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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 13 — Jul. 1, 2013
  • pp: 15618–15626
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Quantum entangling gates using the strong coupling between two optical emitters and nanowire surface plasmons

J. Yang, G. W. Lin, Y. P. Niu, and S. Q. Gong  »View Author Affiliations


Optics Express, Vol. 21, Issue 13, pp. 15618-15626 (2013)
http://dx.doi.org/10.1364/OE.21.015618


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Abstract

We propose a scheme to generate quantum entangling gate using one-dimensional surface plasmon waveguide. The protocol is based on the detection of the transmission spectrum of the single optical plasmons passing through two separate three-level emitters on metallic nanowire waveguide. It is shown that the low efficiency in direct detection of the single photon can be avoided by repeating the measurement of the transmission spectrum.

© 2013 OSA

1. Introduction

Surface plasmons are propagating excitations of charge-density waves and their associated electromagnetic fields on the surface of a conductor [1

1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

]. They play an important role in modern optical researches because of the excellent performance in circumventing the diffraction limit and localizing the electromagnetic energy into nanoscale regions as small as few nanometres [2

2. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010) [CrossRef] .

]. In recent years, there have been great interests in surface plasmon waveguides, which are used to transfer the electromagnetic surface modes on the subwavelength metallic systems. Various surface plasmon waveguides have been proposed, such as channel waveguide [3

3. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006) [CrossRef] [PubMed] .

], dielectric-loaded waveguide [4

4. J. Grandidier, S. Massenot, G. C. Francs, A. Bouhelier, J. C. Weeber, L. Markey, A. Dereux, J. Renger, M. U. Gonzáez, and R. Quidant, “Dielectric-loaded surface plasmon polariton waveguides: figures of merit and mode characterization by image and Fourier plane leakage microscopy,” Phys. Rev. B 78(24), 245419 (2008) [CrossRef] .

], hybrid waveguide [5

5. R. F. Oulton, V. J. Sorger, D. A. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. photonics 2(8), 496–500 (2008) [CrossRef] .

], metal wire waveguide [6

6. J. Yang, Q. Cao, and C. Zhou, “An explicit formula for metal wire plasmon of terahertz wave,” Opt. Express 17, 20806–20815 (2009) [CrossRef] [PubMed] .

9

9. H. Liang, S. Ruan, and M. Zhang, “Terahertz surface wave propagation and focusing on conical metal wires,” Opt. Express 16, 18241–18248 (2008) [CrossRef] [PubMed] .

], and metallic slit waveguide [10

10. M. Wächter, M. Nagel, and H. Kurz, “Metallic slit waveguide for dispersion-free low-loss terahertz signal transmission,” Appl. Phys. Lett. 90, 061111 (2007) [CrossRef] .

]. Recently the strong coupling between the single surface plasmon on the metal wire waveguide and the single emitters has been carried out and described in terms of quantum and nonlinear optical effects [11

11. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006) [CrossRef] [PubMed] .

13

13. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007) [CrossRef] .

]. Besides, coupling light to the free electrons of metals was experimentally demonstrated to generate single optical plasmons(that is, single photons), which is one of the key ingredients in photon-based quantum information processing [14

14. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007) [CrossRef] [PubMed] .

]. And strong coupling was also used to construct a single-photon transistor, which can realize the strong nonlinear interaction between photons [15

15. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Physics 3, 807–812 (2007) [CrossRef] .

]. Up to now, many interesting theoretical and experimental works on the strong coupling between surface plasmon and the optical emitter have been widely carried out [16

16. C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienaa, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett. 7, 2784–2788 (2007) [CrossRef] [PubMed] .

25

25. Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012) [CrossRef] [PubMed] .

].

As we all know, quantum entanglement is one of the most striking features of quantum mechanics, and it has been widely used in quantum cryptography, quantum teleportation, and other two-qubit quantum operations [26

26. M. A. Nielsen and I. A. Chuang, Quantum Computing and Quantum Information (Cambridge, 2000).

30

30. C. Cabrillo, J. I. Cirac, P. García-Fernández, and P. Zoller, “Creation of entangled states of distant atoms by interference,” Phys. Rev. A 59, 2 (1999) [CrossRef] .

]. However one of the chief obstacles to the implementation of entanglement by one two-level emitter interacting with the propagating surface plasmon is the imperfect scattering process. Recently, Li and co-authors have proposed a novel scheme for realizing the robust-fidelity atom-photon entangling gate in one-dimensional surface plasmon waveguides [25

25. Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012) [CrossRef] [PubMed] .

]. This scheme uses polarization- or time bin-encoded photonic qubits to filter the imperfect process, and thus it ensures the high-fidelity. In this paper, we propose a scheme to generate the entangled state between the two emitters by trains of single plamons. The protocol is based on measurements of the transmission spectrum of the incident single optical plasmons passing through two separate three-level emitters on a metallic nanowire waveguide one by one. The transmission spectrum can be easily measured as long as the number of the incident single plasmons is large enough. Therefore, this scheme can avoid the low efficiency in the detection of the single photon and high fidelity is accordingly guaranteed. In addition, it can also reduce the bad influence of the imperfect scattering process and the finite Purcell factors on the fidelity of the entanglement. It should be pointed out that repeated measurements have already been used in other schemes for the generation of quantum logic gates. For example, the repeat-until-success scheme has been adopted to implement deterministic entangling logic gates in linear optics network and atom-cavity system. The gate success probability can be as high as 100% in principle [31

31. Y. L. Lim, A. Beige, and L. C. Kwek, “Repeat-until-success linear optics distributed quantum computing” Phys. Rev. Lett. 95, 030305 (2005) [CrossRef] .

].

The paper is organized as follows. In Section 2, we shall establish the physical model and its theoretical description. By solving the single plasmon scattering process in the system of two emitters strongly coupling to a set of traveling electromagnetic modes, we shall derive an explicit analytical expression for the transmission and reflection spectrum of the propagating single plasmon. Then we shall discuss the specific transmission spectrum for the different states of the two emitters. In Section 3, we shall propose the detailed scheme to generate quantum entangling gate and discuss the advantages of our protocol. Finally, our main conclusions are summarized in Section 4.

2. Model setup and exact solutions

We construct a general one-dimensional model with two emitters strongly coupling to a set of traveling electromagnetic modes. The configuration of the system is exhibited in Fig. 1. Two Λ-type three-level emitters are placed proximally to the different locations of the surface of metal wire, whose ground state, metastable state and excited state are denoted as |gn, |sn and |en (n = 1, 2), respectively. The tiny light emitters addressed here can be quantum dots, nitrogen-vacancy center or atoms.

Fig. 1 Schematic diagram of a metal nanowire couple to a pair three-level emitters.

The nanowire behaves as a 1D continuum for the coherent transportation of photons, and the propagating single surface plasmon is described by annihilation operations ak. The energies of the states |gn and |en are Ωg,n = 0(the energy origin)and Ωe,n = Ωn respectively. Here, the metastable state |sn is used for the storage of qubits. The metastable state is not affected during the emitter-surface plasmon interaction, so it can be omitted in the Hamiltonians. The total Hamiltonian can be written as
H=Ω1|ee|1+Ω2|ee|2+kh¯ωkak+ak+kVk(ak++ak)(S1++S1+S2++S2).
(1)

In Eq.(1), the first and the second terms represent the energies of the excited states of the two emitters, where σ̂een = |e〉 〈e|n are the electronic population operators on the excited states. The third term stands for the energies of the propagating surface plasmon modes with frequency ωk, which is the frequency of the mode of the radiation field corresponding to wave vector k. In the fourth terms, Sn+ = |e〉 〈g|n is the transition from the ground state to the exited state of the n-th emitters. The transitions between the ground state and the excited state of the two emitters are coupled to the propagating surface plasmon modes with the coupling constant Vk. Here the coupling strength between the surface-plasmon modes and the tiny light emitters can be quite large because Vk1/Veff, where Veff refers to the effective mode volume for the surface plasmon on the metallic nanowire.

The scattering problem for a single photon in a one-dimensional waveguide coupled to a two-level quantum emitter has been solved exactly [15

15. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Physics 3, 807–812 (2007) [CrossRef] .

, 24

24. D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New Journal of Physics 12, 043052 (2012) [CrossRef] .

, 32

32. J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguide coupled to a two-level system,” Opt. Lett. 30, 2001–2003 (2005) [CrossRef] [PubMed] .

, 33

33. J. T. Shen and S. Fan, “Theory of single-photon transport in a single mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A 79, 023837 (2009) [CrossRef] .

]. Here we solve the case for the two three-level emitters strongly coupling to a set of traveling electromagnetic modes. In one dimension, when the resonance of the atom is away from the cutoff frequency of the dispersion relation, we can rewrite the total Hamiltonian of the system in real space
H=Hp+He+Hc.
(2)
Equation (2) contains three parts, which describes in order: the propagation of the plasmon, the free two two-level emitters, and the couplings
Hp=dx[ivgCR+xCR+ivgCL+xCL],
(3)
He=Ω1|ee|1+Ω2|ee|2,
(4)
Hc=dxV1δ(x+d)[CR+(x)S1+CR(x)S1++CL+(x)S1+CL(x)S1+]+dxV2δ(xd)[CR+(x)S2+CR(x)S2++CL+(x)S2+CL(x)S2+],
(5)
where vg is the group velocity of the plasmons and can be simplified as the velocity of the light [15

15. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Physics 3, 807–812 (2007) [CrossRef] .

]. The operator CR+(x) [CL+(x)] represents the bosonic operator creating a right(left-propagating) surface plasmon mode at x coordinate. Here we assume that a linear and nonde-generate dispersion relation holds over the relevant frequency range, and that a single plasmons comes from the left with energy Ek = kvg.

The stationary state of the system can be written as
|Ek=dx[ϕk,R+(x)CR+(x)+ϕk,L+(x)CL+(x)]|0,g1,g2+ek1|0,e1,g2+ek2|0,g1,e2.
(6)
It should be indicated that the single photon process defines a conservation rule of the total occupation number, which means that the photon exists in the surface plasmon modes or that one of the two emitters is in the excited state. Therefore the present system described by this Hamiltonian has the bases |0, e1, g2〉, |0, g1, e2〉 and |1, g1, g2〉, where |0〉 is the vacuum state of the incident pulse with zero photons. Thus the energy eigenvectors can be expanded in the base of an invariant subspace in the form. The coefficients ekn(n = 1, 2) are the probability amplitudes of the two emitters in the excited states respectively. For a plasmon incident from the left, ϕk,R+(x) and ϕk,L+(x) take the forms
ϕk,R+(x)=exp(ikx)θ[(x+d)]+t1exp(ikx)[θ(x+d)θ(xd)]+texp(ikx)θ(xd),
(7)
ϕk,L+(x)=rexp(ikx)θ[(x+d)]+r1exp(ikx)[θ(x+d)θ(xd)],
(8)
where r and t1 are the transmission and reflection amplitudes at the −d site, and r1 and t are those at the d-th site. Since we only care about the overall performance of the system, we need to obtain the coefficients r and t.

The eigen-equation H |Ek〉 = Ek |Ek〉 results in the following equation:
V1[ϕk,R*(d)+ϕk,L*(d)]+Ω1ek,1=Ekek,1,
(9)
V2[ϕk,R*(d)+ϕk,L*(d)]+Ω2ek,2=Ekek,2,
(10)
ivgxϕk,R*(d)+V1ek,1=Ekϕk,R*(d),
(11)
ivgxϕk,R*(d)+V2ek,2=Ekϕk,R*(d).
(12)

We can finally find the exact value of transmission amplitude for a monochromatic input single plasmons with wave number k given by
t(k)=cosb1cosb2ei(b1+b2)1+sinb1sinb2ei(b1+b2+4kd),
(13)
T(k)=|t(k)|2=cos2b1cos2b21+sin2b1sin2b2+2sinb1sinb2cos(b1+b2+4kd),
(14)
where the phase shifts of the two emitters are
b1=arctan{V12vg(Ω1Ek)},
(15)
b2=arctan{V22vg(Ω2Ek)}.
(16)

For simplicity we shall only discuss the transmission amplitude, the corresponding reflection amplitude is determined by R = 1 − T.

For the two emitters in the state |g1, s2〉 or |s1, g2〉, which is equal to the case when the single plasmon couples only with one emitter, the total transmission can be simplified as
Tgs(k)=cos2b.
(18)

For the simplest case when the two emitters are located in the metastable states |s1, s2〉, the incident plasmons totally arrive at the terminal end of the metal wire because the surface plasmons do not interact with the two emitters at all. Then the total transmission can be written as
Tss(k)=1.
(19)

To get an intuitive impression on the three different scattering effects, we plot the transmission spectrum as a function of the incident plasmon wave number k for three different states of the two emitters in Fig. 2. Here we assume that Ω1 = Ω2 and that the plasmon energy Ek = c|k|. The incident plasmon wave number k (−3 ≤ k ≤ 5) and the distance d = 10a are properly chosen, where a is the lattice constant, and all other parameters are in units of k.

Fig. 2 The photon transmission coefficient as a function of the photon wave number k for three different states Tgg(k)(blue solid line), Tgs(k)(black cashed line), Tss(k)(red ”o” signs).

3. Entangling gate for the two emitters

In what follows, we shall illustrate the procedure to generate heralded entanglement by detecting the transmission spectrum. The two emitters are initially prepared in the superposition state, i.e.(|g1〉 + |s1〉) ⊗ (|g2〉 + |s2〉). This step can be realized by the following procedure. Because the two emitters are separated, we can manipulate either of the emitters independently. Therefore, we simply describe the preparation of superposition state of the single emitters. Firstly, we initialize the emitter in |g〉 and apply two classical fields on the two transitions between |g〉 → |e〉 and |g〉 → |s〉 with Rabi frequencies Ω1(t) and Ω2(t) respectively to form two-photon Raman resonant. Now the effective Hamiltonian can be written as Heff = Ωeff (|g〉 〈s|+|s〉 〈g|), where Ωeff = Ω1Ω2/Δ, and Δ is the single photon detuning of the two classical fields from their corresponding transitions. Performing the effective Hamiltonian on the ground state and choosing appropriate time to satisfy Ωefft = π/4, we can finally get the superposition state we need. The qubit can be prepared in arbitrary superposition state and was already experimentally demonstrated [34

34. M. P. A. Jones, J. Beugnon, A. Gaëtan, J. Zhang, G. Messin, A. Browaeys, and P. Grangier, “Fast quantum state control of a single trapped neutral atom,” Phys. Rev. A 75, 040301(R) (2007) [CrossRef] .

].

When the preparation of superposition is completed, the incident trains of single plasmons interact continuously with the two emitters in the process of the transmission and finally can be detected in terms of the transmission spectrum. If the transmission spectrum acts as the parabolic curve, the detection projects the two-emitters state onto an entangled state 1/2(|g1,s2+|s1,g2). Then the success is heralded and the corresponding entangled state between the two emitters is generated. If the transmission spectrum we get is either of the other curves shown in Fig. 2, the operation should be discarded. This scheme can avert the low efficiency of the detection of single photon. Furthermore, it also lowers harmful impact of the imperfect reflection, infinite Purcell factor and low-sensitivity detector on the detection when continuous measurement are carried out.

Then we shall demonstrate the advantages of our scheme. As we have stated above that the protocol is based on measurements of the transmission spectrum of the incident single optical plasmons passing through two separate three-level emitters on a metallic nanowire waveguide one by one. The procedure of the generation of the entangled gate is as follows. We initialize both of the emitters in superposition state, i.e.(|g1〉 + |s1〉) ⊗ (|g2〉 + |s2〉), and send trains of single plasmons to interact with the two emitters successively. Then the quantum state of the whole system can be written as
|Ψ=12|g1g2i=1n|Ai+12|s1s2i=1n|Bi+12(|g1s2+|s1g2)i=1n|C,
(20)
where n denotes the number of the incident single plasmons. Here three quantum state |A〉, |B〉 and |C〉 denote three different photon states after the scattering process. If the transmitted photons are detected to be in state |C〉, the detection projects the two-emitters state onto the entangled state. While if the transmitted photons are detected to be in state |A〉 or |B〉, the operation should be discarded. Obviously, we can see that the transmission spectrum can be easily measured as long as the number of the incident single plasmons is large enough. Therefore, this scheme can avoid the low efficiency in the detection of the single photon and high fidelity is accordingly guaranteed. It has already been experimentally demonstrated that high resolution can be obtained by measurements of the transmission spectrum [36

36. H. Zhang, R. McConnell, S. Ćuk, Q. Lin, M. H. S. Smith, I. D. Leroux, and V. Vuletić, “Collective state measurement of mesoscopic ensembles with single-atom resolution,” Phys. Rev. Lett. 109, 133603 (2012) [CrossRef] [PubMed] .

].

Lastly it should be pointed out that the surface plasmons experience losses as they propagate along the nanowire, which would potentially limit their feasibility as long-distance carriers of information and in large-scale devices. However, in our system, we can realize the strong coupling between the emitters and the wire plasmons based on the following two aspects. On one hand, it is known that three distinct decay channels exist in the coupling interaction between the emitters and the propagating surface plasmon [14

14. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007) [CrossRef] [PubMed] .

]. First, direct optical emission into free-space modes is possible. Second, non-radiative emission via ohmic losses in the conductor exists. Last and most importantly, the spontaneous emission rate into the surface plasmons can be expressed as Γpl ∝ (λ0/R)3, where R is the radius of the metal wire. So the strong coupling between the emitter and the surface plasmon can be achieved by decreasing R, whereas non-radiative damping becomes significant only for very small wire-emitter separation [11

11. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006) [CrossRef] [PubMed] .

]. Thus for an optimally placed emitter, the spontaneous emission rate Γpl into surface plasmons can far exceed the radiative and non-radiative rates, which results in highly efficient coupling to surface plasmons. This enhancement can be characterized by an effective Purcell factor, P ≡ Γpl/Γ′, where Γ′ includes contributions both from emission into free space and non-radiative emission via ohmic losses in the conductor. In general, the effective Purcell factor can exceed 103 in realistic systems according to rigorous numerical calculations [15

15. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Physics 3, 807–812 (2007) [CrossRef] .

]. On the other hand, the propagating surface plasmon is used to generate the entangled states between the two emitters. If we can properly dispose the two emitters in the characteristic dissipation length, the surface plasmon can be used to achieve entangled gate over a short distance, but are rapidly in- and out-coupled to conventional waveguides for long-distance transport, as proposed by the authors in Ref. [15

15. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Physics 3, 807–812 (2007) [CrossRef] .

]. Thus, we can ensure the strong coupling and the low losses at the same time. In order to present the main physics, we neglect dissipation, decoherence and nonuniform couplings in this paper. These effects shall be studied in the future.

4. Conclusions

In summary, we have proposed a scheme to generate the entangled state between the two emitters using measurements of the transmission spectrum by continuous detection trains of single plasmons. By preparing the two emitters in the superposition state and controlling the incident single surface plasmons passing through the two emitters one by one, we can detect the transmission spectrum of the trains of the single plasmons. If the transmission spectrum is detected as the parabolic curve, the success is heralded and the corresponding entangled state between the two emitters is generated. This scheme can avoid the low efficiency in the direct detection of the single photon and pioneers a new method for quantum entanglement and quantum information processing.

Acknowledgments

The work is supported by the China Post-doctoral Science Foundations (Grant Nos. 2011M500552, 2011M500054), the Fundamental Research Funds for the Central Universities( WM1214019), and the National Natural Science Foundation of China( 11274112, 11204080, 11074263).

References and links

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H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

2.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010) [CrossRef] .

3.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006) [CrossRef] [PubMed] .

4.

J. Grandidier, S. Massenot, G. C. Francs, A. Bouhelier, J. C. Weeber, L. Markey, A. Dereux, J. Renger, M. U. Gonzáez, and R. Quidant, “Dielectric-loaded surface plasmon polariton waveguides: figures of merit and mode characterization by image and Fourier plane leakage microscopy,” Phys. Rev. B 78(24), 245419 (2008) [CrossRef] .

5.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. photonics 2(8), 496–500 (2008) [CrossRef] .

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14.

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15.

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16.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienaa, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett. 7, 2784–2788 (2007) [CrossRef] [PubMed] .

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D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New Journal of Physics 12, 043052 (2012) [CrossRef] .

25.

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012) [CrossRef] [PubMed] .

26.

M. A. Nielsen and I. A. Chuang, Quantum Computing and Quantum Information (Cambridge, 2000).

27.

S. Haroche and J. M. Raimond, Exploring the Quantum (Oxford, 2006) [CrossRef] .

28.

A. Gonzalez-Tudela, D. Martin-Cano, E. Moreno, L. Martin-Moreno, C. Tejedor, and F. J. Garcia-Vidal, “Entanglement of two qubits mediated by one-dimensional plasmonic waveguides,” Phys. Rev. Lett. 106, 020501 (2011) [CrossRef] [PubMed] .

29.

L. Slodickačka, G. Hétet, N. Röck, P. Schindler, M. Hennrich, and R. Blatt, “Atom-atom entanglement by single-photon detection,” Phys. Rev. Lett. 110, 083603 (2013) [CrossRef] [PubMed] .

30.

C. Cabrillo, J. I. Cirac, P. García-Fernández, and P. Zoller, “Creation of entangled states of distant atoms by interference,” Phys. Rev. A 59, 2 (1999) [CrossRef] .

31.

Y. L. Lim, A. Beige, and L. C. Kwek, “Repeat-until-success linear optics distributed quantum computing” Phys. Rev. Lett. 95, 030305 (2005) [CrossRef] .

32.

J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguide coupled to a two-level system,” Opt. Lett. 30, 2001–2003 (2005) [CrossRef] [PubMed] .

33.

J. T. Shen and S. Fan, “Theory of single-photon transport in a single mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A 79, 023837 (2009) [CrossRef] .

34.

M. P. A. Jones, J. Beugnon, A. Gaëtan, J. Zhang, G. Messin, A. Browaeys, and P. Grangier, “Fast quantum state control of a single trapped neutral atom,” Phys. Rev. A 75, 040301(R) (2007) [CrossRef] .

35.

H. S. Nguyen, G. Sallen, C. Voisin, Ph. Roussignol, C. Diederichs, and G. Cassabois, “Ultra-coherent single photon source,” Appl. Phys. Lett. 99, 26 (2011) [CrossRef] .

36.

H. Zhang, R. McConnell, S. Ćuk, Q. Lin, M. H. S. Smith, I. D. Leroux, and V. Vuletić, “Collective state measurement of mesoscopic ensembles with single-atom resolution,” Phys. Rev. Lett. 109, 133603 (2012) [CrossRef] [PubMed] .

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

History
Original Manuscript: April 29, 2013
Revised Manuscript: May 25, 2013
Manuscript Accepted: June 6, 2013
Published: June 21, 2013

Citation
J. Yang, G. W. Lin, Y. P. Niu, and S. Q. Gong, "Quantum entangling gates using the strong coupling between two optical emitters and nanowire surface plasmons," Opt. Express 21, 15618-15626 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-15618


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References

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  24. D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New Journal of Physics12, 043052 (2012). [CrossRef]
  25. Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett.109, 160504 (2012). [CrossRef] [PubMed]
  26. M. A. Nielsen and I. A. Chuang, Quantum Computing and Quantum Information (Cambridge, 2000).
  27. S. Haroche and J. M. Raimond, Exploring the Quantum (Oxford, 2006). [CrossRef]
  28. A. Gonzalez-Tudela, D. Martin-Cano, E. Moreno, L. Martin-Moreno, C. Tejedor, and F. J. Garcia-Vidal, “Entanglement of two qubits mediated by one-dimensional plasmonic waveguides,” Phys. Rev. Lett.106, 020501 (2011). [CrossRef] [PubMed]
  29. L. Slodickačka, G. Hétet, N. Röck, P. Schindler, M. Hennrich, and R. Blatt, “Atom-atom entanglement by single-photon detection,” Phys. Rev. Lett.110, 083603 (2013). [CrossRef] [PubMed]
  30. C. Cabrillo, J. I. Cirac, P. García-Fernández, and P. Zoller, “Creation of entangled states of distant atoms by interference,” Phys. Rev. A59, 2 (1999). [CrossRef]
  31. Y. L. Lim, A. Beige, and L. C. Kwek, “Repeat-until-success linear optics distributed quantum computing” Phys. Rev. Lett.95, 030305 (2005). [CrossRef]
  32. J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguide coupled to a two-level system,” Opt. Lett.30, 2001–2003 (2005). [CrossRef] [PubMed]
  33. J. T. Shen and S. Fan, “Theory of single-photon transport in a single mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A79, 023837 (2009). [CrossRef]
  34. M. P. A. Jones, J. Beugnon, A. Gaëtan, J. Zhang, G. Messin, A. Browaeys, and P. Grangier, “Fast quantum state control of a single trapped neutral atom,” Phys. Rev. A75, 040301(R) (2007). [CrossRef]
  35. H. S. Nguyen, G. Sallen, C. Voisin, Ph. Roussignol, C. Diederichs, and G. Cassabois, “Ultra-coherent single photon source,” Appl. Phys. Lett.99, 26 (2011). [CrossRef]
  36. H. Zhang, R. McConnell, S. Ćuk, Q. Lin, M. H. S. Smith, I. D. Leroux, and V. Vuletić, “Collective state measurement of mesoscopic ensembles with single-atom resolution,” Phys. Rev. Lett.109, 133603 (2012). [CrossRef] [PubMed]

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