Quantum nondemolition measurements on two-level atomic systems and temporal Bell inequalities

The evolution of a two-level system subjected to stimulated transitions which is undergoing a sequence of measurements of the level occupation probability is evaluated. Its time correlation function is compared to the one obtained through the pure Schr?dinger evolution. Systems of this kind have been recently proposed for testing the quantum mechanical predictions against those of macrorealistic theories, by means of temporal Bell inequalities. The classical requirement of noninvasivity, needed to define correlation functions in the realistic case, finds a quantum counterpart in the quantum nondemolition condition. The consequences on the observability of quantum mechanically predicted violations to temporal Bell inequalities are drawn and compared to the already dealt case of the rf-SQUID dynamics. Received: 28 March 1996 / Revised version: 13 August 1996     

Deterministic generation of squeezing for a cavity field with a collection of driven atoms

We propose an efficient scheme for realizing squeezing for a cavity mode. In the scheme, a collection of ladder-type three-level atoms are trapped in a cavity and driven by two classical fields. Under certain conditions, the cavity field deterministically evolves to a squeezed state. The scheme can also be used for conditional generation of superpositions of different squeezed vacuum states.     

Closing the detection loophole in the Bell test for local models based upon three hidden variables

Locality and fair sampling are proved to be contradictory assumptions in hidden variable models of the Bell test that are based upon a 3-dimensional sample space. This result makes the class of 3-dimensional hidden variable models incompatible with quantum mechanics in the ideal case, independently of detection efficiencies.     

Manipulation of optical fields by atomic interferometry: Quantum variations on a theme by young

We analyze the principle of a very general and conceptually simple method for manipulating optical fields by coupling them into a matter waves Young double slit apparatus. The field, non resonant with the atoms, acts as a phase-retarding medium in one of the arms of the interferometer and shifts the atomic fringe pattern. The method constitutes a simple quantum nondemolition measuring scheme of the photon number. Non classical states such as Schrödinger cats and Fock states of the field are generated in the measurement process. The analysis of the atomic interferometer with optical retarding fields provides a very simple and striking illustration of basic concepts of the quantum measurement theory and of the principle of complementarity. This scheme, which would be very difficult to implement in the optical domain, is equivalent to a more feasible and recently proposed Ramsey interference method to measure small microwave fields with beams of Rydberg atoms.Associé au Centre National de la Recherche Scientifique et à l'Université Pierre et Marie Curie     

Experimental local realism tests without fair sampling assumption

Following the theoretical suggestion of [E. Santos, Phys. Lett. A 327, 33 (2004); E. Santos, Eur. Phys. J. D 42, 501 (2007)], we present experimental results addressed to test restricted families of local realistic models, but without relying on the fair sampling assumption.     

Proposal for generating a two-photon added coherent state via down-conversion with a single crystal

Zavatta et al. [A. Zavatta, S. Viciani, M. Bellini, Science 306 (2004) 660; A. Zavatta, S. Viciani, M. Bellini, Phys. Rev. A 72 (2006) 023820], using parametric down-conversion, have carried out experiments to conditionally generate a single-photon added coherent state. In this Letter, we propose an extension of their method in order to generate the two-photon added coherent state, and point the way toward generating m-photon added coherent states for m>2, all using only one down-conversion crystal.     

Generation of a displaced qubit and entangled displaced photon state via conditional measurement and their properties

We study optical schemes for generating both a displaced photon and a displaced qubit via conditional measurement. Combining one mode prepared in different microscopic states (one-mode qubit, single photon, vacuum state) and another mode in macroscopic states (coherent state, single photon added coherent state), a conditional state in the other output mode exhibits properties of a superposition of the displaced vacuum and a single photon. We propose to use the displaced qubit and entangled states composed of the displaced photon as components for quantum information processing. Basic states of such a qubit are distinguishable from each other with high fidelity. We show that the qubit reveals both microscopic and macroscopic properties. Entangled displaced states with a coherent phase as an additional degree of freedom are introduced. We show that additional degree of freedom enables to implement complete Bell state measurement of the entangled displaced photon states.     

A ponderomotive scheme for QND measurement of quadrature component

We propose a scheme for quantum nondemolition (QND) measurement of the quadrature component of a traveling wave, which uses the nonlinear ponderomotive interaction of electromagnetic waves reflected from a movable mirror. The influence of mechanical and optical losses and of imbalance in the interferometer arms is analyzed. Received: 27 March 1996 / Revised version: 25 September 1996     

Analysis of a recent experiment seemingly favouring local realism against quantum mechanics

A recent experiment by Brida et al. [Eur. Phys. J. D 44, 547 (2007)] is analyzed with the conclusion that the results disagree with standard quantum predictions but fit a simple local hidden variables model. New experiments are proposed which might throw new light on the anomaly.     

Bell inequalities for a sensible family of local hidden variable theories testable at low detection efficiency

A family of local models containing two angles as hidden variables is defined for experiments measuring polarization correlation of optical photons. Searching for the best model of the family, that is giving predictions most close to quantum mechanics, allows deriving Bell-type inequalities which may be tested with relatively low detection efficiency.     

ac Stark effect for a two-level atom in a squeezed vacuum via a two-photon process

The nondegenerate two-photon interaction of a two-level atom with a broadband multimode squeezed vacuum is investigated. We find that in the two-photon process the squeezed vacuum has a driving effect on the atom which can lead to an ac Stark effect when the average photon number of the squeezed vacuum is larger than a critical value. Received: 2 February 1999 / Received in final form: 20 April 1999     

Testing Bell inequalities in photonic crystals

We show how entangled atomic pairs can be prepared in order to test the Bell inequalities. The scheme is based on the interaction of the atoms with a highly localized field mode within a photonic crystal. The potential of using optically separated transitions and the stability of the entangled state to spontaneous emission could lead to the closure of the communication and the detection loopholes appearing in experiments so far. The robustness of the scheme against detector inefficiencies, the spread in the atomic velocities and the fact that the entangled pairs are not generated simultaneously is also studied. Received 31 July 2001 and Received in final form 30 November 2001     

Squeezing in a spin chain with site-dependent periodic and long-range interactions

Numerical and analytical results for the squeezing factor, ζ², in a pseudo-spin s-1/2 chain. The open chain is composed by N two-level atoms with site-dependent interactions. The time evolution of the squeezing factor is studied, as well as its dependence on the number of atoms and on the interactions. It is found that long-range interactions may optimize the degree of spin squeezing.     

Dynamical creation of entanglement versus disentanglement in a system of three-level atoms with vacuum-induced coherences

The dynamics of entanglement between three-level atoms coupled to the common vacuum is investigated. We show that the collective effects such as collective damping, dipole-dipole interaction and the cross coupling between orthogonal dipoles, play a crucial role in the process of creation of entanglement. In particular, the additional cross coupling enhances the production of entanglement. For the specific initial states we find that the effect of delayed sudden birth of entanglement, recently invented by Ficek and Tana? [Ficek, R. Tana?, Phys. Rev. A 77 (2008) 054301] in the case of two-level atoms, can also be observed in the system. When the initial state is entangled, the process of spontaneous emission causes destruction of correlations and its disentanglement. We show that the robustness of initial entanglement against the noise can be changed by local operations performed on the state.     

Atom interferometry in a static electric field: Measurement of the Aharonov-Casher phase

Consecutive, phase-coherent, near-resonant optical excitations of atoms have been used to realize an atom interferometer with a beam of thermal calcium atoms. We have measured the topological phase shift due to the interaction of a static electric field with the magnetic dipole moment of a moving atom (Aharonov-Casher effect). The observed phase shift was proportional to the electric field and, within our experimental uncertainty, independent of the particle's velocity. The measured value of the phase shift has been found to agree with the predicted one within a relative uncertainty of 2.2%.Dedicated to H. Walther on the occasion of his 60th birthday     

Scheme for reliable realization of quantum logic gates for two atoms separately trapped in two distant cavities via optical fibers

An approach for realizing conditional phase gate for two atoms separately trapped in two distant cavities mediated by an optical fiber is proposed. Utilizing the adiabatic passage, the atomic spontaneous emission, and the decays of the fiber and cavities are avoided under certain condition. The effects of the losses in the fiber and cavities on the fidelity are analyzed. Moreover, our scheme is not restricted to Lamb-Dicke limit. We also generalize the approach to generate one-dimensional cluster state and entangled state for two collections of atoms.     

Establishment of Entanglement for Two Atoms Trapped in Two Distant Bad Cavities

A scheme is presented for generation of entangled states for two atoms trapped in two distant bad cavities. The scheme can work with bad cavities with the coupling strength smaller than the cavity decay rate, which is important from the viewpoint of experiment. In the scheme the atoms have no probability of being populated in the excited state and thus the atomic spontaneous emission is suppressed, which increases the probability of success. The fidelity of the entangled state is not affected by the detection eflciency. Furthermore, the scheme does not require the detection of the left-polarized photon and right-polarized photon at the same time.     

Atom-field entanglement in two-atom Jaynes-Cummings model with nondegenerate two-photon transitions

An exact solution of the problem of two two-level atoms with nondegenerate two-photon transitions and nondegenerate Raman transitions interacting with two-mode radiation field is presented. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent fields. The atom-field entanglement is investigated on the basis of the reduced atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process for both models is shown. Conditions and times of disentanglement are derived.     

Experimental study of a Back Action Evading device for continuos measurements on a macroscopic harmonic oscillator at the quantum limit level

The Back Action Evading technique is a particular kind of quantum non demolition measurement, first proposed by Caves et al. in 1980 [3]. We present an experimental study to implement the Back Action Evading measurement scheme in monitoring the amplitude of an harmonic oscillator excited by a classical force. Results showing the agreement of our theoretical model with the experimental behaviour of our apparatus in the classical regime are presented. We discuss also the optimization of the performance of our set-up, which should allow to monitor our oscillator in quantum regime even below the standard quantum limit level. Received: 22 March 1996     

Physics of a Kind of Normally Ordered Gaussian Operators in Quantum Optics

Based on the technique of integration within an ordered product of operators we investigate a completeness relation of pure states （such as the coordinate eigenstate, the momentum eigenstate and the coherent state） into normally ordered Gaussian forms. The Weyl ordering invariance under similarity transformations is employed to reveal physical meaning of a kind of normally ordered Gaussian operators, which have the similar forms to the bivariate normal distributions in statistics, i.e., the thermo mixed state density matrix.