Abstract
We present and numerically investigate the protocol of measuring the probability density of a rotated quadrature χ(ϕ) of a microwave mode in an arbitrary quantum state, where ϕ is a quadrature phase. The protocol is adapted to the measuring procedure used in the CQED (Cavity Quantum Electrodynamics) experiments. The method is based on measuring the integral detection probability of detection of m atoms – probes in the excited state from the set of n atoms crossing the cavity. The relation between the random variables m = m(ϕ) and χ = χ(ϕ) is identified. The protocol describes the procedure of choosing parameters, such as interaction time, and the number of atoms in series n. The method contains a single fitting parameter that is selected in the process of numerical simulation. Quality selection is determined by Kolmogorov’s test. The result of the calculation using the protocol is the convolution of the required distribution with the instrument function of the method. The parameters of the instrument function are described. Numerical simulations are performed for typical parameters of the experimental setup, showing the effectiveness of the proposed method.
Graphical abstract
Similar content being viewed by others
References
G.M. D’Ariano, U. Leonhardt, H. Paul, Phys. Rev. A 52, R1801 (1995)
D.T. Smithey, M. Beck, M.G. Raymer, A. Faridani, Phys. Rev. Lett. 70, 1244 (1993)
D.T. Smithey, M. Beck, J. Cooper, M.G. Raymer, Phys. Rev. A 48, 3159 (1993)
M.G. Raymer, M. Beck, D.F. McAlister, Phys. Rev. Lett. 72, 1137 (1994)
U. Leonhardt, H. Paul, Prog. Quant. Electr. 19, 89 (1995)
K. Vogel, H. Risken, Phys. Rev. A 40, 2847 (1989)
S.N. Filippov, V.I. Man’ko, Phys. Rev. A 84, 033827 (2011)
Th. Richter, Phys. Rev. A 53, 1197 (1996)
A. Wunsche, Phys. Rev. A 54, 5291 (1996)
S. Mancini, O.V. Man’ko, V.I. Man’ko, P. Tombesi, J. Phys. A: Math. Gen. 34, 3461 (2001)
V.V. Dodonov, J. Opt. B: Quantum Semiclass. Opt. 4, S98 (2002)
V.I. Man’ko, G. Marmo, A. Porzio, S. Solimeno, F. Ventriglia, Phys. Scr. 83, 045001 (2011)
S. Mancini, P. Tombesi, V.I. Manko, Europhys. Lett. 37, 79 (1997)
O. Man’ko, V.I. Man’ko, J. Russian Laser Res. 24, 497 (2003)
S. Wallentowitz, W. Vogel, Phys. Rev. A. 53, 4528 (1996)
K. Banaszek, C. Radzewicz, K. Wódkiewicz, J.S. Krasiński, Phys. Rev. A 60, 674 (1999)
J.M. Raimond, M. Brune, S. Haroche, Rev. Mod. Phys. 73, 565 (2001)
A. Blais, Ren-Shou Huang, A. Wallraff, S.M. Girvin, R.J. Schoelkopf, Phys. Rev. A 69, 062320 (2004)
M.H. Devoret, R.J. Schoelkopf, Science 339, 1169 (2013)
M.H. Devoret, J.M. Martinis, Quantum Information Processing 3, 163 (2004)
J. Gabelli, L.-H. Reydellet, G. Fève, J.-M. Berroir, B. Plaçais, P. Roche, D.C. Glattli, Phys. Rev. Lett. 93, 056801 (2004)
C. Eichler, D. Bozyigit, A. Wallraff, Phys. Rev. A 86, 032106 (2012)
D. Bozyigit, C. Lang, L. Steffen, J.M. Fink, C. Eichler, M. Baur, R. Bianchetti, P.J. Leek, S. Filipp, M.P. da Silva, A. Blais, A. Wallraff, Nat. Phys. 7, 154 (2011)
E.P. Menzel, F. Deppe, M. Mariantoni, M.Á. Araque Caballero, A. Baust, T. Niemczyk, E. Hoffmann, A. Marx, E. Solano, R. Gross, Phys. Rev. Lett. 105, 100401 (2010)
R. Bianchetti, S. Filipp, M. Baur, J.M. Fink, M. Göppl, P.J. Leek, L. Steffen, A. Blais, A. Wallraff, Phys. Rev. A 80, 043840 (2009)
C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, A. Wallraff, Phys. Rev. Lett. 106, 220503 (2011)
C. Eichler, D. Bozyigit, C. Lang, M. Baur, L. Steffen, J.M. Fink, S. Filipp, A. Wallraff, Phys. Rev. Lett. 107, 113601 (2011)
M. Hatridge, R. Vijay, D.H. Slichter, J. Clarke, I. Siddiqi, Phys. Rev. B 83, 134501 (2011)
P. Campagne-Ibarcq, P. Six, L. Bretheau, A. Sarlette, M. Mirrahimi, P. Rouchon, B. Huard, Phys. Rev. X 6, 011002 (2016)
C. Eichler, D. Bozyigit, C. Lang, M. Baur, L. Steffen, J.M. Fink, S. Filipp, A. Wallraff, Phys. Rev. Lett. 107, 113601 (2011)
M.P. da Silva, D. Bozyigit, A. Wallraff, A. Blais, Phys. Rev. A 82, 043804 (2010)
N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V.E. Manucharyan, L. Frunzio, D.E. Prober, R.J. Schoelkopf, S.M. Girvin, M.H. Devoret, Nature 465, 64 (2010)
F. Mallet, M.A. Castellanos-Beltran, H.S. Ku, S. Glancy, E. Knill, K.D. Irwin, G.C. Hilton, L.R. Vale, K.W. Lehnert, Phys. Rev. Lett. 106, 220502 (2011)
W.F. Kindel, M.D. Schroer, K.W. Lehnert, Phys. Rev. A 93, 033817 (2016)
Yoni Shalibo, Roy Resh, Ofer Fogel, David Shwa, Radoslaw Bialczak, J.M. Martinis, Nadav Katz, Phys. Rev. Lett. 110, 100404 (2013)
M. Hofheinz, H. Wang, M. Ansmann, R.C. Bialczak, E. Lucero, M. Neeley, A.D. O’Connell, D. Sank, J. Wenner, J.M. Martinis, A.N. Cleland, Nature 459, 546 (2009)
G. Kirchmair, B. Vlastakis, Z. Leghtas, S.E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S.M. Girvin, R.J. Schoelkopf, Nature 495, 205 (2013)
P.J. Bardroff, E. Mayr, W.P. Schleich, Phys. Rev. A 51, 4963 (1995)
P.J. Bardroff, E. Mayr, W.P. Schleich, P. Domokos, M. Brune, J.M. Raimond, S. Haroche, Phys. Rev. A 53, 2736 (1996)
M. Wilkens, P. Meystre, Phys. Rev. A 43, 3832 (1991)
M. Brune, S. Haroche, J.M. Raimond, L. Davidovich, N. Zagury, Phys. Rev. A 45, 5193 (1992)
C.T. Bodendorf, G. Antesberger, M.S. Kim, H. Walther, Phys. Rev. A 57, 1371 (1998)
L.G. Lutterbach, L. Davidovich, Phys. Rev. Lett. 78, 2547 (1997)
P. Lougovski, E. Solano, Z.M. Zhang, H. Walther, H. Mack, W.P. Schleich, Rev. Lett. 91, 010401 (2003)
G. Nogues, A. Rauschenbeutel, S. Osnaghi, P. Bertet, M. Brune, J.M. Raimond, S. Haroche, L.G. Lutterbach, L. Davidovich, Phys. Rev. A 62, 054101 (2000)
M.S. Kim, G. Antesberger, C.T. Bodendorf, H. Walther, Phys. Rev. A 58, R65 (1998)
C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, S. Haroche, Nature 477, 73 (2011)
S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, S. Haroche, Nature 455, 510 (2008)
T. Rybarczyk, B. Peaudecerf, M. Penasa, S. Gerlich, B. Julsgaard, K. Mølmer, S. Gleyzes, M. Brune, J.M. Raimond, S. Haroche, I. Dotsenko, Phys. Rev. A 91, 062116 (2015)
M. Brune, J. Bernu, C. Guerlin, S. Deléglise, C. Sayrin, S. Gleyzes, S. Kuhr, I. Dotsenko, J.M. Raimond, S. Haroche, Phys. Rev. Lett. 101, 240402 (2008)
P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J.M. Raimond, S. Haroche, Phys. Rev. Lett. 89, 200402 (2002)
R. Glauber, Phys. Rev. 131, 2766 (1963)
K.E. Cahill, R.J. Glauber, Phys. Rev. 177, 1882 (1969)
G.P. Miroshnichenko, J. Exp. Theor. Phys. 109, 193 (2009)
G.P. Miroshnichenko, Opt. Spectrosc. 97, 403 (2004)
G.P. Miroshnichenko, J. Exp. Theor. Phys. 107, 952 (2008)
A.A. Borovkov, Mathematical statistics (Gordon and Breach Science Publishers, 1998)
E. Ifeachor, B. Jervis, Digital Signal Processing: A Practical Approach (Addison-Wesley-Publishing Company, 1993)
H.-J. Briegel, B.-G. Englert, N. Sterpi, H. Walther, Phys. Rev. A 49, 2962 (1994)
R.R. McGowan, W.C. Schieve, Phys. Rev. A 59, 778 (1999)
D.B. Johnson, W.C. Schieve, Phys. Rev. A 63, 033808 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Miroshnichenko, G.P. Microwave CQED quantum tomography. Eur. Phys. J. D 70, 271 (2016). https://doi.org/10.1140/epjd/e2016-70427-7
Received:
Published:
DOI: https://doi.org/10.1140/epjd/e2016-70427-7