102, 033601 (2009).
[CrossRef] [PubMed]

T. Takano, M. Fuyama, R. Namiki, Y. Takahashi, “Continuous-variable quantum swapping gate between light and atoms,” Phys. Rev. A 78, 010307 (2008).
[CrossRef]

M. Takeuchi, T. Takano, S. Ichihara, A. Yamaguchi, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Fast polarimetry system for the application to spin quantum non-demolition measurement,” Appl. Phys. B 83, 33–36 (2006).
[CrossRef]

M. Takeuchi, S. Ichihara, T. Takano, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin squeezing via one-axis twisting with coherent light,” Phys. Rev. Lett. 94, 023003 (2005).
[CrossRef] [PubMed]

Y. Takahashi, K. Honda, N. Tanaka, K. Toyoda, K. Ishikawa, T. Yabuzaki, “Quantum nondemolition measurement of spin via the paramagnetic faraday rotation,” Phys. Rev. A 60, 4974–4979 (1999).
[CrossRef]

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T. Takano, M. Fuyama, R. Namiki, Y. Takahashi, “Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half,” Phys. Rev. Lett. 102, 033601 (2009).
[CrossRef] [PubMed]

T. Takano, M. Fuyama, R. Namiki, Y. Takahashi, “Continuous-variable quantum swapping gate between light and atoms,” Phys. Rev. A 78, 010307 (2008).
[CrossRef]

M. Takeuchi, T. Takano, S. Ichihara, A. Yamaguchi, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Fast polarimetry system for the application to spin quantum non-demolition measurement,” Appl. Phys. B 83, 33–36 (2006).
[CrossRef]

M. Takeuchi, S. Ichihara, T. Takano, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin squeezing via one-axis twisting with coherent light,” Phys. Rev. Lett. 94, 023003 (2005).
[CrossRef] [PubMed]

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J.-i. Yoshikawa, T. Hayashi, T. Akiyama, N. Takei, A. Huck, U. L. Andersen, A. Furusawa, “Demonstration of deterministic and high fidelity squeezing of quantum information,” Phys. Rev. A 76, 060301 (2007).
[CrossRef]

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M. Takeuchi, T. Takano, S. Ichihara, A. Yamaguchi, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Fast polarimetry system for the application to spin quantum non-demolition measurement,” Appl. Phys. B 83, 33–36 (2006).
[CrossRef]

M. Takeuchi, S. Ichihara, T. Takano, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin squeezing via one-axis twisting with coherent light,” Phys. Rev. Lett. 94, 023003 (2005).
[CrossRef] [PubMed]

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Y. Takahashi, K. Honda, N. Tanaka, K. Toyoda, K. Ishikawa, T. Yabuzaki, “Quantum nondemolition measurement of spin via the paramagnetic faraday rotation,” Phys. Rev. A 60, 4974–4979 (1999).
[CrossRef]

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R. Inoue, S.-I.-R. Tanaka, R. Namiki, T. Sagawa, Y. Takahashi, “Unconditional quantum-noise suppression via measurement-based quantum feedback,” Phys. Rev. Lett. 110, 163602 (2013).
[CrossRef] [PubMed]

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Y. Takahashi, K. Honda, N. Tanaka, K. Toyoda, K. Ishikawa, T. Yabuzaki, “Quantum nondemolition measurement of spin via the paramagnetic faraday rotation,” Phys. Rev. A 60, 4974–4979 (1999).
[CrossRef]

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C. M. Trail, P. S. Jessen, I. H. Deutsch, “Strongly enhanced spin squeezing via quantum control,” Phys. Rev. Lett. 105, 193602 (2010).
[CrossRef]

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Y. Miwa, J.-i. Yoshikawa, P. van Loock, A. Furusawa, “Demonstration of a universal one-way quantum quadratic phase gate,” Phys. Rev. A 80, 050303 (2009).
[CrossRef]

M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, P. van Loock, “Quantum computing with continuous-variable clusters,” Phys. Rev. A 79, 062318 (2009).
[CrossRef]

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

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[CrossRef]

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M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, Y.-Z. Zheng, “Continuous-variable controlled-z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
[CrossRef]

Weedbrook, C.

M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, P. van Loock, “Quantum computing with continuous-variable clusters,” Phys. Rev. A 79, 062318 (2009).
[CrossRef]

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

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M. Takeuchi, T. Takano, S. Ichihara, A. Yamaguchi, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Fast polarimetry system for the application to spin quantum non-demolition measurement,” Appl. Phys. B 83, 33–36 (2006).
[CrossRef]

M. Takeuchi, S. Ichihara, T. Takano, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin squeezing via one-axis twisting with coherent light,” Phys. Rev. Lett. 94, 023003 (2005).
[CrossRef] [PubMed]

Y. Takahashi, K. Honda, N. Tanaka, K. Toyoda, K. Ishikawa, T. Yabuzaki, “Quantum nondemolition measurement of spin via the paramagnetic faraday rotation,” Phys. Rev. A 60, 4974–4979 (1999).
[CrossRef]

Yamaguchi, A.

M. Takeuchi, T. Takano, S. Ichihara, A. Yamaguchi, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Fast polarimetry system for the application to spin quantum non-demolition measurement,” Appl. Phys. B 83, 33–36 (2006).
[CrossRef]

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Y. Miwa, J.-i. Yoshikawa, P. van Loock, A. Furusawa, “Demonstration of a universal one-way quantum quadratic phase gate,” Phys. Rev. A 80, 050303 (2009).
[CrossRef]

J.-i. Yoshikawa, T. Hayashi, T. Akiyama, N. Takei, A. Huck, U. L. Andersen, A. Furusawa, “Demonstration of deterministic and high fidelity squeezing of quantum information,” Phys. Rev. A 76, 060301 (2007).
[CrossRef]

Young, Y. E.

A. Kuzmich, L. Mandel, J. Janis, Y. E. Young, R. Ejnisman, N. P. Bigelow, “Quantum nondemolition measurements of collective atomic spin,” Phys. Rev. A 60, 2346–2350 (1999).
[CrossRef]

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M. Reck, A. Zeilinger, H. J. Bernstein, P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[CrossRef] [PubMed]

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M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, Y.-Z. Zheng, “Continuous-variable controlled-z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
[CrossRef]

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L.-M. Duan, J. I. Cirac, P. Zoller, E. S. Polzik, “Quantum communication between atomic ensembles using coherent light,” Phys. Rev. Lett. 85, 5643–5646 (2000).
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Figures (3)

Fig. 1
Fig. 1

Scheme setup for realization of optical QP gate in an atomic ensemble. The light beam first enters an atomic ensemble at an angle α with respect to z to experience Ĥ1 interaction. The outgoing beam then passes through a delay line. After the whole of the beam run through the atomic sample, it enters the ensemble again to experience Ĥ2 interaction and subsequently Ĥ3 interaction. When the beam exits, an optical QP gate is performed.

Fig. 2
Fig. 2

(a) Gate operation fidelity for coherent states vs coupling κ̃ in the presence of atomic decay and light reflection. Inset: the gate fidelity in its dependent on ξ for different decay rate and κ̃ = 2. (b) Gate operation fidelity for squeezed states vs coupling κ̃ including 10% atomic decay and 10% light losses. Inset: the gate fidelity in its dependent on input squeezing for decay parameters η = ξ = 0.10 and coupling κ̃ = 0.10. Choosing the light losses ξ = 0.05, the fidelity of a fixed QP operation with s = 3 / 2 varies with the atomic decay (c) for ρ = 30 and with the optical depth (d). The inset of (d) shows how the optimal η varies with r.

Fig. 3
Fig. 3

(a) The optimized polarization squeezing ζ vs coupling κ̃ in the presence of atomic decay and light reflection. The inset shows how the optimal parameters smin and θ vary with κ̃. (b) Optimized squeezing vs light losses ξ for different atomic decay.

Equations (22)

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D ^ 2 ( s ) x ^ D ^ 2 ( s ) = x ^ , D ^ 2 ( s ) p ^ D ^ 2 ( s ) = p ^ + s x ^ ,
e i A ^ s e i B ^ s e i A ^ s e i B ^ s e [ A ^ , B ^ ] s 2 + O ( s 3 )
x ^ L out 1 ( t ) = x ^ L in ( t ) , p ^ L out 1 ( t ) = p ^ L in ( t ) κ [ x ^ A ( t ) sin α + p ^ A ( t ) cos α ] .
d d t x ^ A ( t ) = κ x ^ L in ( t ) cos α , d d t p ^ A ( t ) = κ x ^ L in ( t ) sin α .
x ^ A ( t ) = x ^ A ( 0 ) + κ cos α 0 t x ^ L in ( τ ) d τ , p ^ A ( t ) = p ^ A ( 0 ) κ sin α 0 t x ^ L in ( τ ) d τ .
y out 1 = S ( κ ˜ , α ) y in ,
S ( κ ˜ , α ) = ( 1 0 0 0 0 1 κ ˜ sin α κ ˜ cos α κ ˜ cos α 0 1 0 κ ˜ sin α 0 0 1 ) ,
S ( α , β ) = ( 1 0 0 0 κ ˜ 2 sin 2 ϕ 1 2 κ ˜ sin ϕ + cos ϕ 2 κ ˜ cos ϕ + cos ϕ 2 κ ˜ cos ϕ + cos ϕ 0 1 0 2 κ ˜ sin ϕ + cos ϕ 0 0 1 )
S ( α , β , θ ) = ( 1 0 0 0 κ ˜ 2 f α β , α θ , β θ s 1 κ ˜ f α , β , θ s κ ˜ f α , β , θ c κ ˜ f α , β , θ c 0 1 0 κ ˜ f α , β , θ s 0 0 1 ) .
f α , β , θ s = f α , β , θ c = 0 ,
f α β , α θ , β θ s 0 .
x ^ L out 3 = x ^ L in , p ^ L out 3 = p ^ L in 3 2 κ ˜ 2 x ^ L in ,
( x ^ L out 3 p ^ L out 3 ) = ( cos ( s ) sin ( s ) sin ( s ) cos ( s ) ) ( x ^ L out 3 p ^ L out 3 ) .
Δ 2 x ^ L out 3 = 1 2 [ 1 3 2 κ ˜ 2 sin ( 2 s ) + 3 4 κ ˜ 4 cos 2 ( s ) ] ,
y out 1 = D ¯ ( ξ , η ) S ( κ ˜ , α ) y in + D ( ξ , η ) y v 1 ,
y out 3 = D ¯ ( ξ , η ) S ( τ 2 κ ˜ , θ ) [ D ¯ ( ξ , η ) S ( τ κ ˜ , β ) y out 1 + D ( ξ , η ) y v 2 ] + D ( ξ , η ) y v 3 .
x ^ L out 3 = ( 1 ξ ) 3 2 x ^ L in + ξ f ^ x ,
p ^ L out 3 = ( 1 ξ ) 3 2 ( p ^ L in 3 2 κ ˜ 2 x ^ L in ) + η ( 1 ξ ) 3 2 κ ˜ [ ( η 3 2 ) x ^ A in + 3 2 p ^ A in ] + η f ^ A v + ξ f ^ L v ,
( ρ out 3 , ρ out 3 ) = 1 det ( Γ out 3 + Γ out 3 ) + δ δ × exp [ 1 2 𝒜 T ( Γ out 3 + Γ out 3 ) 1 𝒜 ] ,
B ^ i j ( θ 1 ) = ( cos θ 1 0 sin θ 1 0 0 cos θ 1 0 sin θ 1 sin θ 1 0 cos θ 1 0 0 sin θ 1 0 cos θ 1 ) .
D ^ i j ( s ) = ( 1 0 0 0 s 1 0 0 0 0 1 0 0 0 s 1 ) .
i j ( s ) = ( 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 ) .

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