Abstract

We investigate coherent perfect absorption (CPA) in quantum optics, in particular when pairs of squeezed coherent states of light are superposed on an absorbing beam splitter. First, by employing quantum optical input–output relations, we derive the absorption coefficients for quantum coherence and for intensity, and reveal how these will differ for squeezed states. Second, we present the remarkable properties of a CPA gate: two identical but otherwise arbitrary incoming squeezed coherent states can be completely stripped of their coherence, producing a pure entangled squeezed vacuum state that with its finite intensity escapes from an otherwise perfect absorber. Importantly, this output state of light is not entangled with the absorbing beam splitter by which it was produced. Its loss-enabled functionality makes the CPA gate an interesting new tool for continuous-variable quantum state preparation.

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

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2017 (7)

D. G. Baranov, A. Krasnok, T. Shegai, A. Alù, and Y. Chong, “Coherent perfect absorbers: linear control of light with light,” Nat. Rev. Mater. 2, 17064 (2017).
[Crossref]

C. Altuzarra, S. Vezzoli, J. Valente, W. Gao, C. Soci, D. Faccio, and C. Couteau, “Coherent perfect absorption in metamaterials with entangled photons,” ACS Photon. 4, 2124–2128 (2017).
[Crossref]

N.-R. Zhou, J.-F. Li, Z.-B. Yu, L.-H. Gong, and A. Farouk, “New quantum dialogue protocol based on continuous-variable two-mode squeezed vacuum states,” Quantum Inf. Process. 16, 4 (2017).
[Crossref]

S. Zeytinoğlu, A. İmamoğlu, and S. Huber, “Engineering matter interactions using squeezed vacuum,” Phys. Rev. X 7, 021041 (2017).
[Crossref]

A. Streltsov, G. Adesso, and M. B. Plenio, “Colloquium: quantum coherence as a resource,” Rev. Mod. Phys. 89, 041003 (2017).
[Crossref]

D. D. B. Rao, S. Yang, and J. Wrachtrup, “Dissipative entanglement of solid-state spins in diamond,” Phys. Rev. A 95, 022310 (2017).
[Crossref]

B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, “Anti-coalescence of bosons on a lossy beam splitter,” Science 356, 1373–1376 (2017).
[Crossref]

2016 (4)

A. Winter and D. Yang, “Operational resource theory of coherence,” Phys. Rev. Lett. 116, 120404 (2016).
[Crossref]

U. L. Andersen, T. Gehring, C. Marquardt, and G. Leuchs, “30 years of squeezed light generation,” Phys. Scripta 91, 053001 (2016).
[Crossref]

T. Roger, S. Restuccia, A. Lyons, D. Giovannini, J. Romero, J. Jeffers, M. Padgett, and D. Faccio, “Coherent absorption of N00N states,” Phys. Rev. Lett. 117, 023601 (2016).
[Crossref]

N. Kakenov, O. Balci, T. Takan, V. A. Ozkan, H. Altan, and C. Kocabas, “Observation of gate-tunable coherent perfect absorption of terahertz radiation in graphene,” ACS Photon. 3, 1531–1535 (2016).
[Crossref]

2015 (4)

T. Roger, S. Vezzoli, E. Bolduc, J. Valente, J. J. Heitz, J. Jeffers, C. Soci, J. Leach, C. Couteau, N. I. Zheludev, and D. Faccio, “Coherent perfect absorption in deeply subwavelength films in the single-photon regime,” Nat. Commun. 6, 7031 (2015).
[Crossref]

D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, “Quantum harmonic oscillator state synthesis by reservoir engineering,” Science 347, 53–56 (2015).
[Crossref]

A. Metelmann and A. A. Clerk, “Nonreciprocal photon transmission and amplification via reservoir engineering,” Phys. Rev. X 5, 021025 (2015).
[Crossref]

G. Morigi, J. Eschner, C. Cormick, Y. Lin, D. Leibfried, and D. J. Wineland, “Dissipative quantum control of a spin chain,” Phys. Rev. Lett. 115, 200502 (2015).
[Crossref]

2014 (6)

D. D. B. Rao and K. Mølmer, “Deterministic entanglement of Rydberg ensembles by engineered dissipation,” Phys. Rev. A 90, 062319 (2014).
[Crossref]

J. Zhang, C. Guo, K. Liu, Z. Zhu, W. Ye, X. Yuan, and S. Qin, “Coherent perfect absorption and transparency in a nanostructured graphene film,” Opt. Express 22, 12524–12532 (2014).
[Crossref]

S. Huang and G. S. Agarwal, “Coherent perfect absorption of path entangled single photons,” Opt. Express 22, 20936–20947 (2014).
[Crossref]

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref]

F. Liu, Y. D. Chong, S. Adam, and M. Polini, “Gate-tunable coherent perfect absorption of terahertz radiation in graphene,” 2D Mater. 1, 031001 (2014).
[Crossref]

Y. Sun, W. Tan, H.-Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112, 143903 (2014).
[Crossref]

2013 (3)

G. Pirruccio, L. Martín Moreno, G. Lozano, and J. Gómez Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7, 4810–4817 (2013).
[Crossref]

J. Aasi, J. Abadie, B. Abbott, R. Abbott, T. Abbott, M. Abernathy, C. Adams, T. Adams, P. Addesso, and R. Adhikari, et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics 7, 613–619 (2013).
[Crossref]

F. G. Brandao, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, “Resource theory of quantum states out of thermal equilibrium,” Phys. Rev. Lett. 111, 250404 (2013).
[Crossref]

2012 (3)

S. Dutta-Gupta, O. J. F. Martin, S. D. Gupta, and G. S. Agarwal, “Controllable coherent perfect absorption in a composite film,” Opt. Express 20, 1330–1336 (2012).
[Crossref]

S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
[Crossref]

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref]

2011 (6)

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332, 702–704 (2011).
[Crossref]

S. Longhi, “Coherent perfect absorption in a homogeneously broadened two-level medium,” Phys. Rev. A 83, 055804 (2011).
[Crossref]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref]

K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. Plenio, A. Serafini, M. Wolf, and E. Polzik, “Quantum memory for entangled continuous-variable states,” Nat. Phys. 7, 13–16 (2011).
[Crossref]

M. J. Kastoryano, F. Reiter, and A. S. Sørensen, “Dissipative preparation of entanglement in optical cavities,” Phys. Rev. Lett. 106, 090502 (2011).
[Crossref]

H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, “Entanglement generated by dissipation and steady state entanglement of two macroscopic objects,” Phys. Rev. Lett. 107, 080503 (2011).
[Crossref]

2010 (4)

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref]

Y. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
[Crossref]

G. Konstantatos and E. H. Sargent, “Nanostructured materials for photon detection,” Nat. Nanotechnol. 5, 391–400 (2010).
[Crossref]

2009 (1)

R. Tualle-Brouri, A. Ourjoumtsev, A. Dantan, P. Grangier, M. Wubs, and A. S. Sørensen, “Multimode model for projective photon-counting measurements,” Phys. Rev. A 80, 013806 (2009).
[Crossref]

2008 (1)

J. Appel, E. Figueroa, D. Korystov, M. Lobino, and A. Lvovsky, “Quantum memory for squeezed light,” Phys. Rev. Lett. 100, 093602 (2008).
[Crossref]

2006 (1)

J. Heersink, C. Marquardt, R. Dong, R. Filip, S. Lorenz, G. Leuchs, and U. L. Andersen, “Distillation of squeezing from non-Gaussian quantum states,” Phys. Rev. Lett. 96, 253601 (2006).
[Crossref]

2004 (2)

D. Akamatsu, K. Akiba, and M. Kozuma, “Electromagnetically induced transparency with squeezed vacuum,” Phys. Rev. Lett. 92, 203602 (2004).
[Crossref]

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

2003 (1)

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[Crossref]

2001 (1)

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63, 052311 (2001).
[Crossref]

2000 (2)

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: a quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[Crossref]

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
[Crossref]

1999 (3)

M. Ban, “Quantum dense coding via a two-mode squeezed-vacuum state,” J. Opt. B Quantum Semiclass. Opt. 1, L9 (1999).
[Crossref]

G. Milburn and S. L. Braunstein, “Quantum teleportation with squeezed vacuum states,” Phys. Rev. A 60, 937–942 (1999).
[Crossref]

L. Knöll, S. Scheel, E. Schmidt, and D.-G. Welsch, “Quantum-state transformation by dispersive and absorbing four-port devices,” Phys. Rev. A 59, 4716–4726 (1999).
[Crossref]

1998 (1)

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[Crossref]

1996 (1)

S. M. Barnett, C. R. Gilson, B. Huttner, and N. Imoto, “Field commutation relations in optical cavities,” Phys. Rev. Lett. 77, 1739–1742 (1996).
[Crossref]

1995 (1)

R. Matloob, R. Loudon, S. M. Barnett, and J. Jeffers, “Electromagnetic field quantization in absorbing dielectrics,” Phys. Rev. A 52, 4823–4838 (1995).
[Crossref]

1993 (1)

G. Yeoman and S. M. Barnett, “Two-mode squeezed Gaussons,” J. Mod. Opt. 40, 1497–1530 (1993).
[Crossref]

1992 (2)

M. S. Abdalla, “Statistical properties of a new squeezed operator model,” J. Mod. Opt. 39, 771–781 (1992).
[Crossref]

M. S. Abdalla, “The statistical properties of a generalized two-mode squeezed operator,” J. Mod. Opt. 39, 1067–1081 (1992).
[Crossref]

1990 (1)

F. Hong-Yi, “Squeezed states: operators for two types of one-and two-mode squeezing transformations,” Phys. Rev. A 41, 1526–1532 (1990).
[Crossref]

1987 (1)

1983 (1)

D. F. Walls, “Squeezed states of light,” Nature 306, 141–146 (1983).
[Crossref]

1963 (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
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Figures (5)

Fig. 1.
Fig. 1. Sketch of the model system: two quantum states of light are superposed on an absorbing beam splitter. We consider squeezed coherent states that, e.g., can be prepared by sending coherent laser (L) light through a crystal that produces squeezing (S). Squeezing affects the coherent absorption. In turn, the CPA beam splitter gives rise to dissipation-enabled preparation of pure entangled two-mode output squeezed vacuum states (see main text).
Fig. 2.
Fig. 2. Coefficient of coherent absorption AsqC(ξ,θ) of Eq. (23) upon variation of parameters of the squeezed coherent input states, for a beam splitter with t=1/2 and r=1/2. We vary the coherence angle θ=θ1 and the squeezing parameter ξ=ξ1=ξ2, while keeping θ2=ϕ1=ϕ2=0 fixed. Figure is valid for arbitrary equal coherence amplitudes α=β.
Fig. 3.
Fig. 3. Variations in the coefficient of coherent absorption (a) AsqC(ξ1,ξ2) of Eq. (24) and (b) AsqC(ξ1=ξ,ξ2=0) of Eq. (31a). All other parameters are as explained in the main text.
Fig. 4.
Fig. 4. Same as Fig. 2 but for AsqI(ξ,θ) with |α|=|β|=1.
Fig. 5.
Fig. 5. Variations in the coefficient of coherent absorption of intensity AsqI(ξ1=ξ,ξ2=0) of Eq. (31b) for |α|2=103 (solid blue), |α|2=100 (dashed orange), |α|2=103 (dotted yellow), and |α|2=106 (dashed-dotted purple). All the other parameters are as explained in the main text.

Equations (41)

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

b^1=ta^1+ra^2+L^1,
b^2=ra^1+ta^2+L^2,
Iina^1a^1+a^2a^2andIoutb^1b^1+b^2b^2,
AcohI1Iout/Iin,
Cin|a^1|2+|a^2|2,
AcohCΔC/Cin=1Cout/Cin.
D^1(α)exp(|α|2/2)exp(αa^1)exp(α*a^1).
Cin=|α|2+|β|2,
Cout=(|α|2+|β|2)(|t|2+|r|2)+2cos(θ)|α||β|(tr*+rt*),
AcohC=1[|t|2+|r|2+2|α||β|(tr*+rt*)|α|2+|β|2cos(θ)],
α|β=e12(|α|2+|β|2)+αβ*,
αβ*=|α||β|eiθ=12(|α|2+|β|2)+lnα|β,
βα*=|α||β|eiθ=12(|α|2+|β|2)+lnβ|α.
2|α||β|cos(θ)=|α|2+|β|2+ln|α|β|2=|α|2+|β|2+lnF(ρα,ρβ),
AcohC,I=1[|t+r|2+(tr*+rt*)|α|2+|β|2lnF(ρα,ρβ)],
AcohC,I=1+lnF(ρα,ρβ)|α|2+|β|2.
|α1,ζ11=S^1(ζ1)|α1=S^1(ζ1)D^1(α1)|.
S^1(ζ1)e12ζ1*a^1212ζ1a^12
a^1=|α|(eiθ1cosh(ξ1)eiθ1eiϕ1sinh(ξ1)),
a^2=|β|(eiθ2cosh(ξ2)eiθ2eiϕ2sinh(ξ2)).
Cin=γ12|α|2+γ22|β|2,
Cout=(|t|2+|r|2)Cin+Γ(tr*+rt*),
Γ=a^1a^2*+a^2a^1*=2|α||β|(cos(θ)cosh(ξ1)cosh(ξ2)cos(θ1+θ2ϕ2)cosh(ξ1)sinh(ξ2)cos(θ1+θ2ϕ1)sinh(ξ1)cosh(ξ2)+cos(θϕ)sinh(ξ1)sinh(ξ2)),
AsqC=1(|t|2+|r|2+Γ(tr*+rt*)γ12|α|2+γ22|β|2).
AsqC=1(|t|2+|r|2+Ω1Ω2),
Ω1=2[cosh(ξ)cos(ϵ)sinh(ξ)](tr*+rt*),Ω2=cosh(2ξ1)+cosh(2ξ2)cos(ϵ)[sinh(2ξ1)+sinh(2ξ2)],
AsqC=12+cos(θ)1+e2ξ[cosh(2ξ)cos(2θ)sinh(2ξ)].
AsqC=112(12eξe2ξ1+e2ξ2).
ΔI=Iin(1(|t|2+|r|2)Γ(t*r+r*t)Iin),
AsqI=1(|t|2+|r|2)Γ(t*r+r*t)Iin=AΓ(t*r+r*t)Iin,
IinAsqI=IinAΓ(t*r+r*t).
CinAsqC=CinAΓ(t*r+r*t).
ΔIΔC=(IinCin)A.
AsqI=12+(cos(θ)/2)e2ξe2ξ+[1cos(2θ)2]sinh(2ξ)+sinh2(ξ)|α|2,
AsqC=12+eξ1+e2ξ=1+coshξ2coshξ,
AsqI=12+eξ1+e2ξ+sinh2(ξ)|α|2.
|ψin=|α,ζ11|β,ζ22|BS=S^2(ζ2)D^2(β)S^1(ζ1)D^1(α)||BS=S^1(ζ1)S^2(ζ2)D^1(α)D^2(β)||BS=e12(ζ2*a^22+ζ1*a^12)12(ζ2a^22+ζ1a^12)×D^1(α)D^2(β)||BS,
b^=Ta^+Ag^.
Tcpa=(trrt)=12(1111)=12(1σx),Acpa=12(1111)=12(1+σx)
a^=Tcpab^Acpah^.
|ψout=e14ζ*(b^1b^2)214ζ(b^1b^2)2|e14ζ*(h^1+h^2)214ζ(h^1+h^2)2|α,αBS,