Abstract
A scheme is presented for generating steady three- (four-) dimensional entangled states for two atoms trapped in a strongly dissipative single-mode (double-mode) cavity via quantum-jump-based feedback. The cavity decay is no longer undesirable, but plays an integral part in the schemes. Numerical results show that the target states could be obtained from any initial states via quantum-jump-based feedback. Moreover, our scheme is insensitive to moderate fluctuations of experimental parameters and detection inefficiencies without atomic decay since the system can always reach the target state. Nevertheless, the atomic decay still plays a negative role in the current scheme. The scheme can be generalized to realize \(N\)-dimensional entanglement for two atoms.
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Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)
Gordon, G., Rigolin, G.: Generalized teleportation protocol. Phys. Rev. A 73, 042309 (2006)
Zheng, S.B., Guo, G.C.: Scheme for atomic-state teleportation between two bad cavities. Phys. Rev. A 73, 032329 (2006)
Vitanov, N.V., Stenholm, S.: Analytic properties and effective two-level problems in stimulated Raman adiabatic passage. Phys. Rev. A 55, 648–660 (1997)
Rauschenbeutel, A., Nogues, G., Osnaghi, S., Bertet, P., Brune, M., Raimond, J., Haroche, S.: Step-by-Step engineered multiparticle entanglement. Science 288, 2024–2028 (2000)
Sackett, C.A., Kielpinski, D., King, B.E., Langer, C., Meyer, V., Myatt, C.J., Rowe, M., Turchette, Q.A., Itano, W.M., Wineland, D.J., Monroe, C.: Experimental entanglement of four particles. Nature 404, 256 (2000)
Pan, J.W., Daniell, M., Gasparoni, S., Weihs, G., Zeilinger, A.: Experimental demonstration of four-photon entanglement and high-fidelity teleportation. Phys. Rev. Lett. 86, 4435–4438 (2001)
Roos, C.F., Riebe, M., Häffner, H., Hänsel, W., Benhelm, J., Lancaster, G.P.T., Becher, C., Schmidt-Kaler, F., Blatt, R.: Control and measurement of three-qubit entangled states. Science 304, 1478–1480 (2004)
Haroche, S., Kleppner, D.: Cavity quantum electrodynamics. Phys. Today 42, 24 (1989)
Walther, H., Varcoe, B.T.H., Englert, B.G., Becker, T.: Cavity quantum electrodynamics. Rep. Prog. Phys. 69, 1325 (2006)
Metz, J., Beige, A.: Macroscopic quantum jumps and entangled state preparation. Phys. Rev. A 76, 022331 (2007)
Birnbaum, K.M., Boca, A., Miller, R., Boozer, A.D., Northup, T.E., Kimble, H.J.: Photon blockade in an optical cavity with one trapped atom. Nature (London) 436, 87–90 (2005)
Wieman, C.E., Pritchard, D.E., Wineland, D.J.: Atom cooling, trapping, and quantum manipulation. Rev. Mod. Phys. 71, S253–S262 (1999)
Leibfried, D., Blatt, R., Monroe, C., Wineland, D.: Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281–324 (2003)
Bruß, D., Macchiavello, C.: Optimal eavesdropping in cryptography with three-dimensional quantum states. Phys. Rev. Lett. 88, 127901 (2002)
Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88, 127902 (2002)
Zou, X.B., Pahlke, K., Mathis, W.: Generation of an entangled state of two three-level atoms in cavity QED. Phys. Rev. A 67, 044301 (2003)
Li, W.A., Huang, G.Y.: Deterministic generation of a three-dimensional entangled state via quantum Zeno dynamics. Phys. Rev. A 83, 022322 (2011)
Chen, L.B., Shi, P., Zheng, C.H., Gu, Y.J.: Generation of three-dimensional entangled state between a single atom and a Bose-Einstein condensate via adiabatic passage. Opt. Express 20, 14547–14555 (2012)
Shen, L.T., Wu, H.Z., Chen, R.X.: Robust generation of a four-dimensional entangled state in separate cavities via quantum Zeno dynamics. J. Phys. B 44, 205503 (2011)
Wang, X.T., Schirmer, S.G.: Generating maximal entanglement between non-interacting atoms by collective decay and symmetry breaking. (2010) arXiv:1005.2114v2
Kastoryano, M.J., Reiter, F., Sorensen, A.S.: Dissipative preparation of entanglement in optical cavities. Phys. Rev. Lett. 106, 090502 (2011)
Busch, J., De, S., Ivanov, S.S., Torosov, B.T., Spiller, T.P., Beige, A.: Cooling atom-cavity systems into entangled states. Phys. Rev. A 84, 022316 (2011)
Shen, L.T., Chen, X.Y., Yang, Z.B., Wu, H.Z., Zheng, S.B.: Steady-state entanglement for distant atoms by dissipation in coupled cavities. Phys. Rev. A 84, 064302 (2011)
Reiter, F., Kastoryano, M.J., Sørensen, A.S.: Driving two atoms in an optical cavity into an entangled steady state using engineered decay. New J. Phys. 14, 053022 (2012)
Carvalho, A.R.R., Reid, A.J.S., Hope, J.J.: Controlling entanglement by direct quantum feedback. Phys. Rev. A 78, 012334 (2008)
Shao, X.Q., Zheng, T.Y., Zhang, S.: Engineering steady three-atom singlet states via quantum-jump-based feedback. Phys. Rev. A 85, 042308 (2012)
Wang, J., Wiseman, H.M., Milburn, G.J.: Dynamical creation of entanglement by homodyne-mediated feedback. Phys. Rev. A 71, 042309 (2005)
Stevenson, R.N., Hope, J.J., Carvalho, A.R.R.: Engineering steady states using jump-based feedback for multipartite entanglement generation. Phys. Rev. A 84, 022332 (2011)
Carvalho, A.R.R., Hope, J.J.: Stabilising entanglement by quantum jump-based feedback. Phys. Rev. A 76, 010301(R) (2007)
Pan, J.W., Simon, C., Brukner, Č., Zeilinger, A.: Entanglement purification for quantum communication. Nature (London) 410, 1067 (2001)
Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)
Ticozzi, F., Viola, L.: Analysis and synthesis of attractive quantum Markovian dynamics. Automatica 45, 2002–2009 (2009)
Schirmer, S.G., Wang, X.: Stabilizing open quantum systems by Markovian reservoir engineering. Phys. Rev. A 81, 062306 (2010)
Nußmann, S., Hijlkema, M., Weber, B., Rohde, F., Rempe, G., Kuhn, A.: Submicron positioning of single atoms in a microcavity. Phys. Rev. Lett. 95, 173602 (2005)
Fushman, I., Englund, D., Faraon, A., Stoltz, N., Petroff, P., Vučković, J.: Controlled phase shifts with a single quantum dot. Science 320, 769–772 (2008)
Dayan, B., Parkins, A.S., Aoki, T., Ostby, E.P., Vahala, K.J., Kimble, H.J.: A photon turnstile dynamically regulated by one atom. Science 319, 1062–1065 (2008)
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This project was supported by the National Natural Science Foundation of China under Grant Nos. 11064016 and 61068001.
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Wu, QC., Ji, X. Generation of steady three- and four-dimensional entangled states via quantum-jump-based feedback. Quantum Inf Process 12, 3167–3178 (2013). https://doi.org/10.1007/s11128-013-0592-y
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DOI: https://doi.org/10.1007/s11128-013-0592-y