Table of contents

A system with variable number of electrons is described in which the states representing coherent superpositions of states with even and odd numbers of electrons may occur. An experiment is suggested which generalizes the experiment of Nakamura et al. and may provide direct evidence of such coherence and, thereby, justify the reality of a superspace.

I discuss various direct calculations of the properties of the one-band Hubbard model on a square lattice and conclude that these properties sufficiently resemble those of the cuprate superconductors that no more complicated interactions are necessary to cause high T_c superconductivity. In particular, I discuss phonon effects and conclude that these may be effective in reducing T_c and the gap in electron-doped materials.

The aim of this paper is to emphasize the role of coupling between electronic and mechanical degrees of freedom taking place on a nanometer length scale. Such coupling affects significantly the electrical properties of nanocomposite materials which are usually heteroconducting and heteroelastic by their nature. As examples of nanoelectromechanics in normal and superconducting composites a self-assembled single electronic device exhibiting a dynamical instability leading to shuttling of electrical charge by a movable Coulomb dot is discussed along with an example of shuttling of Cooper pairs by a movable Single Cooper Pair Box.

We review aspects of electrical transport in metallic single wall carbon nanotubes (SWCNT) related to the spin of the conductance electrons. For large contact resistances, R ≫ h/2e², a SWCNT exhibits Coulomb blockade, and transmission can only occur, when a gate voltage leads to an energy degeneracy for two different numbers of electrons in the SWCNT. The Coulomb blockade gate voltage change is directly proportional to the addition energy for single electron tunnelling. In certain ideal cases every second of the populated electronic states has a higher addition energy, indicating that two spindegenerate electrons are roomed at each orbital state. A low addition energy therefore corresponds to approaching an even number of electrons. The odd-even alternation can be checked in a magnetic field, since then the odd additional electron may enter in one of two Zeeman states. If the high resistance contact is a tunnel junction, the transmission reflects the density of states. This leads to a direct detection of the so-called Luttinger liquid state of the electrons. Ferromagnetic contacts to the SWCNT leads to a conductance which depends on the orientation of the magnetic domains in the contacts. The magnetoresistance effect can be much larger than expected from a simple spin-valve phenomenon. For any intermediate normal metal (Au) contact resistances, R ∼ h/2e², the Coulomb blockade may still separate the single electron states in the SWCNT with odd and even numbers of electrons. However, at the lowest temperatures the transmission only shows Coulomb blockade for even number of electrons. In the situations with odd number of electrons a coherent tunnelling process dominates. This shortage of the blockade is rooted in the Kondo states formed in the two Au electrodes by exchange interaction due to the spin state in the SWCNT. This tunnelling process is a result of a net spin on the SWCNT and consequently a spin degeneracy. A triplet state is forced into degeneracy with the singlet state in a suitable magnetic field. The situation in a magnetic field is particularly simple in a SWCNT, in contrast to conventional quantum dots, because the tiny diameter of the SWCNT practically speaking precludes orbital effects.

The metal-insulator (M-I) transition in conducting polymers is particularly interesting; critical behavior has been observed over a relatively wide temperature range in a number of systems, including polyacetylene, polypyrrole, poly (phenylene vinylene) and polyaniline. In each case, metallic, critical and insulating regimes have been identified through Zabrodskii plots of the logarithmic derivative of the conductivity. The critical regime (in which the conductivity varies as T^β, where β ≈ 1/3) is tunable by varying the extent of disorder and by applying external pressure and/or an external magnetic field. The transitions from metallic to critical behavior and from critical to insulating behavior have been induced with a magnetic field and from insulating to metallic behavior with applied pressure.

This paper summarizes recent work at MIT which was presented at the Nobel Jubilee Symposium. These examples demonstrate the broad range of topics which are covered by research on quantum-degenerate gases: superfluidity, phonons, boson and fermion mixtures, atom optics. For further reading and references to other work, we refer to the original publications.

Recent experiments and theories advancing the fundamental understanding of copperoxide superconductors are briefly discussed.

After the extensive worldwide research of the last 15 years, great progress has been made in all areas of high temperature superconductivity, namely, materials, science, and technology. In this presentation, I shall first summarize what we know and do not know about the materials and physics, but only of the cuprate high temperature superconductors because of their higher transition temperatures, and describe the material challenges encountered in unraveling the mystery of superconductivity in this class of materials. I shall then present results of two recent interesting experiments concerning the propositions of the possible co-existence of superconductivity and ferromagnetism in cuprates, and the possible existence of high temperature superconductivity in multi-wall carbon nanotubes, respectively. Finally, I shall briefly comment on the recent reports of exciting results for field-induced superconductivity.

We review some aspects of the physics of high temperature superconductivity (HTS) related to coherent phenomena and unconventional pairing symmetry. We discuss the role of the Josephson effect as a very powerful probe of the underlying physics of HTS, concentrating on phase-sensitive experiments. We then proceed to some consequences of d-wave symmetry, including possible broken time-reversal symmetry, Andreev bound states, and the presence of an imaginary component of the order parameter (OP) in the presence of surfaces and interfaces. Finally we discuss some aspects of HTS grain boundary Josephson junctions which allow fundamental studies and potential applications, in particular the possibility of employing grain boundary Josephson junctions for π-circuitry and d-wave qubit arrays.

We have studied the De Haas-van Alphen oscillations of unconventional superconductor for magnetic field well below H_c2. We find that the amplitude of the oscillation is increased substantially relative to that of an s-wave gap material.

Experiments with small capacitance Josephson junction arrays are described that demonstrate the quantum behavior of the phase of the superconducting condensate. This quantum behavior is based on the complementarity of phase and number for a condensate state of many bosons. A key factor to observation of this quantum behavior is the coupling of the superconducting condensate state to dissipation in the electrodynamic environment of the Josephson junction. It is shown how one-dimensional Josephson junction arrays can be used to design an environment with very weak coupling to dissipation, allowing for measurement of condensate with well defined number. The well defined number is manifest in the Coulomb blockade of Cooper pair tunneling.

I briefly examine the motivation for experiments designed to test quantum mechanics against an alternative, "common-sense" view of the everyday world which I denote "macrorealism", and review how far existing experiments go towards settling the issue.

We present a review of recent results concerning the physics of ultracold trapped dipolar gases. In particular, we discuss the Bose-Einstein condensation for dipolar Bose gases and the BCS transition for dipolar Fermi gases. In both cases we stress the dominant role of the trap geometry in determining the properties of the system. We present also results concerning bosonic dipolar gases in optical lattices and the possibility of obtaining a variety of different quantum phases in such a case. Finally, we analyze various possible routes towards achieving ultracold dipolar gases.

Using an atom interferometer method, we measure the recoil velocity of a cesium atom due to the coherent scattering of a photon. This measurement is used to obtain a value of ℏ/M_Cs and the fine structure constant, α. The current fractional uncertainty is Δα/α = 7.4 × 10^-9.

This paper discusses the excitations in a condensed Bose system as manifestations of the dynamics of the phase. It is argued that the standard approach based on spontaneous symmetry breaking is not viable; a superselection rule enforces strict particle conservation. Some recent theoretical results are used to show how the significance of the phase dynamics can be retained without violating the superselection rule.

Two states of a flux qubit with three Josephson junctions were shown in a single measurement with a dc-SQUID. The qubit is an aluminum superconductor loop surrounded by a dc-SQUID for readout. It has two states, which have persistent currents flowing in opposite directions. The readout data for three samples with different junction sizes suggest that the probability distribution for the double-well potential depends on the ratio of E_J/E_C, where E_J is the Josephson energy and E_C is the charging energy. The probability distribution was estimated by calculating the wavefunctions and energy levels for the measured samples. We measured the retrapping current of a dc-SQUID without the qubit as a function of the magnetic field. It was found that the relative phase relation for the magnetic field dependence of the retrapping current jumped from 0 to π at E_J ≈ E_C. This jump can be explained phenomenologically by taking into account the two kinds of dissipation arising from ac currents flowing through the lead and along the SQUID loop. The fact that the jump occurred at E_J ≈ E_C strongly suggests that the quantum nature of the electromagnetic environment needs to be taken into account in order to understand the origin of the dissipation.

We predict a distinctive change of magnetic properties and considerable increase of the Curie temperature caused by the strain fields of grain boundaries in ferromagnetic films. It is shown that a sheet of spontaneous magnetization may arise along a grain boundary at temperatures greater than the bulk Curie temperature. The temperature dependence and space distribution of the magnetization in a ferromagnetic film with grain boundaries is calculated. We found that 45° grain boundaries can produce long-range strain fields that result in a magnetic sheet along the boundary of width 0.5 ÷ 1 μm at temperatures higher than the bulk Curie temperature of about 10² K.

The predominant d_x²-y²-wave pairing-symmetry of most high-T_c superconductors provides the opportunity to fabricate Josephson junction circuits in which part of the junctions are biased by a phase difference of the superconducting order parameter of π. To explore the road to such π-electronics, we have fabricated and studied all-high-T_c dc superconducting quantum interference devices (dc SQUIDs) realized with thin film technology, of which the Josephson junctions consist of one standard junction and one junction with a π-phase shift.

These π-SQUIDs provide clear evidence of the d_x²-y²-wave symmetry of the order parameter, the amount of complex admixtures of other symmetry components being undetectably small. This seems to contradict other experiments, the results of which have been presented as evidence for an s-wave order parameter or for complex admixtures. Possible solutions to resolve this apparent contradiction are presented. In particular it is pointed out that even in the bulk of a superconductor the order parameter symmetry (the admixture of various symmetry components) may be spatially dependent.

Two groups, in Orsay and in Paris, have recently obtained experimental evidence for Bose-Einstein condensation on He⁴ atoms in the metastable state 2³S₁. The condensates which have been obtained are the first ones where atoms are condensed, not in their electronic ground state, but in an excited state, in this case a metastable state about 20 eV above the ground state. In principle, Penning collisions should very rapidly destroy the cloud of cold metastable atoms and it seems hopeless to observe Bose-Einstein condensation in such a system. But, as suggested by Shlyapnikov et al, the conservation of the total spin during the collision reduces the Penning collision cross-sections by several orders of magnitude and this explains why large enough densities of metastable atoms can be obtained to observe the condensation. We briefly describe the first experimental results which have been obtained in Paris. Atoms are optically detected by optical imaging at 1083 nm (wavelength of the transition connecting the metastable state 2³S₁ to the triplet state 2³P₂). The evolution of the anisotropy of the images during a ballistic expansion gives clear evidence for the condensation. Orders of magnitude are also obtained for the scattering length describing the collision between 2 metastable atoms. The large value of this scattering length (of the order of 10 nm) allows one to reach the so called hydrodynamic regime where the mean free path between 2 collisions in the thermal cloud becomes smaller than the size of the cloud. Preliminary results showing the transition between the collisionless regime and the hydrodynamic regime are presented and compared to theoretical predictions.

In the early days of superconductivity, Ivar Giaver discovered that it was possible to make a novel DC transformer by using one superconductor to drag vortices through another. An analogous effect was predicted to exist in quantum Hall bilayers and has recently been discovered experimentally by Eisenstein's group at Caltech. Similarly, new experiments from the Caltech group have demonstrated the existence of a Josephson-like 'supercurrent' branch for electrons coherently tunnelling between the two layers.

Impurity-Helium solids are highly porous van der Waals solids made up of impurity atoms, molecules, or clusters of atoms and molecules surrounded by thin layers of solid helium. The results of structural investigations via ultrasound and x-ray diffraction are reported. Preliminary nuclear magnetic resonance measurements on D₂ impurities in these solids are discussed. Recent electron paramagnetic resonance experiments have explored exchange tunneling reactions in the Impurity-Helium solids. In particular, when D atoms are introduced into an Impurity-Helium solid containing H₂, the concentration of H atoms is observed to increase, possibly as a result of the reactions D + H₂ → H + HD and D + HD → H + D₂.

We review recent experiments in which Rydberg atoms interacting with microwave photons in a superconducting cavity are used to perform quantum information manipulations. We describe quantum phase gates using atoms and photons as "qubits", various engineered entanglement experiments involving up to three particles at a time and ideal non-destructive measurements of single photons. We also analyse an atomic interferometry experiment which illustrates the link between the notions of complementarity and entanglement. We finally recall previous experiments performed with the same set-up, in which we had generated and studied quantum superpositions of coherent fields with different phases, the so called "Schrödinger cat states" of the field. The decoherence of these states was experimentally studied. We conclude by discussing some of the perspectives opened by this line of research.

We present a comprehensive and self-consistent theory of relative-phase measurements and the associated Hermitian relative-phase operator of two harmonic oscillators. We find that since Nature does not favor any particular initial condition of the two oscillators, the relative-phase operator is not unique. We show that the relative-phase eigenstates are maximally entangled. Therefore, most relative-phase operators lack a classical correspondence, even in the high-excitation limit. Furthermore, we find that the relative phase and the excitation number difference are noncommuting, noncanonical observables and we derive a commutation relation.

Motivated by recent experiments with Josephson-junction circuits we reconsider decoherence effects in quantum two-level systems (TLS). On one hand, the experiments demonstrate the importance of 1/f noise, on the other hand, by operating at symmetry points one can suppress noise effects in linear order. We, therefore, analyze noise sources with a variety of power spectra, with linear or quadratic coupling, which are longitudinal or transverse relative to the eigenbasis of the unperturbed Hamiltonian. To evaluate the dephasing time for transverse 1/f noise second-order contributions have to be taken into account. Manipulations of the quantum state of the TLS define characteristic time scales. We discuss the consequences for relaxation and dephasing processes.

We have investigated coherent properties of an artificial two-level system realized in a small-Josephson-junction circuit. Two charge-number states of a small superconducting electrode connected to a reservoir via a Josephson junction were used as the two relevant states. Coherent manipulations of the charge-number states by applying a gate-voltage pulse were demonstrated, and decoherence of the system was studied through a spin-echo-type experiment. The result suggested that low-frequency energy-level fluctuations due to 1/f background charge noise is a dominant source of the dephasing.

We have designed and operated a novel superconducting tunnel junction circuit which behaves as a controllable atom, with a ground and first excited state forming an effective spin 1/2. These two states are the symmetric and antisymmetric combinations of two charge configurations of a Cooper pair box. Any spin orientation corresponding to an arbitrary superposition of these two states can be prepared by applying NMR-like microwave pulses to the gate of the box. The spin state is readout by measuring the voltage response to a probe current pulse applied to the bridge formed by the two junctions of the box and an additional large, shunting junction. In a sample whose transition period is 60 ps, coherent superpositions decay with a 0.5 μs time constant, as measured by a Ramsey fringes experiment. This result is a step towards the realization of a solid-state quantum information processor.

We describe fabrication and measurements of Single Electron Transistors operated in the Radio Frequency mode (RF-SET). We demonstrate very high sensitivity for RF-SETs and we evaluate the back-action from an RF-SET, when used as a read-out device for charge qubits. We conclude that single-shot read-out is possible with a signal to noise ratio greater than one, and that niobium qubits would substantially improve the signal to noise ratio. Furthermore we describe how the RF-SET could be used to read out a differential qubit in a gradiometer coupling.

The INSQUID (INductive Superconducting QUantum Interference Device) can measure the flux state of a superconducting qubit rapidly, while allowing the quantum state of the qubit to evolve with low levels of back action. The INSQUID consists of a dc SQUID with unshunted junctions connected in parallel with a superconducting inductor; the qubit is placed inside the SQUID loop. The inductor is coupled to a readout dc SQUID with resistively-shunted junctions. By applying appropriate fluxes to the input SQUID and the inductor, the INSQUID can be turned "off", so that virtually no flux noise is coupled from the readout SQUID to the qubit. Different flux biases turn the INSQUID "on", enabling the readout SQUID to measure the flux state of the qubit. The INSQUID can also be used to turn on and off the coupling between two or more qubits.

In this paper initial experiments towards constructing simple quantum gates in a solid state material are presented. Instead of using specially tailored materials, the aim is to select a subset of randomly distributed ions in the material, which have the interaction necessary to control each other and therefore can be used to do quantum logic operations. The experimental results demonstrate that part of an inhomogeneously broadened absorption line can be selected as a qubit and that a subset of ions in the material can control the resonance frequency of other ions. This opens the way for the construction of quantum gates in rare-earth-ion doped crystals.

Coherence, condensation, and phase transitions are central concepts in physics. Several of the recent Nobel Prizes in Physics have been given to pioneers of these fields. Systems can condense to condensates where particles act coherently, that is in exactly the same way. Photons in a laser is a well known example. Another example is the recent experimental realization of a Bose Einstein condensate (BEC) in dilute gases where the wave functions of atoms overlap and form a coherent state at low temperature, where all condensed atoms move together. BEC's are similar to superfluid and superconducting systems. Related phenomena occur in these condensates. For example, vortices of different kinds appear under rotation in BEC and superfluid ³He and ⁴He and correspond to quantized fluxons in superconductors under magnetic fields. Macroscopic quantum phenomena, another token of coherence, are typical of superconductors and occur also in the superfluids, including BEC. Coherence is of utmost importance in so called quantum computers, a new concept based upon the probability of a two state system to be in one or the other of the states and where a number of operations have to be performed within a decoherence time.

A Nobel Symposium provides an excellent opportunity to bring together a group of outstanding scientists for a stimulating exchange of ideas and results. The Nobel symposia are small meetings and participation is by invitation only, typically 20-40 participants. In 2001, the Nobel Foundation celebrated the 100th anniversary of the first Nobel Prize and all previous Nobel laureates were invited to attend the Nobel ceremonies in Stockholm. This gave an excellent opportunity for arranging jubilee symposia with topics that would attract several of the laureates. Our chosen subject of Condensation and Coherence in Condensed System (CoCoCo) attracted sixteen Nobel laureates and another thirty-five leading scientists who met in Göteborg during four days before leaving for the festivities in Stockholm. The program had to be concentrated to certain aspects and we apologize to all prominent scientists in the field that could not be invited due to space limits.

Our idea was to bring scientists together from several related sub-disciplines: atomic physics, quantum optics, condensed matter physics, for cross breeding of ideas, concepts and experience. Subject like phase transitions in strongly coupled systems, Bose-Einstein condensation in weakly coupled systems, macroscopic quantum phenomena, coherence in mesoscopic structures, and quantum information were intensively discussed from different points of view. Coherence phenomena in condensed systems were emphasized. A special session was devoted to the emerging field of quantum computing with experimental and theoretical results reported for different types of qu-bits. The 2001 Nobel Prize to Eric Cornell, Wolfgang Ketterle, and Carl Wieman, "for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates" gave an extra flavor to the theme of the Centennial Symposium.

The Symposium was sponsored by the Nobel Foundation through its Nobel Symposium Committee. Lectures were given at Ågrenska Villan, a former merchant mansion that was donated to the Göteborg University, at the Microtechnology Center of Chalmers, and at Universeum, the new science center in Göteborg. Several of the sessions were open to invited scientists or to a broader audience, which could enjoy reviews of central topics. High school students and His Majesty the King of Sweden had the possibility to meet and interview many of the laureates during the visit at Universeum. Receptions were sponsored by the City of Göteborg and Chalmers University of Technology and gave participants opportunities to meet local scientists, students, and industrialists as well as to enjoy music and a guided tour of arts. The symposium was organized by Sune Svanberg, Mats Jonson, and Tord Claeson. Valuable hints were given by Anders Bárány, the secretary of the Nobel Committee of Physics. Many of the participants gave valuable comments regarding the planning of the CoCoCo symposium. Special thanks are due to our "sounding board": Anthony Leggett, Hans Mooij, Doung Osheroff, Bill Phillips, and Stig Stenholm. Per Delsing had the responsibility of editing the Proceedings. Our secretary, Ann-Marie Frykestig, and technician, Staffan Pehrson, did outstanding jobs organizing practical matters. Several of the members of our local university community helped with odds and ends. Mariana Ravneva ivanova and Madeline Claeson directed an appreciated companions program.

The Proceedings contain most of the material presented at the Symposium. A few contributions that summarized results published elsewhere are exempted. We hope that these Proceedings will convey to the reader some of the excitement felt by the participants during the Symposium. We also want to express our thanks to sponsors and contributors to the successful scientific event.