Skip to main content
Erschienen in: Optical and Quantum Electronics 2/2021

01.02.2021

Realization of the quantum CNOT gate based on multiphoton process in multimode Cavity QED

verfasst von: M. Hammani, A. Chouikh, T. Said, M. Bennai

Erschienen in: Optical and Quantum Electronics | Ausgabe 2/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We propose a scheme for implementing the CNOT gate in which the photonic qubits encoded on the cavity modes and a four-level atom passes through the cavity. The location of the resonance is predicted from the use of effective three-level Hamiltonian. First, we have theoretically studied the interaction of multi-level atom with multi-mode fields in a cavity by using the shore’s method. Next we have numerically calculated the probability of the state of the interest as well as the fidelity of this scheme. We have also used the wave-function and the density matrix approaches to study theoretically and numerically the effects of decoherence in the implementation of the gate.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Alqahtani, M.M., Everitt, M.S., Garraway, B.M.: Cavity QED Photons for Quantum Information Processing. (2014). arXiv:1407,0654v1 [quant-ph] Alqahtani, M.M., Everitt, M.S., Garraway, B.M.: Cavity QED Photons for Quantum Information Processing. (2014). arXiv:​1407,0654v1 [quant-ph]
Zurück zum Zitat Arias, A., Helmrich, S., Schweiger, C., Ardizzone, L., Lochead, G., Whitlock, S.: Versatile: high-power 460nm laser system for Rydberg excitation of ultracold potassium. Opt. Express 25, 14829 (2017)ADSCrossRef Arias, A., Helmrich, S., Schweiger, C., Ardizzone, L., Lochead, G., Whitlock, S.: Versatile: high-power 460nm laser system for Rydberg excitation of ultracold potassium. Opt. Express 25, 14829 (2017)ADSCrossRef
Zurück zum Zitat Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elemntary gates for quntum computation. Phys. Rev. A 52(5), 3457–3467 (1995)ADSCrossRef Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elemntary gates for quntum computation. Phys. Rev. A 52(5), 3457–3467 (1995)ADSCrossRef
Zurück zum Zitat Barnett, S.M., Radmore, P.M.: Methods in Theoretical Quantum Optics. Clarendon, Oxford (2002)MATHCrossRef Barnett, S.M., Radmore, P.M.: Methods in Theoretical Quantum Optics. Clarendon, Oxford (2002)MATHCrossRef
Zurück zum Zitat Boozer, A.D., Boca, A., Miller, R., Northup, T.E., Kimble, H.J.: Reversible State Transfer between Light and a Single Trapped Atom. Phys. Rev. Lett. 98(19), 193601 (2007)ADSCrossRef Boozer, A.D., Boca, A., Miller, R., Northup, T.E., Kimble, H.J.: Reversible State Transfer between Light and a Single Trapped Atom. Phys. Rev. Lett. 98(19), 193601 (2007)ADSCrossRef
Zurück zum Zitat Brattke, S., Varcoe, B.T.H., Walther, H.: Generation of photon number states on demand via cavity quantum electrodynamics. Phys. Rev. Lett. 86(16), 3534–3537 (2001)ADSCrossRef Brattke, S., Varcoe, B.T.H., Walther, H.: Generation of photon number states on demand via cavity quantum electrodynamics. Phys. Rev. Lett. 86(16), 3534–3537 (2001)ADSCrossRef
Zurück zum Zitat Chang, J.T., Zubairy, M.S.: Three-qubit phase gate based on cavity quantum electrodynamics. Phys. Rev. A 77(1), 012329 (2008)ADSCrossRef Chang, J.T., Zubairy, M.S.: Three-qubit phase gate based on cavity quantum electrodynamics. Phys. Rev. A 77(1), 012329 (2008)ADSCrossRef
Zurück zum Zitat Chouikh, Abdelhaq, et al.: Implementation of universal two-and three-qubit quantum gates in a cavity QED. Opt. Quant. Electron. 48(10), 463 (2016)CrossRef Chouikh, Abdelhaq, et al.: Implementation of universal two-and three-qubit quantum gates in a cavity QED. Opt. Quant. Electron. 48(10), 463 (2016)CrossRef
Zurück zum Zitat Cirac, J.I., Zoller, P.: Quantum computations with cold trapped ions. Phys. Rev. Lett. 74(20), 4091–4094 (1995)ADSCrossRef Cirac, J.I., Zoller, P.: Quantum computations with cold trapped ions. Phys. Rev. Lett. 74(20), 4091–4094 (1995)ADSCrossRef
Zurück zum Zitat Dalibard, J., Castin, Y., Mølmer, K.: Wave-function approach to dissipative processes in quantum optics. Phys. Rev. Lett. 68(5), 580–583 (1992)ADSCrossRef Dalibard, J., Castin, Y., Mølmer, K.: Wave-function approach to dissipative processes in quantum optics. Phys. Rev. Lett. 68(5), 580–583 (1992)ADSCrossRef
Zurück zum Zitat Dum, R., Zoller, P., Ritsch, H.: Monte Carlo simulation of the atomic master equation for spontaneous emission. Phys. Rev. A 45, 4879 (1992)ADSCrossRef Dum, R., Zoller, P., Ritsch, H.: Monte Carlo simulation of the atomic master equation for spontaneous emission. Phys. Rev. A 45, 4879 (1992)ADSCrossRef
Zurück zum Zitat Everitt, M.S., Garraway, B.M.: Multiphoton resonances for all-optical quantum logic with multiple cavities. Phys. Rev. A 90(1), 012335 (2014)ADSCrossRef Everitt, M.S., Garraway, B.M.: Multiphoton resonances for all-optical quantum logic with multiple cavities. Phys. Rev. A 90(1), 012335 (2014)ADSCrossRef
Zurück zum Zitat Garraway, B.M., Sherman, B., Moya-Cessa, H., Knight, P.L., Kurizki, G.: Generation and detection of nonclassical field states by conditional measurements following two-photon resonant interactions. Phys. Rev. A 49(1), 535–547 (1994)ADSCrossRef Garraway, B.M., Sherman, B., Moya-Cessa, H., Knight, P.L., Kurizki, G.: Generation and detection of nonclassical field states by conditional measurements following two-photon resonant interactions. Phys. Rev. A 49(1), 535–547 (1994)ADSCrossRef
Zurück zum Zitat Gotzinger, S., Menezes, L de S., Mazzei, A., Kuhn, S., Sandoghdar, V., Benson, O.: Controlled Photon Transfer between Two Individual Nanoemitters via Shared High-Q Modes of a Microsphere Resonator. Nano Lett. 6(6), 11511154 (2006)CrossRef Gotzinger, S., Menezes, L de S., Mazzei, A., Kuhn, S., Sandoghdar, V., Benson, O.: Controlled Photon Transfer between Two Individual Nanoemitters via Shared High-Q Modes of a Microsphere Resonator. Nano Lett. 6(6), 11511154 (2006)CrossRef
Zurück zum Zitat Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)ADSCrossRef Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)ADSCrossRef
Zurück zum Zitat Gurudev Dutt, M.V., Cheng, Jun, Li, Bo, Xiaodong, Xu, Xiaoqin Li, P.R., Berman, D.G., Steel, Bracker, A. S.: Stimulated and spontaneous optical generation of electron spin coherence in charged GaAs quantum dots. Phys. Rev. Lett. 94(22), 227403 (2005)ADSCrossRef Gurudev Dutt, M.V., Cheng, Jun, Li, Bo, Xiaodong, Xu, Xiaoqin Li, P.R., Berman, D.G., Steel, Bracker, A. S.: Stimulated and spontaneous optical generation of electron spin coherence in charged GaAs quantum dots. Phys. Rev. Lett. 94(22), 227403 (2005)ADSCrossRef
Zurück zum Zitat Hofheinz, M., Weig, E.M., Ansmann, M., Bialczak, R.C., Lucero, E., Neeley, M., O’Connell, A.D., Wang, H., Martinis, J.M., Cleland, A.N.: Generation of Fock states in a superconducting quantum circuit. Nature 454, 310–314 (2008)ADSCrossRef Hofheinz, M., Weig, E.M., Ansmann, M., Bialczak, R.C., Lucero, E., Neeley, M., O’Connell, A.D., Wang, H., Martinis, J.M., Cleland, A.N.: Generation of Fock states in a superconducting quantum circuit. Nature 454, 310–314 (2008)ADSCrossRef
Zurück zum Zitat Jonathan, A.J., Michele, M., Rasmus, H.H.: Implementation of a quantum Search algorithm on a quantum computer. Nature 393, 344–346 (1998)ADSCrossRef Jonathan, A.J., Michele, M., Rasmus, H.H.: Implementation of a quantum Search algorithm on a quantum computer. Nature 393, 344–346 (1998)ADSCrossRef
Zurück zum Zitat Kok, P., Munro, W., Nemoto, K., Ralph, T., Dowling, J., Milburn, G.: Publisher’s note: linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135 (2007)ADSCrossRef Kok, P., Munro, W., Nemoto, K., Ralph, T., Dowling, J., Milburn, G.: Publisher’s note: linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135 (2007)ADSCrossRef
Zurück zum Zitat Kollar, A.J., Papageorge, A.T., Vaidya, V.D., Guo, Y., Keeling, J., Lev, B.L.: Supermode-density-wave-polariton condensation with a Bose–Einstein Condensate in multimode cavity. Nat. Commun. 8(14386), 17 (2017) Kollar, A.J., Papageorge, A.T., Vaidya, V.D., Guo, Y., Keeling, J., Lev, B.L.: Supermode-density-wave-polariton condensation with a Bose–Einstein Condensate in multimode cavity. Nat. Commun. 8(14386), 17 (2017)
Zurück zum Zitat Kuhr, S., Gleyzes, S., Guerlin, C., Bernu, J., Ho, U.B., Del eglise, S., Osnaghi, S., Brune, M., Raimond, J. M., Haroche, S., Jacques, E., Bosland, P., Visentin, B.: Ultrahigh finesse Fabry-Pérot superconducting resonator. Appl. Phys. Lett. 90, 164101 (2007)ADSCrossRef Kuhr, S., Gleyzes, S., Guerlin, C., Bernu, J., Ho, U.B., Del eglise, S., Osnaghi, S., Brune, M., Raimond, J. M., Haroche, S., Jacques, E., Bosland, P., Visentin, B.: Ultrahigh finesse Fabry-Pérot superconducting resonator. Appl. Phys. Lett. 90, 164101 (2007)ADSCrossRef
Zurück zum Zitat Lambropoulos, P., Petrosyan, D.: Fundamentals of Quantum Optics and Quantum Information. Springer-Verlag, Berlin Heidelberg (2007) Lambropoulos, P., Petrosyan, D.: Fundamentals of Quantum Optics and Quantum Information. Springer-Verlag, Berlin Heidelberg (2007)
Zurück zum Zitat Lazarou, C., Garraway, B.M.: Adiabatic entanglement in two-atom cavity QED. Phys. Rev. A 77(2), 023818 (2008)ADSCrossRef Lazarou, C., Garraway, B.M.: Adiabatic entanglement in two-atom cavity QED. Phys. Rev. A 77(2), 023818 (2008)ADSCrossRef
Zurück zum Zitat Lee, H., Chen, T., Li, J., Yang, K.Y., Jeon, S., Painter, O., Vahala, K.J.: Chemically etched ultrahigh-Q wedge-resonator on a silicon chip. Nat. Photonics 6, 369373 (2012)CrossRef Lee, H., Chen, T., Li, J., Yang, K.Y., Jeon, S., Painter, O., Vahala, K.J.: Chemically etched ultrahigh-Q wedge-resonator on a silicon chip. Nat. Photonics 6, 369373 (2012)CrossRef
Zurück zum Zitat Mabuchi, H., Doherty, A.C.: Cavity quantum electrodynamics: cohernece in context. Science 298(5597), 1372–1377 (2002)ADSCrossRef Mabuchi, H., Doherty, A.C.: Cavity quantum electrodynamics: cohernece in context. Science 298(5597), 1372–1377 (2002)ADSCrossRef
Zurück zum Zitat Maller, K.M., Lichtman, M.T., Xia, T., Sun, Y., Piotrowicz, M.J., Carr, A.W., Isenhower, L., Saffman, M.: Rydberg-blockade controlled-not gate and entanglement in a two-dimensional array of neutral-atom qubits. Phys. Rev. A 92, 022336 (2015)ADSCrossRef Maller, K.M., Lichtman, M.T., Xia, T., Sun, Y., Piotrowicz, M.J., Carr, A.W., Isenhower, L., Saffman, M.: Rydberg-blockade controlled-not gate and entanglement in a two-dimensional array of neutral-atom qubits. Phys. Rev. A 92, 022336 (2015)ADSCrossRef
Zurück zum Zitat McMahon, D.: Quantum computing explained. John Wiley & Sons (2007) McMahon, D.: Quantum computing explained. John Wiley & Sons (2007)
Zurück zum Zitat Meschede, D., Walther, H., Müller, G.: One-atom maser. Phys. Rev. Lett. 54(6), 551–554 (1985)ADSCrossRef Meschede, D., Walther, H., Müller, G.: One-atom maser. Phys. Rev. Lett. 54(6), 551–554 (1985)ADSCrossRef
Zurück zum Zitat Mølmer, K., Castin, Y., Dalibard, J.: Monte Carlo wave-function method in quantum optics. JOSA B 10, 524 (1993)ADSCrossRef Mølmer, K., Castin, Y., Dalibard, J.: Monte Carlo wave-function method in quantum optics. JOSA B 10, 524 (1993)ADSCrossRef
Zurück zum Zitat Nielsen et, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH Nielsen et, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH
Zurück zum Zitat Raimond, J.M., Brune, M., Haroche, S.: Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565 (2001)MathSciNetMATHADSCrossRef Raimond, J.M., Brune, M., Haroche, S.: Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565 (2001)MathSciNetMATHADSCrossRef
Zurück zum Zitat Raimond, J.M., Facchi, P., Peaudecerf, B., Pascazio, S., Sayrin, C., Dotsenko, I., Gleyzes, S., Brune, M., Haroche, S.: Quantum Zeno dynamics of a field in a cavity. Phys. Rev. A 86(3), 032120 (2012)ADSCrossRef Raimond, J.M., Facchi, P., Peaudecerf, B., Pascazio, S., Sayrin, C., Dotsenko, I., Gleyzes, S., Brune, M., Haroche, S.: Quantum Zeno dynamics of a field in a cavity. Phys. Rev. A 86(3), 032120 (2012)ADSCrossRef
Zurück zum Zitat Rauschenbeutel, A., Nogues, G., Osnaghi, S., Bertet, P., Brune, M., Raimond, J.M., Haroche, S.: Coherent operation of a tunable quantum phase gate in cavity QED. Phys. Rev. Lett. 83, 5166 (1999)ADSCrossRef Rauschenbeutel, A., Nogues, G., Osnaghi, S., Bertet, P., Brune, M., Raimond, J.M., Haroche, S.: Coherent operation of a tunable quantum phase gate in cavity QED. Phys. Rev. Lett. 83, 5166 (1999)ADSCrossRef
Zurück zum Zitat Rempe, G., Schmidt-Kaler, F., Walther, H.: Observation of sub-Poissonian photon statistics in a micromaser. Phys. Rev. Lett. 64(23), 2783 (1990)ADSCrossRef Rempe, G., Schmidt-Kaler, F., Walther, H.: Observation of sub-Poissonian photon statistics in a micromaser. Phys. Rev. Lett. 64(23), 2783 (1990)ADSCrossRef
Zurück zum Zitat Said, T., Chouikh, A., Essammouni, K., Bennai, M.: Implementing N-Quantum Phase Gate via Circuit QED with qubit-qubit interaction. Mod. Phys. Lett. B 30(5), 1650050 (2016)ADSCrossRef Said, T., Chouikh, A., Essammouni, K., Bennai, M.: Implementing N-Quantum Phase Gate via Circuit QED with qubit-qubit interaction. Mod. Phys. Lett. B 30(5), 1650050 (2016)ADSCrossRef
Zurück zum Zitat Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)MathSciNetMATHCrossRef Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)MathSciNetMATHCrossRef
Zurück zum Zitat Shore, B.: Two-level behavior of coherent excitation of multilevel systems. Phys. Rev. A 24, 1413 (1981)ADSCrossRef Shore, B.: Two-level behavior of coherent excitation of multilevel systems. Phys. Rev. A 24, 1413 (1981)ADSCrossRef
Zurück zum Zitat Specht, H.P., Nölleke, C., Reiserer, A., Uphoff, M., Figueroa, E., Ritter, S., Rempe, G.: A single-atom quantum memory. Nature 473, 190193 (2011)CrossRef Specht, H.P., Nölleke, C., Reiserer, A., Uphoff, M., Figueroa, E., Ritter, S., Rempe, G.: A single-atom quantum memory. Nature 473, 190193 (2011)CrossRef
Zurück zum Zitat van Enk, S.J., Kimble, H.J., Mabuchi, H.: Quantum information processing in cavity-QED. Quantum Inf. Process. 3(1–5), 75–90 (2004)MATHCrossRef van Enk, S.J., Kimble, H.J., Mabuchi, H.: Quantum information processing in cavity-QED. Quantum Inf. Process. 3(1–5), 75–90 (2004)MATHCrossRef
Zurück zum Zitat Varcoe, B.T.H., Brattke, S., Weidinger, M., Walther, H.: Preparing pure photon number states of the radiation field. Nature 403, 743–746 (2000)ADSCrossRef Varcoe, B.T.H., Brattke, S., Weidinger, M., Walther, H.: Preparing pure photon number states of the radiation field. Nature 403, 743–746 (2000)ADSCrossRef
Zurück zum Zitat Varcoe, B.T., Brattke, S., Walther, H.: The creation and detection of arbitrary photon number states using cavity QED. New J. Phys. 6(1), 97 (2004).ADSCrossRef Varcoe, B.T., Brattke, S., Walther, H.: The creation and detection of arbitrary photon number states using cavity QED. New J. Phys. 6(1), 97 (2004).ADSCrossRef
Zurück zum Zitat Vernooy, D. W., Ilchenko, V. S., Mabuchi, H., Streed, E. W., & Kimble, H. J.: High-Q measurements of fused-silica microspheres in the near infrared. Opt. Lett. 23(4), 247–249 (1998)ADSCrossRef Vernooy, D. W., Ilchenko, V. S., Mabuchi, H., Streed, E. W., & Kimble, H. J.: High-Q measurements of fused-silica microspheres in the near infrared. Opt. Lett. 23(4), 247–249 (1998)ADSCrossRef
Zurück zum Zitat Walther, H., Varcoe, B. T., Englert, B. G., Becker, T.:. Cavity quantum electrodynamics. Rep. Prog. Phys., 69(5), 1325 (2006)ADSCrossRef Walther, H., Varcoe, B. T., Englert, B. G., Becker, T.:. Cavity quantum electrodynamics. Rep. Prog. Phys., 69(5), 1325 (2006)ADSCrossRef
Zurück zum Zitat Zhang, X. L., Gill, A. T., Isenhower, L., Walker, T. G., Saffman, M.: Fidelity of a Rydberg-blockade quantum gate from simulated quantum process tomography. Phys. Rev. A. 85(4), 042310 (2012)ADSCrossRef Zhang, X. L., Gill, A. T., Isenhower, L., Walker, T. G., Saffman, M.: Fidelity of a Rydberg-blockade quantum gate from simulated quantum process tomography. Phys. Rev. A. 85(4), 042310 (2012)ADSCrossRef
Metadaten
Titel
Realization of the quantum CNOT gate based on multiphoton process in multimode Cavity QED
verfasst von
M. Hammani
A. Chouikh
T. Said
M. Bennai
Publikationsdatum
01.02.2021
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 2/2021
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-020-02685-y

Weitere Artikel der Ausgabe 2/2021

Optical and Quantum Electronics 2/2021 Zur Ausgabe