Macroscopic Coherence Research Articles

Signatures for Generalized Macroscopic Superpositions

We develop criteria sufficient to enable detection of macroscopic coherence where there are not just two macroscopically distinct outcomes for a pointer measurement, but rather a spread of outcomes over a macroscopic range. The criteria provide a means to distinguish a macroscopic quantum description from a microscopic one based on mixtures of microscopic superpositions of pointer-measurement eigenstates. The criteria are applied to Gaussian-squeezed and spin-entangled states.

The interface between quantum mechanics and general relativity

The generation, as well as the detection, of gravitational radiation by means of charged superfluids is considered. One example of such a “charged superfluid” consists of a pair of Planck-mass-scale, ultracold “Millikan oil drops”, each with a single electron on its surface in a strong magnetic field, in which the oil of the drop is replaced by superfluid helium. When levitated in a magnetic trap, and subjected to microwave-frequency electromagnetic radiation, a pair of such “Millikan oil drops” separated by a microwave wavelength can become an efficient quantum transducer between quadrupolar electromagnetic and gravitational radiation. This leads to the possibility of a Hertz-like experiment, in which the source of microwave-frequency gravitational radiation consists of one pair of “Millikan oil drops” driven by microwaves, and the receiver of such radiation consists of another pair of “Millikan oil drops” in the far field driven by the gravitational radiation generated by the first pair. The second pair then back-converts the gravitational radiation into detectable microwaves. The enormous enhancement of the conversion efficiency for these quantum transducers over that for electrons arises from the fact that there exists macroscopic quantum phase coherence in these charged superfluid systems.

Macroscopic coherence of a single exciton state in an organic quantum wire

Macroscopic quantum coherence has been observed in some many-body systems including superconductors, quantum liquids1 and cold atom condensates2, but never for a single quasi-particle state. In an ideal semiconductor, excitons (electron–hole pairs bound by the Coulomb interaction) can, in principle, exist as delocalized plane waves extending over the entire volume. However, any kind of disorder prevents long-range spatial coherence from emerging. There has been evidence for the formation of macroscopic coherent states only in condensate phases such as in the case of microcavity polaritons condensation3,4 or in a dense quasi-two-dimensional exciton gas5. It is unclear however, whether in this latter case the observations are really related to macroscopic coherence6. Here, we show that a single exciton state in an individual ordered conjugated polymer chain7,8, shows macroscopic quantum spatial coherence reaching tens of micrometres, limited by the chain length. The spatial coherence of the k=0 exciton state is demonstrated by selecting two spatially separated emitting regions of the chain and observing their interference.

Macroscopic phase coherence of defective vortex lattices in two dimensions

The superfluid density is calculated theoretically for incompressible vortex lattices in two dimensions that have isolated dislocations quenched in by a random arrangement of pinned vortices. The latter are assumed to be sparse and to be fixed to material defects. It is shown that the pinned vortices act to confine a single dislocation of the vortex lattice along its glide plane. Plastic creep of the two-dimensional vortex lattice is thereby impeded, and macroscopic phase coherence results at low temperature in the limit of a dilute concentration of quenched-in dislocations.

Macroscopic coherence effects in a mesoscopic system: Weak localization of thin silver films

We present an advanced undergraduate experiment on weak localization in thin silver films with a thickness between 60–200 Å, a mesoscopic length scale. At low temperatures, the inelastic dephasing length for electrons exceeds the film thickness, and the film becomes quasi-two-dimensional. In this limit, theory predicts corrections to the Drude conductivity due to the coherent interference between the wave functions of the conducting electrons, a macroscopically observable effect known as weak localization. This correction can be destroyed by the application of a magnetic field, and the resulting magnetoresistance curve provides information about electron transport in the film.

Excitonic condensation in quasi-two-dimensional systems

We present a low energy model for the Bose–Einstein condensation in a quasi-two-dimensional excitonic gas. Using the flow equations of the renormalization group and a Φ 4 model with the dynamical critical exponent z = 2 we calculate the temperature dependence of the critical density, coherence length, magnetic susceptibility, and specific heat. The model can be relevant for the macroscopic coherence observed in GaAs/AlGaAs coupled quantum wells.

A growth pathway for highly ordered quantum dot arrays

To realize the desired zero-dimensional behavior of a quantum dot ensemble, the ability to fabricate quantum dots with a high packing density and a high degree of size, shape, and spacing uniformity is crucial. Here we report highly ordered InAs nanodot arrays grown by molecular-beam epitaxy on nonlithographically nanopatterned GaAs. Approximately 20 billion dots are grown in a 1cm2 area with the smallest size dispersion ever reported and forming a lateral superlattice in hexagonal dense packing form. These techniques presage a pathway to controlled growth of periodic quantum dot superstructures, which offer macroscopic spatial coherence in the interaction of quantum dots with radiation.

Topology-induced confined superfluidity in inhomogeneous arrays

We report a study of the zero-temperature phase diagram of the Bose-Hubbard model on topologically inhomogeneous arrays. We show that the usual Mott-insulator and superfluid domains, in the paradigmatic case of the comb lattice, are separated by regions where the superfluid behavior of the bosonic system is confined along the comb backbone. The existence of such confined superfluidity, arising from topological inhomogeneity, is proved by different analytical and numerical techniques which we extend to the case of inhomogeneous arrays. We also discuss the relevance of our results to real systems exhibiting macroscopic phase coherence, such as coupled Bose condensates and Josephson arrays.

?Pseudogap? State of Novel Superconductors: Energy Scales and Structural and Diamagnetic Transitions

High Tc cuprates are characterized by three characteristic energy scales: Tc, T*c, and T*. The lowest scale, Tc, corresponds to the usual transition to the dissipationless state (R=0) with a macroscopic phase coherence. The higher energy scale, T*c, describes the diamagnetic transition. The region T*c>T>Tc is characterized by the presence of superconducting regions embedded in a normal metallic matrix. The highest energy scale (T*) corresponds to the formation of the structure, phase separation, and to the opening of the CDW gap.

Probing decoherence with electromagnetically induced transparency in superconductive quantum circuits.

Superconductive quantum circuits comprise quantized energy levels that may be coupled via microwave electromagnetic fields. Described in this way, one may draw a close analogy to atoms with internal (electronic) levels coupled by laser light fields. In this Letter, we present a superconductive analog to electromagnetically induced transparency that utilizes superconductive quantum circuit designs of present day experimental consideration. We discuss how a superconductive analog to electromagnetically induced transparency can be used to establish macroscopic coherence in such systems and, thereby, be utilized as a sensitive probe of decoherence.

Coherence window in the dynamics of quantum nanomagnets

Decoherence in many solid-state systems is anomalously high, frustrating efforts to make solid-state qubits. We show that in nanomagnetic insulators in large transverse fields, there can be a fairly narrow field region in which both phonon and nuclear spin-mediated decoherence are drastically reduced. As examples we calculate decoherence rates for the $Fe$-8 nanomolecule, for $Ni$ particles, and for $Ho$ ions in $LiHo_xY_{1-z}F_4$. The reduction in the decoherence, compared to low field rates, can exceed 6 orders of magnitude. The results also give limitations on the observability of macroscopic coherence effects in magnetic systems.

Exciton–polariton lasing in a microcavity

The formation of macroscopic coherence associated with a Bose–Einstein phase transition in excitons has long been sought for. We review our recent observation of related effects of exciton–polariton lasing in a semiconductor microcavity.

Papers presented at the 7th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors (NOEKS 7)

AbstractThe 7th International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors (NOEKS 7) was held at Uni‐versit�t Karlsruhe from 24‐28 February 2003. Topics of NOEKS 7 were: Ultrafast dynamics (coherent effects, coherent control, quantum kinetics, THz‐experiments), photonic crystals (2D and 3D photonic band gap materials), quantum dot physics (quantum dots, quantum wires), spin effects (spin dephasing, spin transport), disorder‐related effects, organic semiconductors, semiconductor quantum optics (luminescence, photon statistics), device physics (quantum cascade lasers, superlattices, interband lasers), and Bose‐Einstein condensation of excitons.The cover picture is taken from Ref. [1] and shows the spatial pattern of the indirect exciton PL intensity in GaAs/AlGaAs coupled quantum wells. Around the laser excitation spot, it ex‐hibits an external ring structure with a periodic array of circular‐shaped structures which is due to the formation of an exciton gas with macroscopic coherence.The full proceedings of NOEKS 7, guest‐edited by Martin Wegener, are published in physica status solidi (c) 0, No. 5 (2003). Since 1988, all previous NOEKS proceedings have also appeared in physica status solidi.

Chaos and the quantum phase transition in the Dicke model

We investigate the quantum-chaotic properties of the Dicke Hamiltonian; a quantum-optical model that describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. This model exhibits a zero-temperature quantum phase transition in the N --> infinity limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite N, and by analyzing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase transition. Our considerations of the wave function indicate that this is connected with a delocalization of the system and the emergence of macroscopic coherence. We also derive a semiclassical Dicke model that exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.

A multiple beam interferometer for Bose‐Einstein condensates

AbstractWe condense 87Rb atoms in the combined potential of an optical standing wave superimposed on a harmonic magnetic trap. By releasing the atoms from the combined trap we realise a multiple beam atom interferometer. The measured atomic interferogram provides information about macroscopic coherence throughout the sample. The atomic distribution is characterised by interference peaks. The time evolution of the peaks, their relative population, as well as their radial size are in agreement with the predictions of theory. By a perturbation of the magnetic trap we induce an oscillating atomic current related to coherent tunnelling of the Bose‐Einstein condensates through the optical barriers. The frequency and amplitude of the oscillations are in agreement with a model based on the Josephson current‐phase relations.

The most general form of a coarse-grained position operator

An improvement with the correct transformation properties on the previously derived coarse-grained position operator is made. This most general form of the operator may be more useful for physical problems than the previous one. In fact, in addition to the discussions with respect to the microscopic and macroscopic limits, quantum coherence and decoherence in the macroscopic system can be discussed with this general form. It is pointed out that decoherence generally occurs in almost all the macroscopic systems and the realization of the macroscopic coherence is the extremely exceptional case.

From local to macroscopic coherence in systems with composite quasiparticles

Strongly interacting systems are characterized by heavily dressed entities with internal degrees of freedom, which, on a local level, can be described in terms of coherent quantum states. We examine the modification of these local coherent quantum states when such entities condense into a macroscopic coherent quantum state, such as superfluidity. As an example, we consider a system of electrons coupled to local lattice deformations. Significant changes in the phonon clouds surrounding the charge carriers occur when the system develops into a spatially phase-locked state. The question of localized self-trapped charge carriers (bipolarons) in the normal state becoming delocalized upon entering the superconducting phase is discussed in terms of squeezing of the local coherent phonon states. Suggestions for experimental verifications of these features associated with the lattice dynamics are made.

High-occupancy effects and stimulation phenomena in semiconductor microcavities

This paper describes recent work on high-occupancy effects in semiconductor microcavities, with emphasis on the variety of new physics and the potential for applications that has been demonstrated recently. It is shown that the ability to manipulate both exciton and photon properties, and how they interact together to form strongly coupled exciton-photon coupled modes, exciton polaritons, leads to a number of very interesting phenomena, which are either difficult or impossible to achieve in bulk semiconductors or quantum wells. The very low polariton density of states enables state occupancies greater than one to be easily achieved, and hence stimulation phenomena to be realized under conditions of resonant excitation. The particular form of the lower polariton dispersion curve in microcavities allows energy and momentum conserving polariton-polariton scattering under resonant excitation. Stimulated scattering of the bosonic quasi-particles occurs to the emitting state at the center of the Brillouin zone, and to a companion state at high wave vector. The stimulation phenomena lead to the formation of highly occupied states with macroscopic coherence in two specific regions of k space. The results are contrasted with phenomena that occur under conditions of nonresonant excitation. Prospects to achieve "polariton lasing" under nonresonant excitation, and high-gain, room-temperature ultrafast amplifiers and low-threshold optical parametric oscillator under resonant excitation conditions are discussed.

Nonequilibrium polariton dynamics in organic microcavities

Microcavities containing a J-aggregate forming organic dye were prepared in the strong-coupling regime. Changing the position of the neat organic films within the microcavity allows a tuning of the giant Rabi splitting observed. We set the Rabi splitting to 25 meV and study the thermal activation of the higher-energy polariton emission under excitation off resonance. This is found to exhibit an Arrhenius activation with an energy corresponding to the polariton branch splitting. A constant offset to the upper polariton is observed at low temperature. Microsecond gated spectroscopy reveals that thermalization of the system occurs on the time scale of milliseconds, which contrasts with the polariton lifetime in the range of picoseconds. Bulk sample heating cannot fully account for the slow polariton thermalization observed in steady-state experiments, suggesting that long-lived macroscopic polariton coherence influences the polariton relaxation.

Long-range transport in excitonic dark states in coupled quantum wells.

During the past ten years, coupled quantum wells have emerged as a promising system for experiments on Bose condensation of excitons, with numerous theoretical and experimental studies aimed at the demonstration of this effect. One of the issues driving these studies is the possibility of long-range coherent transport of excitons. Excitons in quantum wells typically diffuse only a few micrometres from the spot where they are generated by a laser pulse; their diffusion is limited by their lifetime (typically a few nanoseconds) and by scattering due to disorder in the well structure. Here we report photoluminescence measurements of InGaAs quantum wells and the observation of an effect by which luminescence from excitons appears hundreds of micrometres away from the laser excitation spot. This luminescence appears as a ring around the laser spot; almost none appears in the region between the laser spot and the ring. This implies that the excitons must travel in a dark state until they reach some critical distance, at which they collectively revert to luminescing states. It is unclear whether this effect is related to macroscopic coherence caused by Bose condensation of excitons.