Optimal experiment design for quantum state tomography of a molecular vibrational mode

Optimal experiment design is used to collect a data set for the complete reconstruction of the vibrational quantum state of diatomic potassium molecules with maximum accuracy and a minimum number of experiments. The optimal configuration of experimental settings is obtained by minimizing the Cramer–Rao lower bound to the accuracy, which is attained in our reconstruction. The quantum state is reconstructed from the data set using maximum-likelihood estimation. Both optimal experiment design and maximum-likelihood estimation are solved efficiently as convex optimization problems.

[1]  R. F. Barrow,et al.  Interactions between the A(1) 1Σ+u and b(1) 3Πu states of K2 , 1987 .

[2]  U. Fano.  Description of States in Quantum Mechanics by Density Matrix and Operator Techniques , 1957 .

[3]  Walmsley,et al.  Time-resolved luminescence from coherently excited molecules as a probe of molecular wave-packet dynamics. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[4]  H. Rabitz,et al.  Teaching lasers to control molecules. , 1992, Physical review letters.

[5]  C. Kurtsiefer,et al.  Measurement of the Wigner function of an ensemble of helium atoms , 1997, Nature.

[6]  Walmsley,et al.  Experimental determination of the dynamics of a molecular nuclear wave packet via the spectra of spontaneous emission. , 1993, Physical review letters.

[7]  Z Hradil,et al.  Biased tomography schemes: an objective approach. , 2006, Physical review letters.

[8]  I. Walmsley,et al.  Simultaneous time and frequency gating of weak molecular fluorescence in a thick nonlinear crystal , 2006 .

[9]  Li Li,et al.  The A 1Σ+u state of the potassium dimer , 1990 .

[10]  King,et al.  Experimental Determination of the Motional Quantum State of a Trapped Atom. , 1996, Physical review letters.

[11]  Beck,et al.  Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum. , 1993, Physical review letters.

[12]  I. Walmsley,et al.  Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses. , 1998, Optics letters.

[13]  Ruediger Schack,et al.  Unknown Quantum States and Operations, a Bayesian View , 2004, quant-ph/0404156.

[14]  Rotationally induced collapse and revivals of molecular vibrational wavepackets: model for environment-induced decoherence , 2002 .

[15]  G. D’Ariano,et al.  Maximum-likelihood estimation of the density matrix , 1999, quant-ph/9909052.

[16]  Deepak Boggavarapu,et al.  Ultrafast balanced-homodyne chronocyclic spectrometer , 1996, Photonics West.

[17]  Molecular emission tomography of anharmonic vibrations , 1997 .

[18]  H. Rabitz,et al.  Decoherence of molecular vibrational wave packets: Observable manifestations and control criteria , 2001 .

[19]  S. Lloyd,et al.  Quantum metrology. , 2005, Physical review letters.

[20]  Walmsley,et al.  Experimental determination of the quantum-mechanical state of a molecular vibrational mode using fluorescence tomography. , 1995, Physical review letters.

[21]  M. Manaa,et al.  Spin–orbit interactions, new spectral data, and deperturbation of the coupled b 3∏u and A 1∑u+ states of K2 , 2002 .

[22]  J. P. Woerdman,et al.  Maximum-likelihood estimation of Mueller matrices. , 2005, Optics letters.