Abstract

We introduce a multi-step protocol for optical quantum state engineering that performs as “bright quantum scissors,” namely truncating an arbitrary input quantum state to have at least a certain number of photons. The protocol exploits single-photon pulses and is based on the effect of single-photon Raman interaction, which is implemented with a single three-level Λ system (e.g., a single atom) Purcell-enhanced by a single-sided cavity. A single step of the protocol realizes the inverse of the bosonic annihilation operator. Multiple iterations of the protocol can be used to deterministically generate a chain of single photons in a W state. Alternatively, upon appropriate heralding, the protocol can be used to generate Fock-state optical pulses. This protocol could serve as a useful and versatile building block for the generation of advanced optical quantum states that are vital for quantum communication, distributed quantum information processing, and all-optical quantum computing.

© 2019 Chinese Laser Press

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References

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2019 (1)

B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, “Deterministic creation of entangled atom–light Schrödinger-cat states,” Nat. Photonics 13, 110–115 (2019).
[Crossref]

2018 (2)

O. Bechler, A. Borne, S. Rosenblum, G. Guendelman, O. E. Mor, M. Netser, T. Ohana, Z. Aqua, N. Drucker, R. Finkelstein, Y. Lovsky, R. Bruch, D. Gurovich, E. Shafir, and B. Dayan, “A passive photon-atom qubit swap operation,” Nat. Phys. 14, 996–1000 (2018).
[Crossref]

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, “Bridging ultrahigh-Q devices and photonic circuits,” Nat. Photonics 12, 297–302 (2018).
[Crossref]

2017 (7)

M. Davanco, J. Liu, L. Sapienza, C.-Z. Zhang, J. V. D. M. Cardoso, V. Verma, R. Mirin, S. W. Nam, L. Liu, and K. Srinivasan, “Heterogeneous integration for on-chip quantum photonic circuits with single quantum dot devices,” Nat. Commun. 8, 889 (2017).
[Crossref]

R. S. Daveau, K. C. Balram, T. Pregnolato, J. Liu, E. H. Lee, J. D. Song, V. Verma, R. Mirin, S. W. Nam, L. Midolo, S. Stobbe, K. Srinivasan, and P. Lodahl, “Efficient fiber-coupled single-photon source based on quantum dots in a photonic-crystal waveguide,” Optica 4, 178–184 (2017).
[Crossref]

X. Ji, F. A. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4, 619–624 (2017).
[Crossref]

Y.-M. He, J. Liu, S. Maier, M. Emmerling, S. Gerhardt, M. Davanço, K. Srinivasan, C. Schneider, and S. Höfling, “Deterministic implementation of a bright, on-demand single-photon source with near-unity indistinguishability via quantum dot imaging,” Optica 4, 802–808 (2017).
[Crossref]

M. H. Pfeiffer, J. Liu, M. Geiselmann, and T. J. Kippenberg, “Coupling ideality of integrated planar high-Q microresonators,” Phys. Rev. Appl. 7, 024026 (2017).
[Crossref]

S. Rosenblum, A. Borne, and B. Dayan, “Analysis of deterministic swapping of photonic and atomic states through single-photon Raman interaction,” Phys. Rev. A 95, 033814 (2017).
[Crossref]

K. Koshino, K. Inomata, Z. Lin, Y. Tokunaga, T. Yamamoto, and Y. Nakamura, “Theory of deterministic entanglement generation between remote superconducting atoms,” Phys. Rev. Appl. 7, 064006 (2017).
[Crossref]

2016 (5)

S. Rosenblum, O. Bechler, I. Shomroni, Y. Lovsky, G. Guendelman, and B. Dayan, “Extraction of a single photon from an optical pulse,” Nat. Photonics 10, 19–22 (2016).
[Crossref]

N. Somaschi, V. Giesz, L. De Santis, J. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N. D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10, 340–345 (2016).
[Crossref]

A. Jeantet, Y. Chassagneux, C. Raynaud, P. Roussignol, J.-S. Lauret, B. Besga, J. Estève, J. Reichel, and C. Voisin, “Widely tunable single-photon source from a carbon nanotube in the Purcell regime,” Phys. Rev. Lett. 116, 247402 (2016).
[Crossref]

M. Um, J. Zhang, D. Lv, Y. Lu, S. An, J.-N. Zhang, H. Nha, M. Kim, and K. Kim, “Phonon arithmetic in a trapped ion system,” Nat. Commun. 7, 11410 (2016).
[Crossref]

K. Inomata, Z. Lin, K. Koshino, W. D. Oliver, J.-S. Tsai, T. Yamamoto, and Y. Nakamura, “Single microwave-photon detector using an artificial Λ-type three-level system,” Nat. Commun. 7, 12303 (2016).
[Crossref]

2015 (2)

2014 (5)

D. R. Hamel, L. K. Shalm, H. Hübel, A. J. Miller, F. Marsili, V. B. Verma, R. P. Mirin, S. W. Nam, K. J. Resch, and T. Jennewein, “Direct generation of three-photon polarization entanglement,” Nat. Photonics 8, 801–807 (2014).
[Crossref]

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

K. Inomata, K. Koshino, Z. Lin, W. Oliver, J. Tsai, Y. Nakamura, and T. Yamamoto, “Microwave down-conversion with an impedance-matched Λ system in driven circuit QED,” Phys. Rev. Lett. 113, 063604 (2014).
[Crossref]

A. Goban, C.-L. Hung, S.-P. Yu, J. Hood, J. Muniz, J. Lee, M. Martin, A. McClung, K. Choi, D. E. Chang, O. Painter, and H. J. Kimble, “Atom-light interactions in photonic crystals,” Nat. Commun. 5, 3808 (2014).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref]

2013 (3)

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

J. Gea-Banacloche, “Space-time descriptions of quantum fields interacting with optical cavities,” Phys. Rev. A 87, 023832 (2013).
[Crossref]

J. Gea-Banacloche and W. Wilson, “Photon subtraction and addition by a three-level atom in an optical cavity,” Phys. Rev. A 88, 033832 (2013).
[Crossref]

2012 (1)

M. Bradford and J.-T. Shen, “Single-photon frequency conversion by exploiting quantum interference,” Phys. Rev. A 85, 043814 (2012).
[Crossref]

2011 (2)

LIGO-collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7, 962–965 (2011).
[Crossref]

S. Rosenblum, S. Parkins, and B. Dayan, “Photon routing in cavity QED: beyond the fundamental limit of photon blockade,” Phys. Rev. A 84, 033854 (2011).
[Crossref]

2010 (2)

I. Afek, O. Ambar, and Y. Silberberg, “High-noon states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[Crossref]

K. Koshino, S. Ishizaka, and Y. Nakamura, “Deterministic photon-photon swap gate using a Λ system,” Phys. Rev. A 82, 010301 (2010).
[Crossref]

2009 (1)

G. Lin, X. Zou, X. Lin, and G. Guo, “Heralded quantum memory for single-photon polarization qubits,” Europhys. Lett. 86, 30006 (2009).
[Crossref]

2008 (1)

D. Pinotsi and A. Imamoglu, “Single photon absorption by a single quantum emitter,” Phys. Rev. Lett. 100, 093603 (2008).
[Crossref]

2007 (2)

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[Crossref]

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrodinger cats from photon number states,” Nature 448, 784–786 (2007).
[Crossref]

2006 (2)

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrodinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[Crossref]

F. Dell’Anno, S. De Siena, and F. Illuminati, “Multiphoton quantum optics and quantum state engineering,” Phys. Rep. 428, 53–168 (2006).
[Crossref]

2005 (2)

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

J. Fiurášek, R. García-Patrón, and N. J. Cerf, “Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions,” Phys. Rev. A 72, 033822 (2005).
[Crossref]

2004 (3)

M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
[Crossref]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).
[Crossref]

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[Crossref]

2001 (4)

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[Crossref]

H. Jeong, M. S. Kim, and J. Lee, “Quantum-information processing for a coherent superposition state via a mixed entangled coherent channel,” Phys. Rev. A 64, 052308 (2001).
[Crossref]

L.-M. Duan, M. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[Crossref]

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

2000 (1)

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne–Zeilinger entanglement,” Nature 403, 515–519 (2000).
[Crossref]

1999 (2)

M. Dakna, J. Clausen, L. Knöll, and D.-G. Welsch, “Generation of arbitrary quantum states of traveling fields,” Phys. Rev. A 59, 1658–1661 (1999).
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Figures (11)

Fig. 1.
Fig. 1. Configuration that leads to single-photon Raman interaction (SPRINT). Two optical modes, in this case orthogonal polarizations (H and V), interacting with a three-level Λ system in a single-sided cavity. Each polarization is coupled to a different “leg” of the Λ system. Upon an incident H-polarized single-photon pulse and a Λ system prepared in |gh, destructive interference forces the Λ system to emit back the photon in V and undergo a Raman transition to state |gv. In effect this configuration realizes a unitary swap gate between the photonic and atomic qubit.
Fig. 2.
Fig. 2. Bright quantum scissors (BQS) multi-step protocol. The protocol uses three input channels: a general H-polarized multi-photon quantum state, a V-polarized single photon, and a train of H-polarized single photons. The multi-photon pulse and the V-polarized single-photon pulse interact with the Λ system simultaneously and the resulting pulses are fed back to the system repeatedly. The H-polarized single-photon pulses are interleaved with the multi-photon pulse evolutions and reinitialize the state of the Λ system at every iteration. At the output channels of the protocol we get a train of readout single-photon pulses and a modified multi-photon state. (a) Heralded on the measurement of the nth readout photon in the V-mode, the nth-order BQS operation is applied on the input quantum state. This ensures the presence of more than n photons in the multi-photon output. For n=1, the operation amounts to a realization of the inverse annihilation. (b) Conversely, when choosing to herald on the number of photons in the multi-photon output pulse, a polarization W state manifests in the readout single-photons pulse train.
Fig. 3.
Fig. 3. One-dimensional atom. The effective system considered using the MOU approach in the adiabatic limit. Two modes of light, a^ω and b^ω [or A^(t) and B^(t)], interact with the two transitions of an atom in a Λ configuration.
Fig. 4.
Fig. 4. Optical setup suitable for the implementation of the BQS protocol. H-input and V-input are the sources for the pulses in the two modes. Switchable mirrors M1–M4 are used to repeatedly alternate between directing the readout photons to their respective outputs and rerouting the multi-photon state back into the cavity. Upon measuring a photon in the “single-photon readout V-output” on the nth iteration of the protocol, M2 is turned ON and an |n+ state is measured in “multi-photon output.” On the other hand, when heralding on vacuum in the verification port and M photons in the multi-photon output, a W state is generated at the combination of single-photon readout H- and V-output.
Fig. 5.
Fig. 5. Pulse sequence for |ϕh=|2h. The H- and V-modes are represented by red and blue, respectively. Solid lines refer to pulses we send actively from H- and V-input while dotted lines represent those redirected back into the cavity. The iteration number appears above the relevant pulses.
Fig. 6.
Fig. 6. Efficiency of a^1 as a function of |α|2, the average number of photons in the initial coherent state.
Fig. 7.
Fig. 7. nth-order BQS. Efficiency as a function of the average number of photons in the initial coherent state, |α|2. The resulting state |n+ is guaranteed to have more than n photons.
Fig. 8.
Fig. 8. Generation of a Fock state |3 using the 3rd-order BQS. Fidelity and efficiency as functions of the average number of photons in the coherent state.
Fig. 9.
Fig. 9. Optical setup for Fock state generation via Bell state measurement. First, we direct the kth readout photon (either H or V) to a delay line (mirrors M5 and M6 are OFF). When the (k+1)th readout photon leaves the cavity, we turn M5 and M6 ON in order to direct it to the path with no time delay. The delay time is set such that both the kth and the (k+1)th readout photons enter the 50∶50 beam splitter simultaneously. Coincident detections at the output of the 50∶50 beam splitter guarantee that our state has collapsed on the antisymmetric Bell state [49].
Fig. 10.
Fig. 10. Efficiency of generating a Fock state |k by using an optimal coherent state input (see text).
Fig. 11.
Fig. 11. Efficiency for generating WM states by using an initial coherent state with average photon number of 5 and applying the protocol for 10 iterations.

Equations (36)

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

H=igdωκ/πκiω(|egh|a^ω+|egv|b^ω)ei(ω+δ)t+h.c.,
A^(t)12πdωa^ωeiωt,
B^(t)12πdωb^ωeiωt,
|Nh=1N![dtf(t)A^(t)]N|0,
|Nh,1vkth(N+1)!(k1)!(Nk+1)!×dtB^(t)f(t)[tdt1A^(t1)f(t1)]k1[tdt2A^(t2)f(t2)]Nk+1|0.
|1h,0v,gh|0h,1v,gv.
|Nh,1vkth,gv|Nh,1v(k+1)th,gv,
|Nh,1v(N+1)th,gv|N+1h,0v,gh.
|Nh,1v=1N+1(|Nh,1v1st++|Nh,1v(N+1)th).
|1h,1v,gv=12(|1h,1v2nd+|1h,1v1st)|gvatom12(|2h,0v,gh+|1h,1v2nd,gv)h112(|2h,0v,gv|v1+|1h,1v2nd,gv|h1)atom12(|2h,0v,gv|v1|2h,0v,gh|h1)h212|2h,0v,gv(|v1,h2+|h1,v2)2k+1iterations|2h,0v,gv12(|v1,h2,h3,,hk+1+|h1,v2,h3,,hk+1).
|Nh,1v,gviterationsk+1{for  kN:|N+1h,0v,gv1N+1(|v1,h2,h3,,hk+1+|h1,v2,h3,,hk+1++|h1,,hN,vN+1,hN+2,,hk+1)for  kN1:|N+1h,0v,gv1N+1(|v1,h2,h3,,hk+1+|h1,v2,h3,,hk+1++|h1,,hk,vk+1)+1N+1(|Nh,1v(k+2)th,gv++|Nh,1v(N+1)th,gv)(Nk)terms|h1,,hk+1.
|ψinitial=|ϕh,1v=N=0CN|Nh,1v.
|ψfinal=|v1,h2,h3,,hk+1(N=0CNN+1|N+1h)|0v,gv+|h1,v2,h3,,hk+1(N=1CNN+1|N+1h)|0v,gv++|h1,,hk,vk+1(N=kCNN+1|N+1h)|0v,gv+|h1,,hk+1N=k+1CNN+1(|Nh,1v(k+2)th++|Nh,1v(N+1)th)|gv.
a^a^1=I;a^1a^=I|00|.
a^1=n=01n+1|n+1n|.
a^=n=0n+1|n+1n|,
S^+=n=0|n+1n|,
v1|ψfinal=(N=0CNN+1|N+1h)|0v,gvN=0CNN+1|N+1h=a^1N=0CN|Nh=a^1|ϕh,
η1=N=0|CN|2N+1.
vk|ψfinal=|h1,h2,,hk+1trace  out(N=k1CNN+1|N+1h)|0v,gvtrace outNN=kCN1N|Nh|k+,
η2=N=k|CN1|2N.
P(Nk+1)=N=k+1|CN|21.
ηBQS=1N=k+1(Nk)|CN|2N+1.
a^NN=kCNN+1|N+1h=NN=kCN|Nh,
O^=I^n=0k1|nn|
|χ=|vk|hk+1|ψ1+|hk|vk+1|ψ2.
|χ=|V1H2|ψ1+|H1V2|ψ2.
±12ψ()|=±12(V1H2|H1V2|).
±12ψ()|χ=±12(|ψ1|ψ2).
12(vk,hk+1|hk,vk+1|)|ψfinal=12|h1,,hk1|0v,gvtrace out(N=k1CNN+1|N+1hN=kCNN+1|N+1h)=12Ck1k|kh.
η3=|Ck1|22k.
η4=12k!(k1e)k1.
|Wn=1n(|VHHH+|HVHH++|HHHV).
|ψfinal=N=0k1CNN+1|N+1h,0v,gv(|v1,h2,h3,,hk+1+|h1,v2,h3,,hk+1++|h1,,hN,vN+1,hN+2,,hk+1)+N=kCNN+1|N+1h,0v,gv(|v1,h2,h3,,hk+1+|h1,v2,h3,,hk+1++|h1,,hk,vk+1)+N=k+1CNN+1(|Nh,1v(k+2)th,gv++|Nh,1v(N+1)th,gv)|h1,,hk+1.
Mh,0v|ψfinal=CM1M|gv{for  3Mk:|v1,h2,h3,,hk+1+|h1,v2,h3,,hk+1++|h1,,hM1,vM,hM+1,,hk+1for  Mk+1:|v1,h2,h3,,hk+1+|h1,v2,h3,,hk+1++|h1,,hk,vk+1.
Mh,0v|ψfinal={|WM|hM+1,,hk+1for  3Mk|Wk+1for  Mk+1.