Abstract

We present a modular design for integrated programmable multimode sources of arbitrary Gaussian states of light. The technique is based on current technologies, in particular recent demonstrations of on-chip photon manipulation and the generation of highly squeezed vacuum states in semiconductors. While the design is generic and independent of the choice of integrated platform, we adopt recent experimental results on compound semiconductors as a demonstrative example. Such a device would be valuable as a source for many quantum protocols that range from imaging to communication and information processing.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (4)

M. Stefszky, R. Ricken, C. Eigner, V. Quiring, H. Herrmann, and C. Silberhorn, “Waveguide cavity resonator as a source of optical squeezing,” Phys. Rev. Applied 7, 044026 (2017).
[Crossref]

X. Guo, C. Zou, C. Schuck, H. Jung, R. Cheng, and H. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light Sci. Appl. 6, e16249 (2017).
[Crossref]

N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. C. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Quantum transport simulations in a programmable nanophotonic processor,” Nat. Photonics 11, 447–452 (2017).
[Crossref]

D. Lu, K. Li, J. Li, H. Katiyar, A. J. Park, G. Feng, T. Xin, H. Li, G. Long, A. Brodutch, J. Baugh, B. Zeng, and R. Laflamme, “Enhancing quantum control by bootstrapping a quantum processor of 12 qubits,” npj Quantum Information 3, 45 (2017).
[Crossref]

2016 (8)

P. Hayden, S. Nezami, G. Salton, and B. C. Sanders, “Spacetime replication of continuous variable quantum information,” N. J. Phys. 18, 083043 (2016).
[Crossref]

J. Yoshikawa, S. Yokoyama, T. Kaji, C. Sornphiphatphong, Y. Shiozawa, K. Makino, and A. Furusawa, “Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing,” APL Photonics 1, 060801 (2016).
[Crossref]

G. Cariolaro and G. Pierobon, “Bloch-Messiah reduction of Gaussian unitaries by Takagi factorization,” Phys. Rev. A 94, 062109 (2016).
[Crossref]

W. Clements, P. Humphreys, B. Metcalf, W. S. Kolthammer, and I. Walmsley, “Optimal design for universal multiport interferometers,” Optica 3, 1460–1465 (2016).
[Crossref]

M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18, 103002 (2016).
[Crossref]

N. Harris, D. Bunandar, M. Pant, G. Steinbrecher, J. Mower, M. Prabhu, T. Baehr-Jones, M. Hochberg, and D. Englund, “Large-scale quantum photonic circuits in silicon,” Nanophotonics 5, 456–468 (2016).
[Crossref]

A. Dutt, S. Miller, K. Luke, J. Cardenas, A. Gaeta, P. Nussenzveig, and M. Lipson, “Tunable squeezing using coupled ring resonators on a silicon nitride chip,” Opt. Lett. 41, 223–226 (2016).
[Crossref] [PubMed]

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photo-electric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

2015 (4)

A. Dutt, K. Luke, S. Manipatruni, A. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Applied 3, 044005 (2015).
[Crossref]

J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
[Crossref] [PubMed]

U. L. Andersen, J. S. Neergaard-Nielsen, P. van Loock, and A. Furusawa, “Hybrid discrete- and continuous-variable quantum information,” Nat. Physics 11, 713–719 (2015).
[Crossref]

J. Huh, G. G. Guerreschi, B. Peropadre, J. R. McClean, and A. Aspuru-Guzik, “Boson sampling for molecular vibronic spectra,” Nat. Photonics 9, 615–620 (2015).
[Crossref]

2014 (6)

J. Wang, A. Santamato, P. Jiang, D. Bonneau, E. Engin, J. Silverstone, M. Lermer, J. Beetz, M. Kamp, S. Hüfling, M. Tanner, C. Natarajan, R. Hadfield, S. Dorenbos, V. Zwiller, J. O’Brien, and M. Thompson, “Gallium arsenide (GaAs) quantum photonic waveguide circuits,” Opt. Commun. 327, 49–55 (2014).
[Crossref]

N. Harris, D. Grassani, A. Simbula, M. Pant, M. Galli, T. Baehr-Jones, M Hochberg, D. Englund, D. Bajoni, and C. Galland, “Integrated source of spectrally filtered correlated photons for large-scale quantum photonic systems,” Phys. Rev. X 4, 041047 (2014).

F. Boitier, A. Orieux, C. Autebert, A. Lemaître, E. Galopin, C. Manquest, C. Sirtori, I. Favero, G. Leo, and S. Ducci, “Electrically Injected Photon-Pair Source at Room Temperature,” Phys. Rev. Lett. 112, 183901 (2014).
[Crossref] [PubMed]

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

G. Adesso, S. Ragy, and A. R. Lee, “Continuous variable quantum information: Gaussian states and beyond,” Open Syst. Inf. Dyn. 21, 1440001 (2014).
[Crossref]

N. Menicucci, “Fault-tolerant measurement-based quantum computing with continuous-variable cluster states,” Phys. Rev. Lett. 112, 120504 (2014).
[Crossref] [PubMed]

2013 (7)

S. Yokoyama, R. Ukai, S. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. Yoshikawa, D. Yonezawa, N. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nat. Photonics 7, 982 (2013).
[Crossref]

M. Tillmann, B. Dakić, R. Heilmann, S. Nolte, A. Szameit, and P. Walther, “Experimental boson sampling,” Nat. Photonics 7, 540–544 (2013).
[Crossref]

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8, 104–108 (2013).
[Crossref]

R. Horn, P. Kolenderski, D. Kang, P. Abolghasem, C. Scarcella, A. Frera, A. Tosi, L. Helt, S. Zhukovsky, J. Sipe, G. Weihs, A. Helmy, and T. Jennewein, “Inherent polarization entanglement generated from a monolithic semiconductor chip,” Sci. Rep. 3, 2314 (2013).
[Crossref] [PubMed]

N. Spagnolo, C. Vitelli, L. Aparo, P. Matalon, F. Sciarrino, A. Crespi, R. Ramponi, and R. Osellame, “Three-photon bosonic coalescence in an integrated tritter,” Nat. Commun. 4, 1606 (2013).
[Crossref] [PubMed]

P. Orlandi, F. Morichetti, M. Strain, M. Sorel, A. Melloni, and P. Bassi, “Tunable silicon photonics directional coupler driven by a transverse temperature gradient,” Opt. Lett. 38, 863 (2013).
[Crossref] [PubMed]

B. J. Bijlani, P. Abolghasem, and Amr S. Helmy, “Semiconductor optical parametric generators in isotropic semiconductor diode lasers,” Appl. Phys. Lett. 103, 091103 (2013).
[Crossref]

2012 (2)

P. Shadbolt, M. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. Matthews, M. Thompson, and J. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45 (2012)
[Crossref]

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

2011 (2)

J. P. Sprengers, A. Gaggero, D. Sahin, S. Jahanmirinejad, G. Frucci, F. Mattioli, R. Leoni, J. Beetz, M. Lermer, M. Kamp, S. Höfling, R. Sanjines, and A. Fiore, “Waveguide superconducting single-photon detectors for integrated quantum photonic circuits,” Appl. Phys. Lett. 99, 181110 (2011).
[Crossref]

J. Fiurášek, “Improving entanglement concentration of Gaussian states by local displacements,” Phys. Rev. A 84, 012335 (2011).
[Crossref]

2010 (3)

G. Xiang, T. Ralph, A. Lund, N. Walk, and G. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316 (2010).
[Crossref]

A. Zavatta, J. Fiurášek, and M. Bellini, “A high-fidelity noiseless amplifier for quantum light states,” Nat. Photonics 5, 52 (2010).
[Crossref]

S. Manipatruni, K. Preston, L. Chen, and M. Lipson, “Ultra-low voltage, ultra-small mode volume silicon microring modulator,” Opt. Express 18, 18235 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (2)

S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, “Quantum Illumination with Gaussian States,” Phys. Rev. Lett. 101, 253601 (2008).
[Crossref] [PubMed]

J. Niset, U. L. Andersen, and N. J. Cerf, “Experimentally feasible quantum erasure-correcting code for continuous variables,” Phys. Rev. Lett. 101, 130503 (2008).
[Crossref] [PubMed]

2007 (1)

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, 110501 (2006).
[Crossref] [PubMed]

J. Zhang and S. L. Braunstein, “Continuous-variable Gaussian analog of cluster states,” Phys. Rev. A 73, 032318 (2006).
[Crossref]

2005 (1)

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

2001 (1)

E. Knill, R. Laflamme, and G. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

1998 (1)

T. Erdogan, “Optical add-drop multiplexer based on an asymmetric Bragg coupler,” Opt. Commun. 157, 249 (1998).
[Crossref]

1996 (1)

M. G. Paris, “Displacement operator by beam splitter,” Phys. Lett. A 217, 78–80 (1996).
[Crossref]

1995 (1)

L. Soldano and E. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Light. Technol. 13, 615 (1995).
[Crossref]

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
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1990 (1)

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C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Sci. Rep. (1)

R. Horn, P. Kolenderski, D. Kang, P. Abolghasem, C. Scarcella, A. Frera, A. Tosi, L. Helt, S. Zhukovsky, J. Sipe, G. Weihs, A. Helmy, and T. Jennewein, “Inherent polarization entanglement generated from a monolithic semiconductor chip,” Sci. Rep. 3, 2314 (2013).
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Science (1)

J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
[Crossref] [PubMed]

Other (4)

A. Lvovsky, “Squeezed Light,” in Photonics, Volume 1: Fundamentals of Photonics and Physics, Ed. D. Andrews, ed. (Wiley2015).

Z. Yan, in preparation.

A. Ferraro, S. Olivares, and M. G. a. Paris, Gaussian States in Continuous Variable Quantum Information (Bibliopoli, Napoli Series on Physics and Astrophysics 2005).

B. Dive, A. Pitchford, F. Mintert, and D. Burgarth, “In situ upgrade of quantum simulators to universal computers,” https://arxiv.org/abs/1701.01723 (2017).

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Figures (5)

Fig. 1
Fig. 1 One-mode Gaussian state generation with bulk optics. The initialization stage, highlighted in red, is also used in the N-mode protocol. Squeezed vacuum is generated through SPDC followed by a low-pass filter (LPF) to remove the pump. An electro-optic modulator (EOM) is used to generate a phase shift. Displacement is generated via mixing with a high power phase-locked coherent state. Acronyms: HPF = high-pass filter; DB = displacement beam; LO = local oscillator; HWP+P = half wave plate and polarizer for amplitude control.
Fig. 2
Fig. 2 Phase-space depiction of the four stage process. A one-mode vacuum state (i) is squeezed (ii), rotated (iii) and displaced (iv).
Fig. 3
Fig. 3 (a) The cascaded displacement scheme for N = 4. At each step, a strong coherent state | α k , in mode k is used to displace mode k + 1 by α k + 1 = α k η k and swap with that mode using a beam splitter with reflectivity ηk << 1. Note that the final modes are shifted by −1 with respect to the original modes so that the final mode N is the ancilla which is discarded. (b) Fidelity between a single-mode squeezed vacuum state after an approximate displacement α = 0.5 and the corresponding (ideal) displaced squeezed state (see Sec. 5.1). Larger splitting factors η increase the probability that photons from the squeezed state ‘leak’ into the ancilla mode, or equivalently that noise is added by the ancilla, which degrades the squeezing and hence fidelity.
Fig. 4
Fig. 4 (a) Schematic of a dynamically reconfigurable circuit for generating two-mode Gaussian states. The device includes the three reconfigurable modules (squeezing, rotation and displacement) fed by an external initialization module as in Fig. 1. The 11 electrodes can be used to program the state (see text, Sec 3. 3.2). Five example settings (b) generate the five states depicted in (c) where the (x2, p2) Wigner slice shows the quadrature evolution in mode 2, while the (x1, x2) slice shows correlations between modes. The states are: (1) squeezed vacuum in mode 1 and vacuum in mode 2; (2) two single-mode squeezed states (with mode 1 amplitude-squeezed and mode 2 phase-squeezed); (3) a displaced two-mode squeezed state where x1 and x2 are correlated; (4) a two-mode squeezed state with a different displacement amplitude and where x1 and x2 are now anti-correlated; and (5) two single-mode squeezed states rotated with respect to (2).
Fig. 5
Fig. 5 Impact of loss on the preparation of a squeezed two-mode state by the circuit in Figure 4, with the displacement stage parameters tuned to mitigate errors in targeted vs. actual displacement. (a) Uhlmann fidelity as a function of the squeezing parameter for various values of MZI loss (the loss per coupler and phase-shifter are taken as a fixed fraction of the MZI loss). (b) Comparing the ideal preparation of State 5 in Fig. 4 to a lossy preparation, with and without mitigation via modification to the displacement stage parameters.

Equations (8)

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| G = D ( [ α ] ) R ( [ ζ ] ) S ( [ β 1 m ] ) | 0
R ( [ Δ ] ) D 0 ( α 0 ) | Ψ | vac 0 D N ( α N ) P k = 1 N D k ( α k ) | Ψ | vac 0
U G ( [ θ ] , [ β ] , [ α ] ) = D ( [ α ] ) S ( [ β ] ) R ( [ θ ] ) ,
U G ( [ θ ] , [ β ] , [ α ] ) = D ( [ α ] ) R ( [ ζ ] ) S ( [ β 1 m ] ) R ( [ ζ ] ) R ( [ θ ] )
T k = P k 1 , k e i δ k 1 , k ( a k 1 a k + a k a k 1 ) e i ( ϕ k ϕ k 1 ) a k 1 a k 1
T 1 D 0 ( α 0 ) = P 1 D 0 ( e ϕ 1 α 0 cos δ ) D 1 ( α 1 ) e i δ 0 , 1 ( a 0 a 1 + a 1 a 0 ) e ϕ 1 a 0 a 0 = D 0 ( α 1 ) D 1 ( e ϕ 1 α 0 cos δ ) P 1 e i δ 0 , 1 ( a 0 a 1 + a 1 a 0 ) e ϕ 1 a 0 a 0
k = 1 N T k D 0 ( α 0 ) = D 0. . N ( [ α ] ) × D N [ e i ϕ N α 0 k = N N Cos ( δ k 1 , k ) ] k = 1 N T k
k = 1 N T k = P k = 1 N e i δ k 1 , k ( a 0 a k + a k a 0 ) e i ( ϕ N ) a 0 a 0

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