Maximum likelihood estimation of photon number distribution from homodyne statistics

We present a method for reconstructing the photon number distribution from the homodyne statistics based on maximization of the likelihood function derived from the exact statistical description of a homodyne experiment. This method incorporates in a natural way the physical constraints on the reconstructed quantities, and the compensation for the nonunit detection efficiency.Comment: 3 pages REVTeX. Final version, to appear in Phys. Rev. A as a Brief Repor

Reply on the ``Comment on `Loss-error compensation in quantum- state measurements' ''

The authors of the Comment [G. M. D'Ariano and C. Macchiavello to be published in Phys. Rev. A, quant-ph/9701009] tried to reestablish a 0.5 efficiency bound for loss compensation in optical homodyne tomography. In our reply we demonstrate that neither does such a rigorous bound exist nor is the bound required for ruling out the state reconstruction of an individual system [G. M. D'Ariano and H. P. Yuen, Phys. Rev. Lett. 76, 2832 (1996)].Comment: LaTex, 2 pages, 1 Figure; to be published in Physical Review

Nitrous oxide water column distribution during the transition from anoxic to oxic conditions in the Baltic Sea

International audienceIn January 2003, a major inflow of cold and oxygen-rich North Sea Water in the Baltic Sea terminated an ongoing stagnation period in parts of the central Baltic Sea. In order to investigate the role of North Sea Water inflow to the Baltic Sea with regard to the production of nitrous oxide (N2O), we measured dissolved and atmospheric N2O at 26 stations in the southern and central Baltic Sea in October 2003. At the time of our cruise, water renewal had proceeded to the eastern Gotland Basin, whereas the western Gotland Basin was still unaffected by the inflow. The deep water renewal was detectable in the distributions of temperature, salinity, and oxygen concentrations as well as in the distribution of the N2O concentrations: Shallow stations in the Kiel Bight and Pomeranian Bight were well-ventilated with uniform N2O concentrations near equilibrium throughout the water column. In contrast, stations in the deep basins, such as the Bornholm and the Gotland Deep, showed a clear stratification with deep water affected by North Sea Water. Inflowing North Sea Water led to changed environmental conditions, especially enhanced oxygen (O2) or declining hydrogen sulfide (H2S) concentrations, thus, affecting the conditions for the production of N2O. Pattern of N2O profiles and correlations with parameters like oxygen and nitrate differed between the basins. The dominant production pathway seems to be nitrification rather than denitrification. No indications for advection of N2O by North Sea Water were found. A rough budget revealed a significant surplus of in situ produced N2O after the inflow. However, due to the permanent halocline, it can be assumed that the formed N2O does not reach the atmosphere. Hydrographic aspects therefore are decisive factors determining the final release of produced N2O to the atmosphere

Nitrous oxide in the North Atlantic Ocean

In order to get a comprehensive picture of the distribution of nitrous oxide (N2O) in the North Atlantic Ocean, measurements of dissolved nitrous oxide were made during three cruises in the tropical, subtropical and cold-temperate North Atlantic Ocean in October/November 2002, March/April 2004, and May 2002, respectively. To account for the history of atmospheric N2O, we suggest a new depth-dependent calculation of excess N2O (ΔN2O). N2O depth profiles showed supersaturation throughout the water column with a distinct increasing trend from the cold-temperate to the tropical region. Lowest nitrous oxide concentrations, near equilibrium and with an average of 11.0±1.7 nmol L−1, were found in the cold-temperate North Atlantic where the profiles showed no clear maxima. Highest values up to 37.3 nmol L−1 occurred in the tropical North Atlantic with clear maxima at approximately 400 m. A positive correlation of nitrous oxide with nitrate, as well as excess nitrous oxide with the apparent oxygen utilization (AOU), was only observed in the subtropical and tropical regions. Therefore, we conclude that the formation of nitrous oxide via nitrification occurs in the tropical region rather than in the cold-temperate region of the North Atlantic Ocea

Distribution of N₂O in the Baltic Sea during transition from anoxic to oxic conditions

In January 2003, a major inflow of cold and oxygen-rich North Sea Water terminated an ongoing stagnation period in parts of the central Baltic Sea. In order to investigate the role of North Sea Water inflow in the production of nitrous oxide (N2O), we measured dissolved and atmospheric N<2O at 26 stations in the southern and central Baltic Sea in October 2003. At the time of our cruise, water renewal had proceeded to the eastern Gotland Basin, whereas the western Gotland Basin was still unaffected by the inflow. The deep water renewal was detectable in the distributions of temperature, salinity, and oxygen concentrations as well as in the distribution of the N2O concentrations: Shallow stations in the Kiel Bight and Pomeranian Bight were well-ventilated with uniform N2O concentrations near equilibrium throughout the water column. In contrast, stations in the deep basins, such as the Bornholm and the Gotland Deep, showed a clear stratification with deep water affected by North Sea Water. Inflowing North Sea Water led to changed environmental conditions, especially enhanced oxygen (O2) or declining hydrogen sulphide (H2S) concentrations, thus, affecting the conditions for the production of N2O. Pattern of N2O profiles and correlations with parameters like oxygen and nitrate differed between the basins. Because of the positive correlation between ΔN2O and AOU in oxic waters the dominant production pathway seems to be nitrification rather than denitrification. Advection of N2O by North Sea Water was found to be of minor importance. A rough budget revealed a significant surplus of in situ produced N2O after the inflow. However, due to the permanent halocline, it can be assumed that the N2O produced does not reach the atmosphere. Hydrographic aspects therefore are decisive factors determining the final release of N2O produced to the atmosphere

Measuring quantum optical Hamiltonians

We show how recent state-reconstruction techniques can be used to determine the Hamiltonian of an optical device that evolves the quantum state of radiation. A simple experimental setup is proposed for measuring the Liouvillian of phase-insensitive devices. The feasibility of the method with current technology is demonstrated on the basis of Monte Carlo simulated experiments.Comment: Accepted for publication on Phys. Rev. Lett. 8 eps figures, 4 two-column pages in REVTE

Experimental characterization of frequency dependent squeezed light

We report on the demonstration of broadband squeezed laser beams that show a frequency dependent orientation of the squeezing ellipse. Carrier frequency as well as quadrature angle were stably locked to a reference laser beam at 1064nm. This frequency dependent squeezing was characterized in terms of noise power spectra and contour plots of Wigner functions. The later were measured by quantum state tomography. Our tomograph allowed a stable lock to a local oscillator beam for arbitrary quadrature angles with one degree precision. Frequency dependent orientations of the squeezing ellipse are necessary for squeezed states of light to provide a broadband sensitivity improvement in third generation gravitational wave interferometers. We consider the application of our system to long baseline interferometers such as a future squeezed light upgraded GEO600 detector.Comment: 8 pages, 8 figure

Operational Theory of Homodyne Detection

We discuss a balanced homodyne detection scheme with imperfect detectors in the framework of the operational approach to quantum measurement. We show that a realistic homodyne measurement is described by a family of operational observables that depends on the experimental setup, rather than a single field quadrature operator. We find an explicit form of this family, which fully characterizes the experimental device and is independent of a specific state of the measured system. We also derive operational homodyne observables for the setup with a random phase, which has been recently applied in an ultrafast measurement of the photon statistics of a pulsed diode laser. The operational formulation directly gives the relation between the detected noise and the intrinsic quantum fluctuations of the measured field. We demonstrate this on two examples: the operational uncertainty relation for the field quadratures, and the homodyne detection of suppressed fluctuations in photon statistics.Comment: 7 pages, REVTe

Quantum state reconstruction of the single-photon Fock state

We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state |1> was prepared using conditional measurements on photon pairs born in the process of parametric down-conversion. A probability distribution of the phase-averaged electric field amplitudes with a strongly non-Gaussian shape is obtained with the total detection efficiency of (55+-1)%. The angle-averaged Wigner function reconstructed from this distribution shows a strong dip reaching classically impossible negative values around the origin of the phase space.Comment: 4 pages, 4 figures, to appear in Physical Review Letters. Avoid downloading PDF due to extremely poor figure resolution. Use Postscrip

Parameters estimation in quantum optics

We address several estimation problems in quantum optics by means of the maximum-likelihood principle. We consider Gaussian state estimation and the determination of the coupling parameters of quadratic Hamiltonians. Moreover, we analyze different schemes of phase-shift estimation. Finally, the absolute estimation of the quantum efficiency of both linear and avalanche photodetectors is studied. In all the considered applications, the Gaussian bound on statistical errors is attained with a few thousand data.Comment: 11 pages. 6 figures. Accepted on Phys. Rev.