Non-classical field characterization by high-frequency, time-domain quantum homodyne tomography

We report about the realization and the applications of an efficient pulsed optical homodyne apparatus operating in the time domain at the high repetition rates characteristic of commonly used mode-locked lasers for the analysis of quantum light states. We give a full characterization of our system by shot-noise measurements and by verifying its capability to work in a gated configuration at lower acquisition rates. We demonstrate the potential of this high-frequency time-domain detector by applying it to the reconstruction of the density matrix elements and of the Wigner functions of various field states by means of quantum tomography. Results are shown for the complete characterization of simple coherent states with low average photon number, of single-photon Fock states and of the so-called single-photon added coherent states, which result from the elementary excitation of a classical wave-like field. Wigner functions with negative values are observed for the non-classical states and an overall efficiency of about 60% is obtained for the generation/detection system.

[1]  D. W. Allan,et al.  Statistics of atomic frequency standards , 1966 .

[2]  V. Chan,et al.  Noise in homodyne and heterodyne detection. , 1983, Optics letters.

[3]  P. Mataloni,et al.  Towards a Fock-States Tomographic Reconstruction , 2000 .

[4]  Kumar,et al.  Tomographic measurement of joint photon statistics of the twin-beam quantum state , 2000, Physical review letters.

[5]  Pulsed homodyne measurements of femtosecond squeezed pulses generated by single-pass parametric deamplification. , 2004, Optics letters.

[6]  M. Bellini,et al.  Nonlocal modulations on the temporal and spectral profiles of an entangled photon pair , 2004 .

[7]  R. Birkebak,et al.  Application of the Abel integral equation to spectrographic data. , 1966, Applied optics.

[8]  Parametric down-conversion with coherent pulse pumping and quantum interference between independent fields , 1997 .

[9]  A. Lvovsky,et al.  Quantum state reconstruction of the single-photon Fock state. , 2001, Physical Review Letters.

[10]  Vogel,et al.  Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase. , 1989, Physical review. A, General physics.

[11]  A. Lvovsky,et al.  Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state , 2001, quant-ph/0107080.

[12]  C. Fabre,et al.  I Quantum Fluctuations in Optical Systems , 1992 .

[13]  C. Macchiavello,et al.  Detection of the density matrix through optical homodyne tomography without filtered back projection. , 1994, Physical Review A. Atomic, Molecular, and Optical Physics.

[14]  A. Lvovsky,et al.  Ultrasensitive pulsed, balanced homodyne detector: application to time-domain quantum measurements. , 2001, Optics letters.

[15]  Nonclassical character of statistical mixtures of the single-photon and vacuum optical states , 2001, quant-ph/0109057.

[16]  V. Chan,et al.  Local-oscillator excess-noise suppression for homodyne and heterodyne detection. , 1983, Optics letters.

[17]  J. Wenger,et al.  Pulsed squeezed vacuum measurements without homodyning , 2004 .

[18]  H. Paul,et al.  Measuring the quantum state of light , 1997 .

[19]  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.

[20]  Alessandro Zavatta,et al.  Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection , 2004, quant-ph/0406090.

[21]  B. L. Schumaker,et al.  Noise in homodyne detection. , 1984, Optics letters.

[22]  Beck,et al.  Measurement of number-phase uncertainty relations of optical fields. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[23]  A. Chiummo,et al.  Tomographic characterization of OPO sources close to threshold. , 2005, Optics express.

[24]  A I Lvovsky,et al.  Quantum-optical catalysis: generating nonclassical states of light by means of linear optics. , 2002, Physical review letters.

[25]  M. Vasilyev,et al.  Investigation of the photon statistics of parametric fluorescence in a traveling-wave parametric amplifier by means of self-homodyne tomography. , 1998, Optics letters.

[26]  A. I. Lvovsky,et al.  Synthesis and tomographic characterization of the displaced Fock state of light , 2002 .

[27]  G. D’Ariano.  Tomographic measurement of the density matrix of the radiation field , 1995 .

[28]  F. Arecchi,et al.  Nonlocal pulse shaping with entangled photon pairs. , 2003, Physical review letters.

[29]  Francesco Marin,et al.  Time-domain analysis of quantum states of light: noise characterization and homodyne tomography , 2002 .

[30]  S A Babichev,et al.  Homodyne tomography characterization and nonlocality of a dual-mode optical qubit. , 2004, Physical review letters.

[31]  Yurke,et al.  Measurement of amplitude probability distributions for photon-number-operator eigenstates. , 1987, Physical review. A, General physics.

[32]  M. Bellini,et al.  Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light , 2004, Science.

[33]  G. Agarwal,et al.  Nonclassical properties of states generated by the excitations on a coherent state , 1991 .

[34]  M. Bellini,et al.  Single-photon excitation of a coherent state: Catching the elementary step of stimulated light emission , 2005, quant-ph/0508094.

[35]  S. A. Babichev,et al.  Remote preparation of a single-mode photonic qubit by measuring field quadrature noise. , 2003, Physical review letters.

[36]  S. A. Babichev,et al.  Quantum scissors: Teleportation of single-mode optical states by means of a nonlocal single photon , 2002, quant-ph/0208066.

[37]  R. Brouri,et al.  Non-gaussian statistics from individual pulses of squeezed light , 2004, InternationalQuantum Electronics Conference, 2004. (IQEC)..

[38]  A. I. Lvovsky,et al.  Iterative maximum-likelihood reconstruction in quantum homodyne tomography , 2003, quant-ph/0311097.

[39]  S. Schiller,et al.  Measurement of the quantum states of squeezed light , 1997, Nature.

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

[41]  S. Schiller,et al.  Homodyne tomography of classical and non-classical light , 1997 .

[42]  L. Mandel,et al.  Optical Coherence and Quantum Optics , 1995 .

[43]  Andrew G. Glen,et al.  APPL , 2001 .