M. Dakna

Generating Schrodinger-cat-like states by means of conditional measurements on a beam splitter

A scheme for generating Schrodinger-cat-like states of a single-mode optical field by means of conditional measurement is proposed. Feeding a squeezed vacuum into a beam splitter and counting the photons in one of the output channels, the conditional states in the other output channel exhibit a number of properties that are very similar to those of superpositions of two coherent states with opposite phases. We present analytical and numerical results for the photon-number and quadrature-component distributions of the conditional states and their Wigner and Husimi functions. Further, we discuss the effect of realistic photocounting on the states. @S1050-2947~97!06404-4#

GENERATION OF ARBITRARY QUANTUM STATES OF TRAVELING FIELDS

We show that any single-mode quantum state can be generated from the vacuum by alternate application of the coherent displacement operator and the creation operator. We propose an experimental implementation of the scheme for traveling optical fields, which is based on field mixings and conditional measurements in a beam-splitter array, and calculate the probability of state generation.

Photon-added state preparation via conditional measurement on a beam splitter

Abstract We show that conditional output measurement on a beam splitter may be used to produce photon-added states for a large class of signal-mode quantum states, such as thermal states, coherent states, squeezed states, and displaced photon-number states. Combining a mode prepared in such a state and a mode prepared in a photon-number state, the state of the mode in one of the output channels of the beam splitter “collapses” to a photon-added state, provided that no photons are detected in the other output channel. We present analytical and numerical results, with special emphasis on photon-added coherent and squeezed vacuum states. In particular, we show that adding photons to a squeezed vacuum yields Schrodinger-cat-like states in terms of superpositions of non-Gaussian squeezed coherent states. We finally show that the quantum features of the conditional output states are observed even when the reference mode is prepared in a sub-Poissonian statistical mixture of photon-number states.

NUMBER-PHASE UNCERTAINTY RELATIONS : VERIFICATION BY BALANCED HOMODYNE MEASUREMENT

Although the problem of number-phase uncertainty has been studied widely, there has been no direct experimental verification of fundamental uncertainty relations ~URs!. What can be the best way of doing that? A powerful and perhaps ultimate method for measuring the quantum statistics of traveling optical fields has been balanced homodyne detection. The quantity that is directly measured is the probability distribution p(x,q) of the phase-dependent quadrature x ˆ(q) 5 2 21/2 (ae 2iq 1 a† e iq ), where a ˆ (a ˆ† ) is the bosonic annihilation ~creation! operator of the ~single-mode! signal field andq corresponds to the local-oscillator phase. It has been shown that p(x,q) for all phases q in a p interval contains all knowable information about the quantum state of the signal field and can be used to reconstruct the Wigner function by applying the standard filtered back projection algorithm in the numerical calculation of the inverse Radon transform to be performed @1#. Since the Wigner function is a full description of the quantum state, it can be used to calculate other important features of the field such as the photon-number statistics and phase statistics and their associated URs @2#. The inverse Radon transform requires a threefold integration of the measured data and the calculation of the density matrix in the Fock basis can then be accomplished with two integrals. One summation eventually yields the photon-number moments, and one sum and one integral must be performed to obtain the ~canonical! phase moments. Hence six- and sevenfold transformations of the recorded data are required for UR verification at least. Of course, a large amount of data manipulation accumulates various errors and the physical nature of the uncertainties becomes less transparent. Recent progress has offered possibilities of determining the photon-number statistics in a more direct way avoiding the detour via the Wigner function. It has been shown that both the density-matrix elements % nn8 in the Fock basis @3#

Homodyne measurement of exponential phase moments

It is shown that the exponential moments of the canonical phase can be directly sampled from the data recorded in balanced homodyne detection. Analytical expressions for the sampling functions are derived, which are valid for arbitrary states and bridge the gap between quantum and classical phase. The reconstruction of the canonical phase distribution from the experimentally determined exponential moments is discussed.

Homodyne measurement of exponential phase momenta for quantum-phase reconstruction

Abstract We directly sample the exponential momenta of the canonical phase for various quantum states from the homodyne output. The method enables us to study the phase properties experimentally, without making the detour via reconstructing the density matrix or the Wigner function and calculating the phase statistics from them. In particular, combing the measurement with a measurement of the photon-number variance, we verify fundamental number–phase uncertainty.

Homodyne detection for direct sampling of the London phase distribution

The problem of direct sampling of the London phase distribution in balanced homodyning is studied. For this purpose a continuous sequence of parametrized phase distributions tending to the London phase distribution as the sequence parameter goes to zero is considered. From the integral relation of the parametrized phase distributions to the field-strength distributions measurable in homodyne detection, it is seen that for any non-vanishing sequence parameter the associated phase distribution can be obtained by direct sampling from the measured data. This offers a possibility of asymptotically measuring the London phase distribution. Numerical simulations show that it can be obtained with sufficiently high accuracy.

Direct sampling of the Susskind-Glogower phase distributions

Coarse-grained phase distributions are introduced that approximate to the Susskind-Glogower cosine and sine phase distributions to any desired degree of accuracy. The integral relations between the phase distributions and the phase-parametrized field-strength distributions observable in balanced homodyning are derived and the integral kernels are analyzed. It is shown that the phase distributions can be directly sampled from the field-strength distributions which offers the possibility of measuring the Susskind-Glogower cosine and sine phase distributions with sufficiently high precision. Numerical simulations are performed to demonstrate the applicability of the method.