Pavel Lougovski

Fresnel Representation of the Wigner Function: An Operational Approach

We present an operational definition of the Wigner function. Our method relies on the Fresnel transform of measured Rabi oscillations and applies to motional states of trapped atoms as well as to field states in cavities. We illustrate this technique using data from recent experiments in ion traps [Phys. Rev. Lett. 76, 1796 (1996)]] and in cavity QED [Nature (London) 403, 743 (2000)]]. The values of the Wigner functions of the underlying states at the origin of phase space are W(|0>)(0)=+1.75 for the vibrational ground state and W(|1>)(0)=-1.4 for the one-photon number state. We generalize this method to wave packets in arbitrary potentials.

Generation and purification of maximally entangled atomic states in optical cavities

We present a probabilistic scheme for generating and purifying maximally entangled states of two atoms inside an optical cavity via no-photon detection at the cavity output, where ideal detectors are not required. The intermediate mixed states can be continuously purified so as to violate Bell inequalities in a parametrized manner. The scheme relies on an additional strong-driving field that realizes, atypically, simultaneous Jaynes-Cummings and anti-Jaynes-Cummings interactions.

Solvable model of a strongly driven micromaser

We study the dynamics of a micromaser where the pumping atoms are strongly driven by a resonant classical field during their transit through the cavity mode. We derive a master equation for this strongly driven micromaser, involving the contributions of the unitary atom-field interactions and the dissipative effects of a thermal bath. We find analytical solutions for the temporal evolution and the steady state of this system by means of phase-space techniques, providing an unusual solvable model of an open quantum system, including pumping and decoherence. We derive closed expressions for all relevant expectation values, describing the statistics of the cavity field and the detected atomic levels. The transient regime shows the buildup of mixtures of mesoscopic fields evolving towards a super-Poissonian steady-state field that, nevertheless, yields atomic correlations that exhibit stronger nonclassical features than the conventional micromaser.

Instantaneous measurement of field quadrature moments and entanglement

Abstract.We present a method of measuring expectation values of quadrature moments of a multimode field through two-level probe “homodyning”. Our approach is based on an integral transform formalism of measurable probe observables, where analytically derived kernels unravel efficiently the required field information at zero interaction time, minimizing decoherence effects. The proposed scheme is suitable for fields that, while inaccessible to a direct measurement, enjoy one and two-photon Jaynes-Cummings interactions with a two-level probe, like spin, phonon, or cavity fields. Available data from previous experiments are used to confirm our predictions.

Characterizing entanglement sources

We discuss how to characterize entanglement sources with finite sets of measurements. The measurements do not have to be tomographically complete and may consist of POVMs rather than von Neumann measurements. Our method yields a probability that the source generates an entangled state as well as estimates of any desired calculable entanglement measures, including their error bars. We apply two criteria, namely, Akaikes information criterion and the Bayesian information criterion, to compare and assess different models (with different numbers of parameters) describing entanglement-generating devices. We discuss differences between standard entanglement-verification methods and our present method of characterizing an entanglement source.

A Solvable Open Quantum System: The Strongly Driven Micromaser

A micromaser, where an additional classical field strongly drives the atoms crossing the cavity, provides an example of a solvable open quantum system with pumping and dissipation. The coherent time evolution consists in cavity field displacements correlated with atomic internal states, a different entanglement than the usual Jaynes-Cummings interaction. We provide analytical results and phase space descriptions via the quantum characteristic function. We illustrate bunching and antibunching effects at steady state in atom pair correlation measurements, where the control parameter is simply the atomic velocity.

Multiparticle entanglement and the Schrödinger cat state using ground-state coherences

In this paper we show how ground-state coherences and dispersive interactions of single photons with a collective system produces a variety of multiparticle entangled states and mesoscopic superpositions. Further single photons act as a carrier of information and can entangle macroscopic systems and can produce large phase shifts. Our work produces states as considered by Schrödinger in the cat-paradox, though in our case cat is replaced by the collective atomic system.

Quantum state estimation when qubits are lost: a no-data-left-behind approach*

We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we report the first closed-form Bayesian mean estimate (BME) for the ideal single qubit. Due to computational constraints, we utilize numerical sampling to determine the BME for a photonic two-qubit experiment in which our novel analysis reduces burdens associated with experimental asymmetries and inefficiencies. This method can be applied to quantum states of any dimension and experimental complexity.