K. Wódkiewicz

Coherent states, squeezed fluctuations, and the SU(2) am SU(1,1) groups in quantum-optics applications

The theory of generalized coherent states associated with the SU(2) and SU(1,1) Lie algebras is discussed and applied in an investigation of possible reductions of fluctuations. In the framework of a system of N two-level atoms the squeezing of angular-momentum [SU(2)] fluctuations is exhibited for optical coherent transients involving the photon echo. The SU(1,1) fluctuations are discussed and established for general two-photon processes involving dynamical variables different from the creation and annihilation operators.

Pre-Gaussian noise in strong laser–atom interactions

We present a continuation of a general theoretical approach to noisy laser-atom interactions based on a special Markov-chain description of external fluctuations. This chain, composed of n independent two-state jump processes, forms a non-Gaussian stochastic process from which a detailed discussion of the atomic response can be given. We show that the n-component Markov chain also has the property of pre-Gaussian noise, because in the limit of n → ∞ it converges to a Gaussian stochastic process. We exhibit solutions for the field spectrum and the atomic-fluorescence spectrum for phase, frequency, and amplitude pre-Gaussian fluctuations of the driving-laser light.

Propensity and probability in quantum mechanics

Abstract We give in this letter an operational definition of quantum mechanical propensity based on a realistic measuring process. We show that such a propensity can be defined by a state to be measured, a filter or a reference state and a group of possible “motions” of such filter. Such a propensity exhibits the tendency of the measured state to take up certain states of the filter accessible by its “motion”. We give two examples of such propensities for space-momentum and spin-orientation measurements.

Intrinsic and operational observables in quantum mechanics

The concept of intrinsic and operational observables in quantum mechanics is introduced. In any realistic description of a quantum measurement that includes a macroscopic detecting device, it is possible to construct from the statistics of the recorded raw data a set of operational quantities that correspond to the intrinsic quantum-mechanical observable. This general approach is illustrated by the example of an operational measurement of the position and the momentum of a particle, as well as by an analysis of the operational detection of the phase of an optical field. For the latter we identify the intrinsic phase operator and report its explicit form.

On the operational uncertainty relation

Abstract We derive an operational uncertainty relation for the position and momentum operator taking into account the quantum mechanical properties of the measuring device during a detection process. We show that such an uncertainty relation is different mathematically and physically from the standard results which is obtained with no reference to the simultaneous measurement of the conjugated variables.

Atomic coherent states and reduced quantum fluctuations in optical transients

Abstract We show that the atomic coherent states (the Bloch states) commonly encountered in coherent transient phenomena exhibit squeezing. We illustrate this property calculating the degree of squeezing and the normalized correlation coefficient g (2) for a system of N two-level atoms interacting with a cw laser electric field.

Time-frequency domain analogues of phase space sub-planck structures.

We present experimental data of the frequency-resolved optical gating measurements of light pulses revealing interference features which correspond to sub-Planck structures in phase space. For superpositions of pulses, a small, sub-Fourier shift in the carrier frequency leads to a state orthogonal to the initial one, although in the representation of standard time-frequency distributions these states seem to have a nonvanishing overlap.

Solutions of Langevin equations with multiplicative colored noise

Abstract A Fokker-Planck equation for a nonlinear Langevin equation with multiplicative gaussian noise with arbitrary covariance and small coherence time is derived. An exact steady-state solution of this Fokker-Planck equation is obtained for a lorentzian power spectrum of the driving noise. The crucial influence of the finite coherence time of the noise on the critical properties of the system is exhibited.

Squeezing in higher order nonlinear optical processes

Abstract We examine the squeezing of the signal mode in higher order subharmonic generation processes when the mode is initially in a coherent state. We find that the squeezing is proportional to the amplitude of the initial state so that the vacuum is not squeezed.

Complete positivity conditions for quantum qutrit channels

We present an analysis of complete positivity (CP) constraints on qutrit quantum channels that have a form of affine transformations of generalized Bloch vector. For diagonal (damping) channels we derive conditions analogous to the ones that in qubit case produce tetrahedron structure in the channel parameter space.