Abstract

We induce quantum jumps between the hyperfine ground states of one and two cesium atoms, strongly coupled to the mode of a high-finesse optical resonator, and analyze the resulting random telegraph signals. We identify experimental parameters to deduce the atomic spin state nondestructively from the stream of photons transmitted through the cavity, achieving a compromise between a good signal-to-noise ratio and minimal measurement-induced perturbations. In order to extract optimum information about the spin dynamics from the photon count signal, a Bayesian update formalism is employed, which yields time-dependent probabilities for the atoms to be in one of the two hyperfine states. This analysis is extended to short time bins where a simple threshold analysis would not yield reasonable results. We discuss the effect of super-Poissonian photon number distributions caused by atomic motion.

© 2010 Optical Society of America

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2009 (1)

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

2008 (4)

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schörner, A. Widera, and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

P. J. Windpassinger, D. Oblak, P. G. Petrov, M. Kubasik, M. Saffman, C. L. G. Alzar, J. Appel, J. H. Müller, N. Jærgaard, and E. S. Polzik, “Nondestructive probing of Rabi oscillations on the cesium clock transition near the standard quantum limit,” Phys. Rev. Lett. 100, 103601 (2008).
[CrossRef] [PubMed]

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

A. R. R. Carvalho, A. J. S. Reid, and J. J. Hope, “Controlling entanglement by direct quantum feedback,” Phys. Rev. A 78, 012334 (2008).
[CrossRef]

2007 (7)

A. R. R. Carvalho and J. J. Hope, “Stabilizing entanglement by quantum-jump-based feedback,” Phys. Rev. A 76, 010301 (2007).
[CrossRef]

K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
[CrossRef] [PubMed]

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Reversible state transfer between light and a single trapped atom,” Phys. Rev. Lett. 98, 193601 (2007).
[CrossRef] [PubMed]

T. Wilk, S. C. Webster, H. P. Specht, G. Rempe, and A. Kuhn, “Polarization-controlled single photons,” Phys. Rev. Lett. 98, 063601 (2007).
[CrossRef] [PubMed]

J. Metz and A. Beige, “Macroscopic quantum jumps and entangled-state preparation,” Phys. Rev. A 76, 022331 (2007).
[CrossRef]

S. Gleyzes, S. Kuhr, C. Guerlin, J. Bernu, S. Deleglise, U. B. Hoff, M. Brune, J.-M. Raimond, and S. Haroche, “Quantum jumps of light recording the birth and death of a photon in a cavity,” Nature 446, 297–300 (2007).
[CrossRef] [PubMed]

C. Guerlin, J. Bernu, S. Deléglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, and S. Haroche, “Progressive field-state collapse and quantum non-demolition photon counting,” Nature 448, 889–893 (2007).
[CrossRef] [PubMed]

2006 (3)

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef] [PubMed]

S. Chaudhury, G. A. Smith, K. Schulz, and P. S. Jessen, “Continuous nondemolition measurement of the Cs clock transition pseudospin,” Phys. Rev. Lett. 96, 043001 (2006).
[CrossRef] [PubMed]

K. Murr, S. Nußmann, T. Puppe, M. Hijlkema, B. Weber, S. C. Webster, A. Kuhn, and G. Rempe, “Three-dimensional cavity cooling and trapping in an optical lattice,” Phys. Rev. A 73, 063415 (2006).
[CrossRef]

2005 (2)

S. Nußmann, K. Murr, M. Hijlkema, B. Weber, A. Kuhn, and G. Rempe, “Vacuum-stimulated cooling of single atoms in three dimensions,” Nat. Phys. 1, 122–125 (2005).
[CrossRef]

S. Nußmann, M. Hijlkema, B. Weber, F. Rohde, G. Rempe, and A. Kuhn, “Submicron positioning of single atoms in a microcavity,” Phys. Rev. Lett. 95, 173602 (2005).
[CrossRef] [PubMed]

2004 (3)

M. Keller, B. Lange, K. Hayasaka, W. Lange, and H. Walther, “Continuous generation of single photons with controlled waveform in an ion-trap cavity system,” Nature 431, 1075–1078 (2004).
[CrossRef] [PubMed]

C. Maurer, C. Becher, C. Russo, J. Eschner, and R. Blatt, “A single-photon source based on a single Ca+ ion,” New J. Phys. 6, 94-1–94-19 (2004).
[CrossRef]

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef] [PubMed]

2003 (4)

P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20, 1098–1130 (2003).
[CrossRef]

L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
[CrossRef]

A. S. Sørensen and K. Mølmer, “Measurement induced entanglement and quantum computation with atoms in optical cavities,” Phys. Rev. Lett. 91, 097905 (2003).
[CrossRef] [PubMed]

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Nägerl, D. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

2001 (2)

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[CrossRef]

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278–280 (2001).
[CrossRef] [PubMed]

2000 (1)

Y. Yuzhelevski, M. Yuzhelevski, and G. Jung, “Random telegraph noise analysis in time domain,” Rev. Sci. Instrum. 71, 1681–1688 (2000).
[CrossRef]

1998 (1)

G. Hechenblaikner, M. Gangl, P. Horak, and H. Ritsch, “Cooling an atom in a weakly driven high-Q cavity,” Phys. Rev. A 58, 3030–3042 (1998).
[CrossRef]

1994 (1)

1993 (1)

B. Gao, “Effects of Zeeman degeneracy on the steady-state properties of an atom interacting with a near-resonant laser field: analytic results,” Phys. Rev. A 48, 2443–2448 (1993).
[CrossRef] [PubMed]

1987 (1)

W. M. Itano, J. Berquist, R. G. Hulet, and D. Wineland, “Radiative decay rates in Hg+ from observations of quantum jumps in a single ion,” Phys. Rev. Lett. 59, 2732–2735 (1987).
[CrossRef] [PubMed]

1986 (3)

T. Sauter, W. Neuhauser, R. Blatt, and P. E. Toschek, “Observation of quantum jumps,” Phys. Rev. Lett. 57, 1696–1698 (1986).
[CrossRef] [PubMed]

J. C. Berquist, R. G. Hulet, W. Itano, and D. J. Wineland, “Observation of quantum jumps in a single atom,” Phys. Rev. Lett. 57, 1669–1702 (1986).
[CrossRef]

W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: observation of quantum jumps,” Phys. Rev. Lett. 56, 2797–2799 (1986).
[CrossRef] [PubMed]

1985 (1)

R. J. Cook and H. J. Kimble, “Possibility of direct observation of quantum jumps,” Phys. Rev. Lett. 54, 1023–1026 (1985).
[CrossRef] [PubMed]

1980 (1)

V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, “Quantum nondemolition measurements,” Science 209, 547–557 (1980).
[CrossRef] [PubMed]

1963 (1)

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

Ahmadi, P.

K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
[CrossRef] [PubMed]

Alt, W.

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schörner, A. Widera, and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278–280 (2001).
[CrossRef] [PubMed]

Alzar, C. L. G.

P. J. Windpassinger, D. Oblak, P. G. Petrov, M. Kubasik, M. Saffman, C. L. G. Alzar, J. Appel, J. H. Müller, N. Jærgaard, and E. S. Polzik, “Nondestructive probing of Rabi oscillations on the cesium clock transition near the standard quantum limit,” Phys. Rev. Lett. 100, 103601 (2008).
[CrossRef] [PubMed]

Appel, J.

P. J. Windpassinger, D. Oblak, P. G. Petrov, M. Kubasik, M. Saffman, C. L. G. Alzar, J. Appel, J. H. Müller, N. Jærgaard, and E. S. Polzik, “Nondestructive probing of Rabi oscillations on the cesium clock transition near the standard quantum limit,” Phys. Rev. Lett. 100, 103601 (2008).
[CrossRef] [PubMed]

Becher, C.

C. Maurer, C. Becher, C. Russo, J. Eschner, and R. Blatt, “A single-photon source based on a single Ca+ ion,” New J. Phys. 6, 94-1–94-19 (2004).
[CrossRef]

Beige, A.

J. Metz and A. Beige, “Macroscopic quantum jumps and entangled-state preparation,” Phys. Rev. A 76, 022331 (2007).
[CrossRef]

Bernu, J.

S. Gleyzes, S. Kuhr, C. Guerlin, J. Bernu, S. Deleglise, U. B. Hoff, M. Brune, J.-M. Raimond, and S. Haroche, “Quantum jumps of light recording the birth and death of a photon in a cavity,” Nature 446, 297–300 (2007).
[CrossRef] [PubMed]

C. Guerlin, J. Bernu, S. Deléglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, and S. Haroche, “Progressive field-state collapse and quantum non-demolition photon counting,” Nature 448, 889–893 (2007).
[CrossRef] [PubMed]

Berquist, J.

W. M. Itano, J. Berquist, R. G. Hulet, and D. Wineland, “Radiative decay rates in Hg+ from observations of quantum jumps in a single ion,” Phys. Rev. Lett. 59, 2732–2735 (1987).
[CrossRef] [PubMed]

Berquist, J. C.

J. C. Berquist, R. G. Hulet, W. Itano, and D. J. Wineland, “Observation of quantum jumps in a single atom,” Phys. Rev. Lett. 57, 1669–1702 (1986).
[CrossRef]

Blatt, R.

C. Maurer, C. Becher, C. Russo, J. Eschner, and R. Blatt, “A single-photon source based on a single Ca+ ion,” New J. Phys. 6, 94-1–94-19 (2004).
[CrossRef]

T. Sauter, W. Neuhauser, R. Blatt, and P. E. Toschek, “Observation of quantum jumps,” Phys. Rev. Lett. 57, 1696–1698 (1986).
[CrossRef] [PubMed]

Boca, A.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Reversible state transfer between light and a single trapped atom,” Phys. Rev. Lett. 98, 193601 (2007).
[CrossRef] [PubMed]

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef] [PubMed]

Boozer, A. D.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Reversible state transfer between light and a single trapped atom,” Phys. Rev. Lett. 98, 193601 (2007).
[CrossRef] [PubMed]

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef] [PubMed]

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Nägerl, D. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

Braginsky, V. B.

V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, “Quantum nondemolition measurements,” Science 209, 547–557 (1980).
[CrossRef] [PubMed]

Brune, M.

S. Gleyzes, S. Kuhr, C. Guerlin, J. Bernu, S. Deleglise, U. B. Hoff, M. Brune, J.-M. Raimond, and S. Haroche, “Quantum jumps of light recording the birth and death of a photon in a cavity,” Nature 446, 297–300 (2007).
[CrossRef] [PubMed]

C. Guerlin, J. Bernu, S. Deléglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, and S. Haroche, “Progressive field-state collapse and quantum non-demolition photon counting,” Nature 448, 889–893 (2007).
[CrossRef] [PubMed]

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[CrossRef]

Buck, J. R.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Nägerl, D. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

Cappé, O.

O. Cappé, E. Moulines, and T. Ryden, Inference in Hidden Markov Models (Springer, 2000).

Carvalho, A. R. R.

A. R. R. Carvalho, A. J. S. Reid, and J. J. Hope, “Controlling entanglement by direct quantum feedback,” Phys. Rev. A 78, 012334 (2008).
[CrossRef]

A. R. R. Carvalho and J. J. Hope, “Stabilizing entanglement by quantum-jump-based feedback,” Phys. Rev. A 76, 010301 (2007).
[CrossRef]

Chapman, M. S.

K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
[CrossRef] [PubMed]

Chaudhury, S.

S. Chaudhury, G. A. Smith, K. Schulz, and P. S. Jessen, “Continuous nondemolition measurement of the Cs clock transition pseudospin,” Phys. Rev. Lett. 96, 043001 (2006).
[CrossRef] [PubMed]

Cline, R. A.

Cook, R. J.

R. J. Cook and H. J. Kimble, “Possibility of direct observation of quantum jumps,” Phys. Rev. Lett. 54, 1023–1026 (1985).
[CrossRef] [PubMed]

Cummings, F. W.

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

Dehmelt, H.

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M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schörner, A. Widera, and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef] [PubMed]

Redaelli, G.

R. Paroli, G. Redaelli, and L. Spezia, “Hidden Markov models for time series of overdispersed insurances counts,” in Proceedings of the XXXI International ASTIN Colloquium (Istituto Italiano degli Attuari, 2000), pp. 461–474.

Reick, S.

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schörner, A. Widera, and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Reid, A. J. S.

A. R. R. Carvalho, A. J. S. Reid, and J. J. Hope, “Controlling entanglement by direct quantum feedback,” Phys. Rev. A 78, 012334 (2008).
[CrossRef]

Rempe, G.

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

T. Wilk, S. C. Webster, H. P. Specht, G. Rempe, and A. Kuhn, “Polarization-controlled single photons,” Phys. Rev. Lett. 98, 063601 (2007).
[CrossRef] [PubMed]

K. Murr, S. Nußmann, T. Puppe, M. Hijlkema, B. Weber, S. C. Webster, A. Kuhn, and G. Rempe, “Three-dimensional cavity cooling and trapping in an optical lattice,” Phys. Rev. A 73, 063415 (2006).
[CrossRef]

S. Nußmann, K. Murr, M. Hijlkema, B. Weber, A. Kuhn, and G. Rempe, “Vacuum-stimulated cooling of single atoms in three dimensions,” Nat. Phys. 1, 122–125 (2005).
[CrossRef]

S. Nußmann, M. Hijlkema, B. Weber, F. Rohde, G. Rempe, and A. Kuhn, “Submicron positioning of single atoms in a microcavity,” Phys. Rev. Lett. 95, 173602 (2005).
[CrossRef] [PubMed]

Ritsch, H.

P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20, 1098–1130 (2003).
[CrossRef]

G. Hechenblaikner, M. Gangl, P. Horak, and H. Ritsch, “Cooling an atom in a weakly driven high-Q cavity,” Phys. Rev. A 58, 3030–3042 (1998).
[CrossRef]

Rohde, F.

S. Nußmann, M. Hijlkema, B. Weber, F. Rohde, G. Rempe, and A. Kuhn, “Submicron positioning of single atoms in a microcavity,” Phys. Rev. Lett. 95, 173602 (2005).
[CrossRef] [PubMed]

Russo, C.

C. Maurer, C. Becher, C. Russo, J. Eschner, and R. Blatt, “A single-photon source based on a single Ca+ ion,” New J. Phys. 6, 94-1–94-19 (2004).
[CrossRef]

Ryden, T.

O. Cappé, E. Moulines, and T. Ryden, Inference in Hidden Markov Models (Springer, 2000).

Saffman, M.

P. J. Windpassinger, D. Oblak, P. G. Petrov, M. Kubasik, M. Saffman, C. L. G. Alzar, J. Appel, J. H. Müller, N. Jærgaard, and E. S. Polzik, “Nondestructive probing of Rabi oscillations on the cesium clock transition near the standard quantum limit,” Phys. Rev. Lett. 100, 103601 (2008).
[CrossRef] [PubMed]

Sandberg, J.

W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: observation of quantum jumps,” Phys. Rev. Lett. 56, 2797–2799 (1986).
[CrossRef] [PubMed]

Sauter, T.

T. Sauter, W. Neuhauser, R. Blatt, and P. E. Toschek, “Observation of quantum jumps,” Phys. Rev. Lett. 57, 1696–1698 (1986).
[CrossRef] [PubMed]

Sayrin, C.

C. Guerlin, J. Bernu, S. Deléglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, and S. Haroche, “Progressive field-state collapse and quantum non-demolition photon counting,” Nature 448, 889–893 (2007).
[CrossRef] [PubMed]

Schörner, K.

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schörner, A. Widera, and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Schrader, D.

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef] [PubMed]

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278–280 (2001).
[CrossRef] [PubMed]

Schulz, K.

S. Chaudhury, G. A. Smith, K. Schulz, and P. S. Jessen, “Continuous nondemolition measurement of the Cs clock transition pseudospin,” Phys. Rev. Lett. 96, 043001 (2006).
[CrossRef] [PubMed]

Schuster, I.

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

Smith, G. A.

S. Chaudhury, G. A. Smith, K. Schulz, and P. S. Jessen, “Continuous nondemolition measurement of the Cs clock transition pseudospin,” Phys. Rev. Lett. 96, 043001 (2006).
[CrossRef] [PubMed]

Sørensen, A. S.

A. S. Sørensen and K. Mølmer, “Measurement induced entanglement and quantum computation with atoms in optical cavities,” Phys. Rev. Lett. 91, 097905 (2003).
[CrossRef] [PubMed]

Specht, H. P.

T. Wilk, S. C. Webster, H. P. Specht, G. Rempe, and A. Kuhn, “Polarization-controlled single photons,” Phys. Rev. Lett. 98, 063601 (2007).
[CrossRef] [PubMed]

Spezia, L.

R. Paroli, G. Redaelli, and L. Spezia, “Hidden Markov models for time series of overdispersed insurances counts,” in Proceedings of the XXXI International ASTIN Colloquium (Istituto Italiano degli Attuari, 2000), pp. 461–474.

Stamper-Kurn, D.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Nägerl, D. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

Su, X. H.

L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
[CrossRef]

Thobe, A.

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

Thorne, K. S.

V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, “Quantum nondemolition measurements,” Science 209, 547–557 (1980).
[CrossRef] [PubMed]

Toschek, P. E.

T. Sauter, W. Neuhauser, R. Blatt, and P. E. Toschek, “Observation of quantum jumps,” Phys. Rev. Lett. 57, 1696–1698 (1986).
[CrossRef] [PubMed]

Vorontsov, Y. I.

V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, “Quantum nondemolition measurements,” Science 209, 547–557 (1980).
[CrossRef] [PubMed]

Walther, H.

M. Keller, B. Lange, K. Hayasaka, W. Lange, and H. Walther, “Continuous generation of single photons with controlled waveform in an ion-trap cavity system,” Nature 431, 1075–1078 (2004).
[CrossRef] [PubMed]

Weber, B.

K. Murr, S. Nußmann, T. Puppe, M. Hijlkema, B. Weber, S. C. Webster, A. Kuhn, and G. Rempe, “Three-dimensional cavity cooling and trapping in an optical lattice,” Phys. Rev. A 73, 063415 (2006).
[CrossRef]

S. Nußmann, K. Murr, M. Hijlkema, B. Weber, A. Kuhn, and G. Rempe, “Vacuum-stimulated cooling of single atoms in three dimensions,” Nat. Phys. 1, 122–125 (2005).
[CrossRef]

S. Nußmann, M. Hijlkema, B. Weber, F. Rohde, G. Rempe, and A. Kuhn, “Submicron positioning of single atoms in a microcavity,” Phys. Rev. Lett. 95, 173602 (2005).
[CrossRef] [PubMed]

Webster, S. C.

T. Wilk, S. C. Webster, H. P. Specht, G. Rempe, and A. Kuhn, “Polarization-controlled single photons,” Phys. Rev. Lett. 98, 063601 (2007).
[CrossRef] [PubMed]

K. Murr, S. Nußmann, T. Puppe, M. Hijlkema, B. Weber, S. C. Webster, A. Kuhn, and G. Rempe, “Three-dimensional cavity cooling and trapping in an optical lattice,” Phys. Rev. A 73, 063415 (2006).
[CrossRef]

Widera, A.

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schörner, A. Widera, and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Wilk, T.

T. Wilk, S. C. Webster, H. P. Specht, G. Rempe, and A. Kuhn, “Polarization-controlled single photons,” Phys. Rev. Lett. 98, 063601 (2007).
[CrossRef] [PubMed]

Windpassinger, P. J.

P. J. Windpassinger, D. Oblak, P. G. Petrov, M. Kubasik, M. Saffman, C. L. G. Alzar, J. Appel, J. H. Müller, N. Jærgaard, and E. S. Polzik, “Nondestructive probing of Rabi oscillations on the cesium clock transition near the standard quantum limit,” Phys. Rev. Lett. 100, 103601 (2008).
[CrossRef] [PubMed]

Wineland, D.

W. M. Itano, J. Berquist, R. G. Hulet, and D. Wineland, “Radiative decay rates in Hg+ from observations of quantum jumps in a single ion,” Phys. Rev. Lett. 59, 2732–2735 (1987).
[CrossRef] [PubMed]

Wineland, D. J.

J. C. Berquist, R. G. Hulet, W. Itano, and D. J. Wineland, “Observation of quantum jumps in a single atom,” Phys. Rev. Lett. 57, 1669–1702 (1986).
[CrossRef]

Yi, X. X.

L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
[CrossRef]

You, L.

L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
[CrossRef]

Yuzhelevski, M.

Y. Yuzhelevski, M. Yuzhelevski, and G. Jung, “Random telegraph noise analysis in time domain,” Rev. Sci. Instrum. 71, 1681–1688 (2000).
[CrossRef]

Yuzhelevski, Y.

Y. Yuzhelevski, M. Yuzhelevski, and G. Jung, “Random telegraph noise analysis in time domain,” Rev. Sci. Instrum. 71, 1681–1688 (2000).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nat. Phys. (1)

S. Nußmann, K. Murr, M. Hijlkema, B. Weber, A. Kuhn, and G. Rempe, “Vacuum-stimulated cooling of single atoms in three dimensions,” Nat. Phys. 1, 122–125 (2005).
[CrossRef]

Nature (3)

M. Keller, B. Lange, K. Hayasaka, W. Lange, and H. Walther, “Continuous generation of single photons with controlled waveform in an ion-trap cavity system,” Nature 431, 1075–1078 (2004).
[CrossRef] [PubMed]

S. Gleyzes, S. Kuhr, C. Guerlin, J. Bernu, S. Deleglise, U. B. Hoff, M. Brune, J.-M. Raimond, and S. Haroche, “Quantum jumps of light recording the birth and death of a photon in a cavity,” Nature 446, 297–300 (2007).
[CrossRef] [PubMed]

C. Guerlin, J. Bernu, S. Deléglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, and S. Haroche, “Progressive field-state collapse and quantum non-demolition photon counting,” Nature 448, 889–893 (2007).
[CrossRef] [PubMed]

New J. Phys. (2)

C. Maurer, C. Becher, C. Russo, J. Eschner, and R. Blatt, “A single-photon source based on a single Ca+ ion,” New J. Phys. 6, 94-1–94-19 (2004).
[CrossRef]

M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schörner, A. Widera, and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

Phys. Rev. A (7)

K. Murr, S. Nußmann, T. Puppe, M. Hijlkema, B. Weber, S. C. Webster, A. Kuhn, and G. Rempe, “Three-dimensional cavity cooling and trapping in an optical lattice,” Phys. Rev. A 73, 063415 (2006).
[CrossRef]

J. Metz and A. Beige, “Macroscopic quantum jumps and entangled-state preparation,” Phys. Rev. A 76, 022331 (2007).
[CrossRef]

G. Hechenblaikner, M. Gangl, P. Horak, and H. Ritsch, “Cooling an atom in a weakly driven high-Q cavity,” Phys. Rev. A 58, 3030–3042 (1998).
[CrossRef]

B. Gao, “Effects of Zeeman degeneracy on the steady-state properties of an atom interacting with a near-resonant laser field: analytic results,” Phys. Rev. A 48, 2443–2448 (1993).
[CrossRef] [PubMed]

L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
[CrossRef]

A. R. R. Carvalho and J. J. Hope, “Stabilizing entanglement by quantum-jump-based feedback,” Phys. Rev. A 76, 010301 (2007).
[CrossRef]

A. R. R. Carvalho, A. J. S. Reid, and J. J. Hope, “Controlling entanglement by direct quantum feedback,” Phys. Rev. A 78, 012334 (2008).
[CrossRef]

Phys. Rev. Lett. (16)

A. S. Sørensen and K. Mølmer, “Measurement induced entanglement and quantum computation with atoms in optical cavities,” Phys. Rev. Lett. 91, 097905 (2003).
[CrossRef] [PubMed]

M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera, and D. Meschede, “Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system,” Phys. Rev. Lett. 103, 123006 (2009).
[CrossRef] [PubMed]

S. Nußmann, M. Hijlkema, B. Weber, F. Rohde, G. Rempe, and A. Kuhn, “Submicron positioning of single atoms in a microcavity,” Phys. Rev. Lett. 95, 173602 (2005).
[CrossRef] [PubMed]

K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. 98, 233601 (2007).
[CrossRef] [PubMed]

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Nägerl, D. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef] [PubMed]

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef] [PubMed]

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Reversible state transfer between light and a single trapped atom,” Phys. Rev. Lett. 98, 193601 (2007).
[CrossRef] [PubMed]

T. Wilk, S. C. Webster, H. P. Specht, G. Rempe, and A. Kuhn, “Polarization-controlled single photons,” Phys. Rev. Lett. 98, 063601 (2007).
[CrossRef] [PubMed]

S. Chaudhury, G. A. Smith, K. Schulz, and P. S. Jessen, “Continuous nondemolition measurement of the Cs clock transition pseudospin,” Phys. Rev. Lett. 96, 043001 (2006).
[CrossRef] [PubMed]

P. J. Windpassinger, D. Oblak, P. G. Petrov, M. Kubasik, M. Saffman, C. L. G. Alzar, J. Appel, J. H. Müller, N. Jærgaard, and E. S. Polzik, “Nondestructive probing of Rabi oscillations on the cesium clock transition near the standard quantum limit,” Phys. Rev. Lett. 100, 103601 (2008).
[CrossRef] [PubMed]

J. C. Berquist, R. G. Hulet, W. Itano, and D. J. Wineland, “Observation of quantum jumps in a single atom,” Phys. Rev. Lett. 57, 1669–1702 (1986).
[CrossRef]

W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: observation of quantum jumps,” Phys. Rev. Lett. 56, 2797–2799 (1986).
[CrossRef] [PubMed]

R. J. Cook and H. J. Kimble, “Possibility of direct observation of quantum jumps,” Phys. Rev. Lett. 54, 1023–1026 (1985).
[CrossRef] [PubMed]

T. Sauter, W. Neuhauser, R. Blatt, and P. E. Toschek, “Observation of quantum jumps,” Phys. Rev. Lett. 57, 1696–1698 (1986).
[CrossRef] [PubMed]

W. M. Itano, J. Berquist, R. G. Hulet, and D. Wineland, “Radiative decay rates in Hg+ from observations of quantum jumps in a single ion,” Phys. Rev. Lett. 59, 2732–2735 (1987).
[CrossRef] [PubMed]

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef] [PubMed]

Proc. IEEE (1)

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

Rev. Mod. Phys. (1)

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[CrossRef]

Rev. Sci. Instrum. (1)

Y. Yuzhelevski, M. Yuzhelevski, and G. Jung, “Random telegraph noise analysis in time domain,” Rev. Sci. Instrum. 71, 1681–1688 (2000).
[CrossRef]

Science (2)

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278–280 (2001).
[CrossRef] [PubMed]

V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, “Quantum nondemolition measurements,” Science 209, 547–557 (1980).
[CrossRef] [PubMed]

Other (4)

O. Cappé, E. Moulines, and T. Ryden, Inference in Hidden Markov Models (Springer, 2000).

R. Paroli, G. Redaelli, and L. Spezia, “Hidden Markov models for time series of overdispersed insurances counts,” in Proceedings of the XXXI International ASTIN Colloquium (Istituto Italiano degli Attuari, 2000), pp. 461–474.

The mF distribution within the |F=4⟩ manifold for a coordinate system where the quantization axis is parallel to the electric field, i.e., for π-transitions, it is calculated to be 34.4% in mF=0, 23.9% in mF=±1, 7.8% in mF=±2, 1.1% in mF=±3, and 0.1% in mF=±4.

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

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Figures (13)

Fig. 1
Fig. 1

Schematic setup of MOT, FORT, and cavity mirrors (not to scale). Details of the experimental setup and the stabilization of the cavity resonance frequency are given in [8].

Fig. 2
Fig. 2

Simplified Cs level scheme. (a) An atom in | F = 3 is so far detuned from the cavity resonance that it does not alter its transmission. (b) If the atom is in | F = 4 , it changes the transmission, depending on the cavity-atom detuning Δ c a and the coupling strength g.

Fig. 3
Fig. 3

(a) Black and gray curves show two single traces of quantum jump measurements. The arrows indicate insertion and removal of an atom. At the end of the sequence, the repumper is switched on again to check that the atom was not lost. (b) Ensemble average over 31 single traces. The average dwell time R 43 1 is obtained from the exponential fit. The averaged transmission level at the end of the sequence, when the repumper is switched on, is higher than the initial drop, indicating a lower average coupling strength. This could be caused by increased thermal motion, a redistribution over different m F levels, or a combination of both effects.

Fig. 4
Fig. 4

(a) Normalized one-atom-transmission as a function of the cavity-atom detuning Δ c a . The solid lines are calculated for an atom at rest with effective coupling strengths of g eff / ( 2 π ) = 8 , 9, and 10 MHz for the upper, middle, and lower curves, respectively. (b) Average dwell time R 43 1 as a function of detuning. The shaded area is the result of a theoretical model taking motion of the atom into account, and the range of values represents our limited knowledge about the exact distribution over the Zeeman sublevels.

Fig. 5
Fig. 5

(a) Random telegraph signal for one atom coupled to the cavity. (b) Bayes analysis yielding p 0 ( t ) , i.e., the probability to be in | F = 3 . The cavity-atom detuning is Δ c a = 2 π × 30   MHz ; the bin size is 1 ms.

Fig. 6
Fig. 6

(a) Normalized histogram extracted from 13 telegraph signals of 1000 ms duration each, recorded for a detuning of Δ c a = 2 π × 30   MHz and binned with Δ t b = 1   ms . The solid line is the sum of two Poissonian distributions each with the same average count rate as the corresponding histogram peak. (b) Averaged second-order correlation function g ( 2 ) for the same set of telegraph signals. The blue dashed line is an exponential fit yielding the time constant ( R 10 + R 01 ) 1 = 20   ms .

Fig. 7
Fig. 7

Normalized transmission T 1 (black dots) and T 2 (blue diamonds) for one and two atoms, respectively. The solid lines are calculated according to the effective two-level model (1) for one atom at rest with different values for g eff , and the dashed line shows the theoretically expected two-atom transmission for g eff / ( 2 π ) = 2 × 9 = 12.7   MHz . The one-atom data are the same as in Fig. 4a.

Fig. 8
Fig. 8

(a) Effective coupling as a function of distance Δ y from the cavity center. (b) Transmission level difference Δ T 12 ; (c) quantum jump rate R 43 as a function of detuning Δ c a and distance Δ y . The white solid lines are points of maximum Δ T 12 calculated according to Eq. (12).

Fig. 9
Fig. 9

(a) Example trace of a random telegraph signal for two atoms placed Δ y = 21 μ m away from the cavity center. The cavity-atom detuning is Δ c a = 2 π × 38   MHz . (b) Probabilities for 0, 1, or 2 atoms to be in | F = 4 , calculated using the Bayes method.

Fig. 10
Fig. 10

Normalized photon count histogram (bars) of many two-atom telegraph signals. The right (blue), middle (red), and left (green) lines are independently measured histograms for zero, one, and two atoms coupled continuously to the cavity, respectively. The black line is a weighted sum of those three histograms.

Fig. 11
Fig. 11

(a) Random telegraph signal with 1 ms binning time. (b) Enlarged section of 10 ms showing photon-click times. The quantum jump occurs at about 24.8 ms.

Fig. 12
Fig. 12

Application of the Bayes algorithm for different bin times. (a)–(c) show the histogram of the telegraph signal for bin times of 1 ms, 100 μ s , and 10 μ s , respectively. The transmission signals, generated from the same photon-click record, and p 0 ( t ) are depicted in (d)–(f).

Fig. 13
Fig. 13

Time- and ensemble-averaged entropy S as a function of binning time Δ t b .

Equations (18)

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T 1 ( Δ c a , g eff ) = κ 2 ( Δ c a 2 + γ 2 ) ( γ κ + g eff 2 ) 2 + ( Δ c a κ ) 2 .
d p 0 ( t ) d t = R 01 p 0 ( t ) + R 10 p 1 ( t ) ,
d p 1 ( t ) d t = R 10 p 1 ( t ) + R 01 p 0 ( t ) = d p 0 ( t ) d t .
p ¯ 0 = R 10 R 10 + R 01 ,
p ¯ 1 = R 01 R 10 + R 01 .
P ( n ) = p ¯ 0 P ( n 0 ) + ( 1 p ¯ 0 ) P ( n 1 ) ,
g ( 2 ) ( τ ) = n ( t ) n ( t + τ ) n ( t ) n ( t + τ ) exp ( ( R 10 + R 01 ) τ )     for   τ > 0.
p ̃ 0 ( t i ) = p 0 ( t i 1 ) + ( R 10 p 1 ( t i 1 ) R 01 p 0 ( t i 1 ) ) Δ t b ,
p ̃ 1 ( t i ) = p 1 ( t i 1 ) + ( R 01 p 0 ( t i 1 ) R 10 p 1 ( t i 1 ) ) Δ t b ,
p α ( t i ) p ( α n ( t i ) ) = P ( n ( t i ) α ) p ̃ α ( t i ) α p ̃ α ( t i ) P ( n ( t i ) α )     for   α = 0 , 1.
T 1 = 1 1 + ( g 2 κ Δ c a ) 2 ,     T 2 = 1 1 + ( 2 g 2 κ Δ c a ) 2 ,
| Δ y ( Δ c a ) | = w 0 1 2 ln ( 2 g eff 2 ( 0 ) Δ c a κ ) .
d p 0 d t = R 01 p 0 ( t ) + R 10 p 1 ( t ) ,
d p 1 d t = R 01 p 0 ( t ) R 10 p 1 ( t ) R 12 p 1 ( t ) + R 21 p 2 ( t ) ,
d p 2 d t = R 12 p 1 ( t ) R 21 p 2 ( t ) .
R 21 = 2 T 2 T 1 R 10 ,
R 10 = 104 s 1 ,     R 21 = 52 s 1 ,     R rep = 45 s 1 ,
S = α p α   log   p α ,

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