Table of contents

This is a short summary of the purpose and the contents of the Nobel Symposium. It serves as an introduction to the original papers presented by the participants. The topics are here organized in a way that does not necessarily follow the order of presentation at the Symposium; they have been arranged in a manner that will hopefully facilitate the reading by a more general audience. Short introductions and explanations of basic concepts and nomenclature are given as well as hints towards open questions in the respective areas. These are followed by short comments which indicate how each speaker's contribution fits into this context. We hope that this will inspire a large readership to share with the participants of the Symposium the excitement over the new developments presented here.

Coherent field-emission electron beams and electron holography techniques have made it possible to produce interference micrographs from which the phase distribution of the wavefunction of an electron beam transmitted through an object relative to that of a reference beam can be measured to within 1/100th of the electron wavelength. This has opened up a new way to make ultrafine measurements of material structures and of electromagnetic field distributions. Magnetic lines of force of quantized vortices in a superconducting thin film, for example, have been directly observed by electron-holographic interference microscopy. In addition, the dynamics of individual vortices interacting with pinning centers has been observed in real time by Lorentz microscopy.

Neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment and they are subject to all basic interactions and they are sensitive to topological effects, as well. Related experiments will be discussed. Recent neutron interferometry experiments based on postselection methods renewed the discussion about quantum nonlocality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates a persisting coupling in phase space even in cases of spatially separated Schrödinger Cat-like situations. These states are extremely fragile and sensitive against any kind of fluctuations and other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction volume becomes impossible in principle.

By using quasi-resonant exchanges of energy, linear and angular momentum between atoms and photons, it is possible to polarize atoms, to displace their energy levels and to control their position and their velocity. A few physical mechanisms allowing one to trap atoms and to cool them in the microkelvin, and even in the nanokelvin range, are briefly described and classified with the help of a few simple guidelines. Various possible applications of such ultracold atoms are also reviewed. They take advantage of the long interaction times and long de Broglie wavelengths which are now available with laser cooling and trapping techniques. New quantum situations can also be achieved in these experiments, calling for new theoretical approaches. The last part of this paper is devoted to a brief discussion of these problems.

No. When particle detectors are included particles do not follow the Bohm trajectories as we would expect from a classical type model.

The status of our experimental realization of Bohm's spin-1/2 particle version of the Einstein-Podolsky-Rosen gedankenexperiment is discussed. This new experiment provides a definitive test of the, as yet, untested strong Bell inequalities. It closes the two widely recognized loopholes associated with previous experiments, and has the interesting new feature that the entangled state exists for milliseconds rather than nanoseconds. The spin one-half particles are two ¹⁹⁹Hg atoms in an entangled nuclear spin state with total nuclear spin zero. Measurement of the nuclear spin correlation is achieved by detection of each atom using a spin state selective two photon excitation-ionization scheme.

The state of a quantum system, consisting of two distinct subsystems, is called separable if it can be prepared by two distant experimenters who receive instructions from a common source, via classical communication channels. A necessary condition is derived and is shown to be more sensitive than Bell's inequality for detecting quantum inseparability. Moreover, collective tests of Bell's inequality (namely, tests that involve several composite systems simultaneously) may sometimes lead to a violation of Bell's inequality, even if the latter is satisfied when each composite system is tested separately.

We shall demonstrate that if one can construct a macroscopic state that maintains quantum coherence (a "Schrödinger Cat state"), then it can be used to send a superluminal signal. Since such a device has quantum properties, the experiment can perhaps also be done with a microscopic system, although we discuss in the conclusions why this might not be true.

We take as our model an optical phase shifter of 180°, which we assume can be placed into a beam or not, and that the two possibilities can be quantum mechanically superimposed.

This result depends upon being able to exploit two properties. One is that the device, which becomes a signal transmitter, can be entangled with the signal it is transmitting, thus becoming a GHZ state. The second is a controlled non-unitarity, for a subset of the complete Hilbert space, of a type that has already been used experimentally in two beautiful downconversion interference experiments.

The result is a superluminal transfer of information, but not of energy, using common experimental methods and a device that does not exist as yet, but should in principle be constructable. Although controversial, the result should not be ruled out by proofs that assume conservation of energy and/or unitarity over the entire quantum domain.

Experiments at Berkeley and elsewhere which show that the process of tunneling is apparently superluminal will be reviewed. Conflicting theories for the tunneling time will be compared with experiment. The tunneling particle in the Berkeley experiments was the photon. The measurement of the tunneling time utilized a two-photon light source (spontaneous parametric down-conversion), a Hong-Ou-Mandel interferometer, and a coincidence counter of photon pairs. The tunnel barrier consisted of a photonic-bandgap medium excited at midgap. We find that the peak of a tunneling single-photon wave packet appeared on the far side of the barrier 1.47 ± 0.21 fs earlier than the peak of a wave packet which traveled an equal distance in air. Group velocities which exceed c can also occur in transparent media with inverted atomic populations. Tachyon-like excitations, i.e., collective normal modes of atoms coupled to electromagnetic radiation which possess tachyon-like dispersion relations, occur in these media. However, relativistic causality is not violated by any of these superluminal phenomena.

From data in the present we can predict the future and retrodict the past. These predictions and retrodictions are for histories – most simply time sequences of events. Quantum mechanics gives probabilities for individual histories in a decoherent set of alternative histories. This paper discusses several issues connected with the distinction between prediction and retrodiction in quantum cosmology: the difference between classical and quantum retrodiction, the permanence of the past, why we predict the future but remember the past, the nature and utility of reconstructing the past(s), and information theoretic measures of the utility of history.

There are good motivations for considering some type of quantum histories formalism. Several possible formalisms are known, defined by different definitions of event and by different selection criteria for sets of histories. These formalisms have a natural interpretation, according to which nature somehow chooses one set of histories from among those allowed, and then randomly chooses to realise one history from that set; other interpretations are possible, but their scientific implications are essentially the same.

The selection criteria proposed to date are reasonably natural, and certainly raise new questions. For example, the validity of ordering inferences which we normally take for granted – such as that a particle in one region is necessarily in a larger region containing it – depends on whether or not our history respects the criterion of ordered consistency, or merely consistency.

However, the known selection criteria, including consistency and medium decoherence, are very weak. It is not possible to derive the predictions of classical mechanics or Copenhagen quantum mechanics from the theories they define, even given observational data in an extended time interval. Attempts to refine the consistent histories approach so as to solve this problem by finding a definition of quasiclassicality have so far not succeeded.

On the other hand, it is shown that dynamical collapse models, of the type originally proposed by Ghirardi-Rimini-Weber, can be re-interpreted as set selection criteria within a quantum histories framework, in which context they appear as candidate solutions to the set selection problem. This suggests a new route to relativistic generalisation of these models, since covariant definitions of a quantum event are known.

A description of quantum systems at the time interval between two successive measurements is presented. Two wave functions, the first pre-selected by the initial measurement and the second post-selected by the final measurement describe quantum systems at a single time. It is shown how this approach leads to a new concept: a weak value of an observable. Weak values represent novel characteristics of quantum systems between two measurements. They are outcomes of a standard measuring procedure that fulfills certain requirements of "weakness". We call it weak measurement. Physical meaning and underlying mathematical structure of weak measurements are explored.

Highly regular spatio-temporal or multi-dimensional patterns in the quantum mechanical probability or classical field intensity distributions can appear due to pair interference between individual eigen-modes of the system forming the so called intermode traces. These patterns are strongly pronounced if the intermode traces are multi-degenerate. This phenomenon occurs in many areas of wave physics.

The complete family of squeezed states of a continuous-wave mode pair of the electromagnetic field was generated and analyzed by tomographical methods. Wigner functions, photon number distributions, density matrices, and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub- and super-Poissonian photon statistics, and bifurcations of the phase distribution were observed.

The generation and application of nonclassical light (number-phase squeezed states and single-photon states) from semiconductor lasers and mesoscopic LEDs are discussed. The shot noise suppression in the three-partition processes such as the electron transport in a highly dissipative conductor, the electron injection and tunneling in a pn junction, and the radiative recombination of an electron-hole pair inside a cavity is the basic principle for this generation scheme.

We show that the measured probability distribution of the phase difference between two electromagnetic fields can be sharpened progressively as data involving more and more detected photons are discarded, and that the phase difference can be well-defined even when the mean photon number ⟨n⟩ → 0. In our operational phase theory the variance of the directly measured phase difference has no lower bound other than zero, and this is consistent with the experimental results.

Using a hybrid of a simple interference technique and an application of the quantum Zeno effect, it is possible to optically determine the presence of an absorbing object with an arbitrarily low probability that a photon is actually absorbed. We have demonstrated the feasibility of systems in which up to 85% of the measurements could be "interaction-free". Also, we have started investigating the possibility of using these techniques to allow "interaction-free" imaging of objects; our prototype schemes have shown resolutions of less than 10 µm. Finally, we present a curious phenomenon that occurs when the object in question is only partially transmitting, which should allow a seeming violation of Beer's law.

The goal of the LIGO project (as well as projects VIRGO and GEO-600) is to create terrestrial gravitational wave antennae which will detect bursts of gravitational radiation from astrophysical catastrophies. The sensitivity of the antennae to record the perturbations of the metric (the gravitational wave) has to be at such a level when the quantum behavior of macroscopic test masses (the key elements in the antennae) becomes essential. Therefore experimentalists have to invent and realize technologies which allow to reduce the decoherence of these test masses due to the heat bath and independently to create new methods of quantum measurements which will allow to beat certain limits of sensitivity (the so-called Standard Quantum Limits). These methods may be based on principles of Quantum-Non-Demolition measurements.

An important development in modern physics is the emerging capability for investigations of dynamical processes for open quantum systems in a regime of strong coupling for which individual quanta play a decisive role. Of particular significance in this context is research in cavity quantum electrodynamics which explores quantum dynamical processes for individual atoms strongly coupled to the electromagnetic field of a resonator. An overview of the research activities in the Quantum Optics Group at Caltech is presented with an emphasis on strong coupling in cavity QED which enables exploration of a new regime of nonlinear optics with single atoms and photons.

In this paper recent experiments performed in our laboratory are reviewed dealing with the investigation of quantum phenomena in the radiation interaction of single atoms. The first part describes experiments in single mode cavities using the one-atom maser or micromaser and in the second part experiments with ion traps are summarized. The latter experiments concentrate on the investigation of resonance fluorescence. In addition new experimental proposals using ultracold atoms in cavities and traps are discussed. In those future experiments the interplay between atomic waves and light waves is important and leads to new phenomena in radiation-atom interaction.

Coherent manipulations involving the quantized motional and internal states of a single trapped ion can be used to simulate the dynamics of other systems. We consider some examples, including the action of a Mach Zehnder interferometer which uses entangled input states. Coherent manipulations can also be used to create entangled states of multiple trapped ions; such states can be used to demonstrate fundamental quantum correlations.

We discuss the decay and decoherence of nonclassical states in quantum optics coupled to zero-temperature heat baths, and contrast ensemble behaviour with that of individual realizations. We show how nonclassical states are highly sensitive to dissipation in a number of cases, but present an example of how dissipation can be used to generate nonclassical states.

Experiments involving Rydberg atoms crossing one at a time a superconducting cavity lead to new tests of quantum theory, such as the generation of entangled pairs of atoms of the Einstein-Podolsky-Rosen type, the preparation of mesoscopic superpositions of field states in the cavity ("Schrödinger cats") and the observation of the progressive decoherence of these states. These experiments illustrate basic aspects of the quantum-classical boundary and demonstrate steps of quantum logic operations essential for quantum information processing.

A metallic electrode connected to electron reservoirs by tunnel junctions has a series of charge states corresponding to the number of excess electrons in the electrode. In contrast with the charge state of an atomic or molecular ion, the charge states of such an "island" involve a macroscopic number of conduction electrons of the island. Island charge states bear some resemblance with the photon number states of the cavity in cavity QED, the phase conjugate to the number of electrons being analogous to the phase of the field in the cavity. For a normal island, charge states decay irreversibly into charge states of lower energies. However, the ground state of a superconducting island connected to superconducting reservoirs can be a coherent superposition of charge states differing by two electrons (i.e. a Cooper pair). We describe an experiment in which this Josephson effect involving only one Cooper pair is measured.

We start by reviewing some interesting results in mesoscopic physics illustrating nontrivial insights on Quantum Mechanics. We then review the general principles of dephasing (sometimes called "decoherence") of Quantum-Mechanical interference by coupling to the environment degrees of freedom. A particular recent example of dephasing by a current-carrying (nonequilibrium) system is then discussed in some detail. This system is itself a manifestly Quantum Mechanical one and this is another illustration of detection without the need for "classical observers" etc. We conclude by describing briefly a recent problem having to do with the orbital magnetic response of conduction electrons (another manifestly Quantum Mechanical property): The magnetic response of a normal layer (N) coating a superconducting cylinder (S). Some recent very intriguing experimental results on a giant paramagnetic component of this response are explained using special states in the normal layer. It is hoped that these discussions illustrate not only the vitality and interest of mesoscopic physics but also its extreme relevance to fundamental issues in Quantum Mechanics.

Some recent works on the tunneling of light interstitial particles (protons and positive muons) in metals are reviewed. They provide examples of simple quantum systems coupled to "baths" consisting of phonons and conduction electrons. In the limit of strong coupling to such an environment the positive muons move by quantum diffusion, where coherence is lost between each tunneling event, whereas in the weak coupling limit coherence can be maintained and allow a quantum propagation, i.e. a band-like motion. These phenomena can also be seen as examples of wave-function reduction in the presence of dissipative environments and may help to understand the details of such processes.

The environment – external or internal degrees of freedom coupled to the system – can, in effect, monitor some of its observables. As a result, the eigenstates of these observables decohere and behave like classical states: Continuous destruction of superpositions leads to environment-induced superselection (einselection). Here I investigate it in the context of quantum chaos (i.e., quantum dynamics of systems which are classically chaotic). I show that the evolution of a chaotic macroscopic (but, ultimately, quantum) system is not just difficult to predict (requiring an accuracy exponentially increasing with time) but quickly ceases to be deterministic in principle as a result of the Heisenberg indeterminacy (which limits the resolution available in the initial conditions). This happens after a time t_ℏ which is only logarithmic in the Planck constant. A definitely macroscopic (if somewhat outrageous) example is afforded by various components of the solar system which are chaotic, with the Lyapunov timescales ranging from a bit more than a month (Hyperion) to millions of years (planetary system as a whole). On the timescale t_ℏ the initial minimum uncertainty wavepackets corresponding to celestial bodies would be smeared over distances of the order of radii of their orbits into "Schrödinger cat – like" states, and the concept of a trajectory would cease to apply. In reality, such paradoxical states are eliminated by decoherence which helps restore quantum-classical correspondence. The price for the recovery of classicality is the loss of predictability: In the classical limit (associated with effective decoherence, and not just with the smallness of ℏ) the rate of increase of the von Neumann entropy of the decohering system is independent of the strength of the coupling to the environment, and equal to the sum of the positive Lyapunov exponents. Algorithmic aspects of entropy production are briefly explored to illustrate the effect of decoherence from the point of view of the observer. We show that "decoherence strikes twice", introducing unpredictability into the system and extracting quantum coherence from the observers memory, where it enters as a price for the classicality of his records.

I consider various ways in which the recently stabilized systems of alkali gases in the Bose-condensed state can be used to test rather basic ideas of quantum mechanics, particularly with respect to questions involving the meaning of the "identity" of elementary particles. An essential role, here, is played by the ability to switch tunneling "contact" on and off over timescales small compared to any characteristic dynamical timescale of the system. Apart from their intrinsic interest, these questions may also be relevant to speculations about the "quenching" behavior of the early Universe.

Entanglement, according to the Austrian physicist Erwin Schrödinger the Essence of Quantum Mechanics, has been known for a long time now to be the source of a number of paradoxical and counterintuitive phenomena. Of those the most remarkable one is usually called non-locality and it is at the heart of the Einstein-Podolsky-Rosen Paradox and of the fact that Quantum Mechanics violates Bell's inequalities. Recent years saw an emergence of novel ideas in entanglement of three or more particles. Most recently it turned out that entanglement is an important concept in the development of quantum communication, quantum cryptography and quantum computation. First explicit experimental realizations with two or more photons include quantum dense coding and quantum teleportation.

An expanded theory of information transmission and processing has emerged over the past few years, encompassing the processing and transmission of intact quantum states, the interaction of quantum and classical information, the quantitative theory of entanglement, and the use of quantum information processing to speed up certain classical computations. We review this field, concentrating on the parallels with and differences from classical information theory, which is now best seen as a part of the new theory.

Quantum computers which use quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations can be viewed as multiparticle interferometers. I discuss this approach to quantum computation and argue that it provides additional insights into the nature of quantum algorithms.

We propose a physical implementation for quantum communication in quantum networks. Our scheme demonstrates how to transfer quantum information between spatially separated atoms, which are each inside a high-Q optical cavity, and how to establish a distant maximally entangled pair, by sending photons through a general, noisy channel, such as a standard optical fiber.