Quantum non-demolition measurements with optical solitons

The optical Kerr effect provides an ideal quantum non-demolition interaction. Experiments and proposals using this interaction are reviewed with special emphasis on optical soliton pulses propagating in fibres. The performance of a quantum non-demolition experiment using the optical Kerr effect may be reduced by self-phase modulation of the probe pulse. Proposals to overcome this limitation are discussed. Received: 15 April 1996     

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     

Quantum non-demolition measurements in optics: a review and some recent experimental results

We review the schemes which have been implemented, in order to achieve quantum non-demolition (QND) measurements in the optical domain. The simplest schemes can be obtained using the optical Kerr effect, which yields a crossed-phase modulation coupling between two light beams. Other schemes use either independently generated squeezed light, or coupled-mode parametric amplifiers. These various schemes can be characterized using three criteria, which describe, respectively, the quality of the quantum measurement, the non-destruction of the signal, and the conditional variance of the output signal beam, given the output meter beam (quantum-state preparation criterion). We show that quantitative limits can be defined with respect to these criteria, delimiting classical and quantum domains of operation. Then we present in more detail a new experimental implementation of QND measurements, using three-level atoms inside a doubly-resonant optical cavity.     

Quantum nondemolition measurement of transverse atomic position in Kapitza-Dirac atomic beam scattering

It is demonstrated that one can measure the distribution of the transverse position of an atom crossing one or more optical cavities by monitoring the phase of the standing wave fields in the cavities. For the atom-field interaction the Kapitza-Dirac regime is assumed; it is shown that in this regime the method represents a quantum nondemolition measurement of the atomic position. On the other hand it can be applied to prepare narrow distributions of the transverse atomic position. In order to show this, a numerical simulation is performed, which illustrates the collapse of a broad initial Gaussian wavepacket, which can be coherent or incoherent, to a distribution with narrow peaks. Preparing the cavity fields in a squeezed state, one can greatly enhance the impact of the cavity field measurements on the atomic density matrix.     

Quantum communications

We review recent developments in the use of non-classical light in low light level communications. Three examples using parametrically generated photon pairs are discussed. The first being a simple time coding scheme, the second based on fourth-order interference and the third exploits non-local correlations at the one photon per bit level.     

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     

The magnesium ramsey interferometer: Applications and prospects

In this paper it will be shown that an atom interferometer, based on the coherent splitting of the atomic wavefunction by four travelling waves (Ramsey interferometer), may be explained by a purely mechanical interpretation. As our first application of this Ramsey interferometer we have measured the phase shifts respectively optical length changes in a magnesium atomic beam caused by the acceleration of the partial atomic wave in one arm of the interferometer. This acceleration was achieved by the dipole force exerted by an off-resonant crossing laser beam which interacted with the ground state part of the wavefunction only. Further applications of this interferometer and improvements due to laser cooling will be discussed.     

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.     

Spatio-temporal coupling of laser fluctuations — Observations on a laser with internal frequency conversion

The amplitude of standing wave solid state lasers with frequency conversion inside the resonator can become unstable. We investigated the amplitude fluctuations of an end-pumped Nd:YAG-laser at low pump rates (below 160% threshold pump power) and also above. Detecting the individual mode instabilities separately and comparing them with a theoretical laser model, we can trace the origin of the mechanism leading to the observed fluctuations. At certain well defined discrete pump levels above 160% threshold the instabilities disappear. These stable emission states are associated with particular nonconventional mode patterns, some of them exhibiting a helical phase structure. Based on experimental observations and computer simulations of pump induced resonator aberrations we describe a mechanism for the emergence of the peculiar transversal modes and laser fluctuations.     

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.     

Quantum nondemolition measurement by optomechanical coupling

 We show that a single-port optical cavity with a movable mirror can provide a quantum non-demolition measurement of the intensity of a light beam. Due to radiation pressure, the cavity length is sensitive to the light intensity and can be measured with a secondary light beam. Signal-meter correlations can be made very large even at non-zero temperature. We study these correlations when the moving mirror is a plane–convex crystal resonator and we show the importance of spatial matching between light and acoustic modes. Received: 12 June 1996/Revised version: 3 September 1996     

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.     

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.     

Observable entities in quantum-optics networks

We consider the quantum analogue of the classical Jones calculus for passive linear optical systems. Those points of the theory where quantum features have to be manifestly included are discussed. The use of different quasidistribution functions and their restrictions to the observable variables only is presented. The consistency of the theory and its usefulness are discussed.Dedicated to H. Walther on the occasion of his 60th birthday     

Conditional Schrödinger cats generation and detection by quantum non-demolition measurements

 We show that a Schr?dinger cat state can be generated using a crossed Kerr interaction between two optical modes and an appropriate conditional measurement on one of the modes. The effect of damping on the generation process is analyzed in detail and two possible detection schemes for the cat state are presented. Received: 15 May 1996     

A method for demonstrating violation of local realism with a two-photon downconverter without use of Bell inequalities

We show that the recent proposal by Hardy and Jordan for a test of local realism without the use of Bell inequalities can be implemented in two-photon coincidence measurements with linear polarizers, when the photon pairs are produced by parametric downconversion. If the probabilities measured with real detectors are proportional to the corresponding probabilities determined with ideal detectors, this method does not depend on the use of detectors with high or even known quantum efficiencies.Dedicated to H. Walther on the occasion of his 60th birthday     

Controlled Teleportation of Multi-Qudit Quantum Information

We present a controlled teleportation scheme for teleporting an arbitrary superposition state of an M-qudit quantum system. The scheme employs only one entangled state as quantum channel, which consists of the qudits from Alice, Bob and every agent. The quantum operations used in the teleportation process are a series of qudit Bell measurements, single-qudit projective measurements, qudit H-gates, qudit-Pauli gates and qudit phase gates. It is shown that the original state can be restored by the receiver only on the condition that all the agents collaborate. If any agent does not cooperate, the original state can not be fully recovered.     

Conditional quantum-state engineering in repeated 2-photon down-conversion

The U(1,1) and U(2) transformations realized by three-mode interaction in the respective parametric approximations are studied in conditional measurement, and the corresponding non-unitary transformation operators are derived. As an application, the preparation of single-mode quantum states using an optical feedback loop is discussed, with special emphasis on Fock-state preparation. For that example, the influence of non-perfect detection and feedback is alsoconsidered. Received: 12 July 2000 / Revised version: 19 September 2000 / Published online: 30 November 2000     

Comment on: “A class of bound entangled states” [Phys. Lett. A 352 (2006) 321]

We generalize the condition keeping the special states bound entangled [S.-M. Fei, X. Li-Jost, B.-Z. Sun, Phys. Lett. A 352 (2006) 321] to the general states. Taking the original 4×4$4\times 4$ states as 2×8$2\times 8$ states we show that they still can be bound entangled.     

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