Volume 56, Issue 1-2 - Proceedings of the 3rd Workshop on Mysteries, Puzzles and Paradoxes in Quantum Mechanics

The folklore notion of the "Non-Locality of Quantum Mechanics" is examined from the point of view of hidden-variables theories according to Belinfante's classification in his Survey of Hidden Variables Theories. It is here shown that in the case of EPR, there exist hidden variables theories that successfully reproduce quantum-mechanical predictions, but which are explicitly local. Since such theories do not fall into Belinfante's classification, we propose an expanded classification which includes similar theories, which we term as theories of the "third" kind. Causal implications of such theories are explored. -Pacs: 03.65.Bz

We show how one can ascertain the values of four mutually complementary observables of a spin-1 degree of freedom. -Pacs: 03.65.Bz

Two recent works suggest a possibility of sending signals to a space-like separated region, contrary to the spirit of special relativity. In the first work (J. Grunhaus, S. Popescu, and D. Rohrlich, Phys. Rev. A 53, 3781 (1996)) it has been shown that sending signals to a particular union of space-like separated regions cannot cause causality paradoxes. Another work (Y. Aharonov and L. Vaidman, Phys. Rev. A 61, 052108 (2000)) showed that the relative phase of the quantum superposition of a particle at two separate locations can be measured locally. Together with the possibility of changing the relative phase in a nonlocal way using the potential effect we, apparently, have a method of sending signals to space-like separated regions. These arguments are critically analyzed in this paper.

Recent experiments to test B ell's inequality using entangled photons and ions aimed at tests of basic quantum mechanical principles. Interesting results have been obtained and many loopholes could be closed. In this paper we want to point out that tests of Bell's inequality also play an important role in verifying atom entanglement schemes. We describe as an example a scheme to prepare arbitrary entangled states of N two-level atoms using a leaky optical cavity and a scheme to entangle atoms inside a photonic crystal. During the state preparation no photons are emitted, and observing a violation of B ell's inequality is the only way to test whether a scheme works with a high precision or not.

In this paper we discuss our recent work on the creation of spin-squeezed states in both thermal (room temperature) gasses and in spinor Bose-Einstein condensates.

The two slits interference pattern for single particle is revisited, showing its strict relation to the free particle Schrödinger’s spread and describing the optical analogy. We explicitly show the possibility that spontaneous intrinsic decoherence (SID) can destroy interference pattern and that decoherence becomes stronger at the macroscopic limit.

We summarize unusual bound or localized states in quantum mechanics. Our guide through these intriguing phenomena is the classical physics of the upside-down pendulum, taking advantage of the analogy between the corresponding Newton’s equation of motion and the time independent Schrödinger equation. We discuss the zero-energy ground state in a three-dimensional, spatially oscillating, potential. Moreover, we focus on the effect of the attractive quantum anti-centrifugal potential that only occurs in a two-dimensional situation.

A multiparticle quantum superposition state has been generated by a novel phase-selective parametric amplifier of an entangled two-photon state. This realization is expected to open a new field of investigations on the persistence of the validity of the standard quantum theory for systems of increasing complexity, in a quasi decoherence-free environment. Because of its nonlocal structure the new system is expected to play a relevant role in the modem endeavor on quantum information and in the basic physics of entanglement. - Pacs: 03.65.Bz, 03.67.-a, 42.50.Ar, 89.70.+C

It is shown that the generally accepted statement that one cannot superpose states of different mass in non-relativistic quantum mechanics is inconsistent. It is pointed out that the extra phase induced in a moving system, which was previously thought to be unphysical, is merely the non-relativistic residue of the "twin-paradox" effect. In general, there are phase effects due to proper time differences between moving frames that do not vanish non-relativistically. There are also effects due to the equivalence of mass and energy in this limit. The remedy is to include both proper time and rest energy non-relativis-tically. This means generalizing the meaning of proper time beyond its classical meaning, and introduc­ ing the mass as its conjugate momentum. The result is an uncertainty principle between proper time and mass that is very general, and an integral role for both concepts as operators in non-relativistic physics.

Apparent paradoxes in Quantum Physics demand a sharp distinction between a "real part of the world" and the realm of possibilities. In the former we may distinguish individual elements (coarse events) relating to space-time, with causal connections between them respecting the relativistic locality principle. The latter, quantitatively described by probability assignments conditioned on existing facts and depending on the definition of equivalence classes of situations, cannot be subdivided in space-time categories. There are global correlations (Pauli principle...). The cut between the realms of facts and possibilities implies an evolutionary picture of the "real world" in which the (generalized) arrow of time assumes basic significance. Some deficiencies of existing theory are pointed out.

The quantum Zeno effect (QZE) is the striking prediction that the decay of any unstable quan­ tum state can be inhibited by sufficiently frequent observations (measurements). The consensus

We study the optimal way of creating bi-partite entanglement using a general two-qubit in­ teraction. On the one hand, we analyze the entanglement capability of an arbitrary non-local Hamiltonian acting on two qubits. We explicitly calculate the state which maximizes the entangle­ ment produced per time step 81 during the non-local evolution. On the other hand, we determine the maximal amount of entanglement which can be produced by an arbitrary two-qubit gate. We also give the separable state which leads to the output state containing this amount of entanglement. Furthermore, we consider the situation where auxiliary systems are present. Finally, we determine the non-unitary processes which are able to create entanglement from an initially separable state of two systems.

Interaction-free measurements introduced by Elitzur and Vaidman [Found. Phys. 23,987 (1993)] allow finding infinitely fragile objects without destroying them. Paradoxical features of these and related measurements are discussed. The resolution of the paradoxes in the framework of the Many-Worlds Interpretation is proposed.

We study the possible limitations and sources of decoherence of a scheme for the deterministic generation of polarization-entangled photons based on an appropriately driven single atom trapped within an optical cavity. -Pacs: 03.67.Hk, 42.50.Gy, 32.80.Qk

In this paper we give a survey of our experiments performed with the micromaser on the generation of Fock states. Three methods can be used for this purpose: the trapping states leading to Fock states in a continuous wave operation, state reduction of a pulsed pumping beam, and finally using a pulsed pumping beam to produce Fock states on demand where trapping states stabilize the photon number.

We discuss the properties of decoherence and its role in the appearance of classical properties in open quantum systems. In particular, it is used for classification of pure states with respect to their ability to persist despite the environmental monitoring.

We identify the operators and the corresponding physical quantities whose measurement allows in principle to obtain total teleportation of the unknown spin state of a single electron. We introduce an analogous scheme for a single photon and discuss its experimental implementation.

We investigate the theory of quantum fluctuations in non-equilibrium systems having large crit­ical fluctuations. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction, and also to envisage future tests of quantum theory in regions of macroscopic quantum fluctuations. A long-term objective of this research is to identify suitable physical sys­tems in which macroscopic 'Schrödinger cat'-like behaviour may be observed. We investigate two systems in particular of much current experimental interest, namely the degenerate parametric oscillator near threshold, and the evaporatively cooled (BEC). We compare the results obtained in the positive-P representation, as a fully quantum mechanical calculation, with the truncated Wigner phase space equation, also known as semi-classical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. In the region where the largest quantum fluctuations and Schrödinger cat-like behaviour might be expected, we find that the quantum predictions correspond very closely to the semi-classical theory. Nature abhors observing a Schrödinger cat. -Pacs: 03.65.Bz

Recently it has been proposed to use parity as a measure of the mechanism behind decoherence or the transformation from quantum to classical. Here, we show that the proposed experiment is more feasible than previously thought, as even an initial thermal state would exhibit the hypothesized symmetry breaking. - Pacs: 03.75.Be, 03.65.Nk

We apply a tomographic method we have recently proposed to the reconstruction of the full entangled quantum state for the cyclotron and spin degrees of freedom of a trapped electron. Our numerical simulations show that the entangled state is accurately reconstructed. -Pacs: 03.65.

Recently a class of maximally entangled states has been proposed that has the maximum amount of entanglement for a given purity. We investigate how much such states violate the conventional Bell inequality and discuss its implication.

Let us consider a single particle in an interferometer. If one of the two possible paths is blocked and the particle is detected, we know that the particle has followed the path which is not blocked. This would be an interference-free "which-path" information experiment. However, we no longer have an interfe­rometer, since one path is blocked. An alternative is to interact with the particle, but this would change its momentum and as a consequence the interference fringes would disappear, as discussed by Feynman. We can also consider two particles entangled in direction. Knowing the path followed by one of the par­ticles, it is possible to know the path followed by the other. On the other hand, when this information is erased, interference can be observed. However, this is a two particle interference: no single particle inter­ference can be observed. Retrodiction experiments are also possible, but these are not conclusive. Here we propose a much less intuitive experiment in which, without blocking one path or directly interacting with the particle, it is possible to know the path which is being followed by the particle in the interferom­eter. According to quantum mechanics, this is sufficient to lose the single particle interference. The same idea can be used to test the local pilot wave interpretation, to test quantum nonlocality under new conditions, and to devise an interferometer for a two-photon wave packet. This last result strongly suggests that there must be some connection between the deBroglie wavelength of an N-particle wave packet and entanglement. Wavelength of an /V-particle Wave Packet.

A quantum system being observed evolves more slowly. This "quantum Zeno effect" is reviewed with respect to a previous attempt of demonstration, and to subsequent criticism of the significance of the findings. A recent experiment on an individual cold trapped ion has been capable of revealing the micro-state of this quantum system, such that the effect of measurement is indeed discriminated from dephasing of the quantum state by either the meter or the environment.

We propose a non-collinear experimental scheme for the joint generation of two amplitudesqueezed beams at the frequencies u\ and u>2, fundamental and second harmonics of a Nd:YAG laser pulse. The scheme consists of two successive steps, both involving second-order non-linear interactions in ß - BaB 2 O 4 non-linear crystals. One of the output beams show subPoissonian photon statistics, and this allows to use photodetection instead of homodyne detection for diagnostics

We theoretically examine the behaviour of Cherenkov radiation in a lossy, dispersive and resonant medium when emission is assisted by an external electromagnetic field. Under the appropriate coherence conditions for Cherenkov emission, we anticipate a large increase of the emission yield at resonance. Our predictions are implemented by numerical estimates for cuprous oxide (Cu20 ). Pacs: 61.43.Fs, 77.22.Ch, 75.50.Lk

From the stationary solution of Schrödinger's equation in an interferometer we derive the wave functions of the longitudinal and the transverse motion. The former function is a plane wave. The wave function of the transverse motion is a one dimensional wave packet representing a super­ position of components with various values of the particles transverse momentum. The particles transverse momentum distribution in an interferometer is time independent and is determined by the aperture wave function. Consequently, it is independent of the distance from the slits. As such, it is a very important characteristic of the quantum state. Experimental determination of the mo­ mentum distribution would support the particle and wave interpretation of quantum interference in a new manner.

In this article we present a local hidden variables model for all experiments involving photon pairs produced in parametric down conversion, based on the Wigner representation of the radiation field. A modification of the standard quantum theory of detection is made in order to give a local realistic explanation of the counting rates in photodetectors. This model involves the existence of a real zeropoint field, such that the vacumm level of radiation lies below the threshold of the detectors.

By a Monte Carlo wave function approach we describe the dynamics of a coherently driven micromaser pumped by coherently prepared atoms. The system can exhibit nonclassical effects such as quadrature squeezing, sub-Poissonian photonstatistics, and Rabi oscillations revival. The interplay between driving field and polarised atoms allows manipulating both the photon number and the phase of the cavity field. By varying either the atomic transit time or the injected field intensity, the coherence of the system dynamics can be enhanced or even suppressed, whereas the induced cavity field phase can be shifted.

It is shown that all quantum “contradictions” disappear if one drops the assumption of unique initial conditions for a hidden variable theory for individual quantum processes. Our proposal corresponds with a deterministic world evolution such that local physical conditions are nonreproducible, in agreement with empirical observation

We show that it is possible to associate a de Broglie wavelength to a composite system even when the constituent particles are separated spatially. The nonlocal de Broglie wavelength (A /2) of a two-photon system separated spatially is measured with an appropriate detection system. The two-photon system is prepared in an entangled state in space-momentum variables. - Pacs: 42.50.-p, 42.50.Ar

We show that for an atom in a cavity in the strong coupling regime, flopping between Schrödinger cat states, devised as a superposition of displaced number states, can be accomplished. Beside, the Rabi frequency can be set to zero, so that population trapping or localization can be accomplished. These states could be proved to be useful for quantum computation

A coherent superposition of N Schwarzschild wormholes is proposed as a model for space­ time foam. Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods the Casimir energy. A proposal for an alternative foamy model formed by N

We study for a composite quantum system with a quantum Turing architecture the temporal non-locality of quantum mechanics by using the temporal Bell inequality, which will be derived for a discretized network dynamics by identifying the subsystem indices with (discrete) parameter time. However, the direct “observation” of the quantum system will lead to no violation of the temporal Bell inequality and to consistent histories of any subsystem. Its violation can be demonstrated, though, for a delayedchoice measurement

An alternative interpretation to Bohm’s ‘quantum force’ and ‘active information’ is proposed. Numerical evidence is presented, which suggests that the time series of Bohm’s ‘quantum force’ evaluated at the Bohmian position for non-stationary quantum states are typically non-Gaussian stable distributed with a flat power spectrum in classically chaotic Hamitonian systems. An important implication of these statistical properties is briefly mentioned

Deterministic chaos with its nonlinearities can formally reproduce some of the counterintuitive idiosyncrasies of quantum mechanics. In this paper I raise the question as to whether chaos might possibly supply some of the “hidden variables” that have been sought as underpinnings at a deeper level of quantum mechanics

We study the dephasing noisy effects on a Quantum Phase Gate and the consequences on its universality. To this end we employ two frameworks displaying their differences and analogies. Pacs: 03.67.Lx, 03.65.Bz

In quantum mechanics a particle is represented by a complex wave function. This is similar to the classical description of a distributed particle by a real valued density function. However, while classically the combined density of multiple particles can be decomposed into individual densities; the wave function of a multi-particle system can not always be decomposed into wave functions for the individual particles. Hence the classical assumption that density is a property of physical space, which is only possible because of the special topology of classical configuration space, does not work for quantum systems.

In the Schrödinger cat gedanken experiment a “cat” is in a quantum superposition of two macroscopically distinct states. There is the apparent interpretation that the “cat” is not in one state or the other, “alive” or “dead”. Here this interpretation is proved objectively. I propose the following definition of macroscopic reality: first, that the “cat” is either dead or alive, the measurement revealing which; second, that measurements on other “cats” some distance away cannot induce the macroscopic change, “dead” to “alive” and vice versa, to the “cat”. The predictions of quantum mechanics are shown to be incompatible with this premise.

Twin-beams generated by non degenerate optical parametric oscillators exhibit squeezing in the inten­ sity difference. Here we report intensity noise correlation and single beam spectra for pump power up to 14 times the threshold value. The degree of correlation of the two beams is practically independent of pump level. The single beam spectra confirm presence of relaxation oscillation.

The stochastic methods in Hilbert space have been used both from a fundamental and a practical point of view. The result reported here concerns the application of these methods to model the evolution of quantum systems and does not enter into the question of their fundamental or practical status. It can easily be stated as follows: Once a quantum stochastic evolution scheme is assumed, the incompatibility of the Markov property with the notion of quantum jumps is easily established

We briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between the dynamics of the particle and dynamic structure factor of the medium. - 05.40.Jc, 05.30.Fk, 05.30.Jp, 03.65.Yz