Test of the quantumness of atom-atom correlations in a bosonic gas

It is shown how the quantumness of atom-atom correlations in a trapped bosonic gas can be made observable. Application of continuous feedback control of the center of mass of the atomic cloud is shown to generate oscillations of the spatial extension of the cloud, whose amplitude can be directly used as a characterization of atom-atom correlations. Feedback parameters can be chosen such that the violation of a Schwarz inequality for atom-atom correlations can be tested at noise levels much higher than the standard quantum limit

Determination of entangled quantum states of a trapped atom

We propose a method for measuring entangled vibronic quantum states of a trapped atom. It is based on the nonlinear dynamics of the system that appears by resonantly driving a weak electronic transition. The proposed technique allows the direct sampling of a Wigner-function matrix, displaying all knowable information on the quantum correlations of the motional and electronic degrees of freedom of the atom. It opens novel possibilities for testing fundamental predictions of the quantum theory concerning interaction phenomena.Comment: 7 pages, 3 figures, to be published in Phys. Rev. A 56 (Aug

Quantum state engineering via unitary transformations

We construct a Hamiltonian for the generation of arbitrary pure states of the quantized electromagnetic field. The proposition is based upon the fact that a unitary transformation for the generation of number states has been already found. The general unitary transformation here obtained, would allow the use of nonlinear interactions for the production of pure states. We discuss the applicability of this method by giving examples of generation of simple superposition states. We also compare our Hamiltonian with the one resulting from the interaction of trapped ions with two laser fields.Comment: 5 pages in RevTeX, no figures, accepted for publication in Phys. Rev.

Quantum Limits of Stochastic Cooling of a Bosonic Gas

The quantum limits of stochastic cooling of trapped atoms are studied. The energy subtraction due to the applied feedback is shown to contain an additional noise term due to atom-number fluctuations in the feedback region. This novel effect is shown to dominate the cooling efficiency near the condensation point. Furthermore, we show first results that indicate that Bose--Einstein condensation could be reached via stochastic cooling.Comment: 5 pages, 3 figures, to appear in Phys. Rev.

Direct measurement of the Wigner function by photon counting

We report a direct measurement of the Wigner function characterizing the quantum state of a light mode. The experimental scheme is based on the representation of the Wigner function as an expectation value of a displaced photon number parity operator. This allowed us to scan the phase space point-by-point, and obtain the complete Wigner function without using any numerical reconstruction algorithms.Comment: 4 pages, REVTe

Quadrature-dependent Bogoliubov transformations and multiphoton squeezed states

We introduce a linear, canonical transformation of the fundamental single--mode field operators $a$ and $a^{\dagger}$ that generalizes the linear Bogoliubov transformation familiar in the construction of the harmonic oscillator squeezed states. This generalization is obtained by adding to the linear transformation a nonlinear function of any of the fundamental quadrature operators $X_{1}$ and $X_{2}$, making the original Bogoliubov transformation quadrature--dependent. Remarkably, the conditions of canonicity do not impose any constraint on the form of the nonlinear function, and lead to a set of nontrivial algebraic relations between the $c$--number coefficients of the transformation. We examine in detail the structure and the properties of the new quantum states defined as eigenvectors of the transformed annihilation operator $b$. These eigenvectors define a class of multiphoton squeezed states. The structure of the uncertainty products and of the quasiprobability distributions in phase space shows that besides coherence properties, these states exhibit a squeezing and a deformation (cooling) of the phase--space trajectories, both of which strongly depend on the form of the nonlinear function. The presence of the extra nonlinear term in the phase of the wave functions has also relevant consequences on photon statistics and correlation properties. The non quadratic structure of the associated Hamiltonians suggests that these states be generated in connection with multiphoton processes in media with higher nonlinearities.Comment: 16 pages, 15 figure

Recovering coherence from decoherence: a method of quantum state reconstruction

We present a feasible scheme for reconstructing the quantum state of a field prepared inside a lossy cavity. Quantum coherences are normally destroyed by dissipation, but we show that at zero temperature we are able to retrieve enough information about the initial state, making possible to recover its Wigner function as well as other quasiprobabilities. We provide a numerical simulation of a Schroedinger cat state reconstruction.Comment: 8 pages, in RevTeX, 4 figures, accepted for publication in Phys. Rev. A (november 1999

Simplified Quantum Process Tomography

We propose and evaluate experimentally an approach to quantum process tomography that completely removes the scaling problem plaguing the standard approach. The key to this simplification is the incorporation of prior knowledge of the class of physical interactions involved in generating the dynamics, which reduces the problem to one of parameter estimation. This allows part of the problem to be tackled using efficient convex methods, which, when coupled with a constraint on some parameters allows globally optimal estimates for the Kraus operators to be determined from experimental data. Parameterising the maps provides further advantages: it allows the incorporation of mixed states of the environment as well as some initial correlation between the system and environment, both of which are common physical situations following excitation of the system away from thermal equilibrium. Although the approach is not universal, in cases where it is valid it returns a complete set of positive maps for the dynamical evolution of a quantum system at all times.Comment: Added references to interesting related work by Bendersky et a

Transverse confinement in stochastic cooling of trapped atoms

Stochastic cooling of trapped atoms is considered for a laser-beam configuration with beam waists equal or smaller than the extent of the atomic cloud. It is shown, that various effects appear due to this transverse confinement, among them heating of transverse kinetic energy. Analytical results of the cooling in dependence on size and location of the laser beam are presented for the case of a non-degenerate vapour.Comment: 14 pages, 5 figures, accepted for publication in Journal of Optics