Quantum dots are structures engineered to have desirable quantum-mechanical properties. Much of their potential usefulness stems from the ability to design such structures so that their passive properties can be exploited. However, there are many plans to use dots as the basis of a more active quantum engineering, in which the detailed quantum states of the dot's components are manipulated by externally imposed fields. This leads to a new requirement: our ability to model the time development of individual driven quantum systems. I shall discuss some of the problems which arise when single systems, rather than ensembles, are considered and give examples which illustrate the effects of classical and quantum incoherences. I propose a new classification of incoherent processes, based on their effect on individual wave functions.
Quantum dots are structures engineered to have desirable quantum-mechanical properties. Much of their potential usefulness stems from the ability to design such structures so that their passive properties can be exploited. However, there are many plans to use dots as the basis of a more active quantum engineering, in which the detailed quantum states of the dot's components are manipulated by externally imposed fields. This leads to a new requirement: our ability to model the time development of individual driven quantum systems. I shall discuss some of the problems which arise when single systems, rather than ensembles, are considered and give examples which illustrate the effects of classical and quantum incoherences. I propose a new classification of incoherent processes, based on their effect on individual wave functions.
T hink about coherent systems, and odds are that the first example to cross your mind will be a laser: a device that emits monochromatic light homogenized so that the photons propagate with their phase in lockstep. The well-defined wavefront of the laser beam makes it possible to focus the light to spot sizes on the order of the wavelength of the light without the aberrations usually observed with the random wavefront of incoherent light. The well-defined phase also provides a medium capable of storing and carrying information more efficiently than the intensity-modulated signals typical of incoherent sources. These useful properties of coherence have made lasers almost ubiquitous in science and technology, and that “almost” is shrinking by the day.
In general, coherence comes about when individual components of a system act in unison, either in phase or with a fixed phase difference between the components. More accurately, the system can be described as a local oscillator whose wavefunction contains phase and amplitude terms that define how the system evolves in space and time. The collection of articles in this special issue describes the recent progress and developments of coherence in optical, atomic, and semiconductor systems, and how manipulating that coherence may lead to useful applications and to experimental systems for studying the elements of quantum mechanics.
Since the first demonstration of the laser in 1960, progress in improving the extent of the spatial and temporal coherence of laser light has been steady. Psaltis (p. [1359][1]) reviews developments in optical coherence and highlights examples of the key role coherence has played in applications in imaging, communication, and information processing and storage. Just as lasers revolutionized the field of optics, many researchers have high expectations that other coherent systems will provide similar advances in their respective fields. Exploiting the fundamental tenet of quantum mechanics whereby particles have the properties of waves, Kasevich (p. [1363][2]) reviews coherence effects in collections of cold atoms and describes how the shorter wavelengths associated with atoms and the recent accessibility of bright coherent atom sources may lead to precision measurements beyond anything currently available to the optical regime. For integration and potential applications, the ideal system would be based in semiconductors. Snoke (p. [1368][3]) describes recent work toward the formation of coherent semiconductor systems.
With coherence in the atomic and optical systems generally comprising macroscopic systems, Mabuchi and Doherty (p. [1372][4]) look at coherence effects at the quantum limit, probing the interactions between single atoms and single photons confined to high-quality cavities. In addition to providing invaluable information on the limits of quantum mechanics, such effects might also shed new light on information science in the quantum regime.
The section opens with a pair of News features by staff writers Charles Seife and Robert Service. Seife presents a smattering of common applications that scientists and engineers have found for coherent waves, whether in light, sound, or subatomic particles. Service describes efforts to create new coherent sources of the type of radiation known as “hard” x-rays—a long-sought range of high frequencies with enormous potential for scientific research, technology, and medicine.
[1]: /lookup/doi/10.1126/science.1078823
[2]: /lookup/doi/10.1126/science.1079430
[3]: /lookup/doi/10.1126/science.1078082
[4]: /lookup/doi/10.1126/science.1078446
Coupled quantum dots are an example of the ubiquitous quantum double potential well. In a typical transport experiment, each quantum dot is also coupled to a continuum of states. Our approach takes this into account by using a Green’s function formalism to solve the full system. The time-dependent solution is then explored in different limiting cases. In general, a combination of coherent and incoherent behavior is observed. In the case that the coupling of each dot to the macroscopic world is equal, however, the time evolution is purely coherent. The double-well potential is one of the simplest and best understood problems in modern quantum mechanics. Its utility is likewise unparalleled. Potential applications of double-well devices have been noted in Refs. [1-5]. For such devices to be useful, an understanding of the processes which couple the microscopic device to the macroscopic environment is paramount. That is to say, the decoherence processes of such systems must be well understood. To this end, we consider a simple exactly solvable model of two coupled quantum dots. An excellent review of related systems and some approximate solutions are given in Ref. [6]. Each dot is coupled to an environment (a triple-barrier system) as in Fig. 1. The environment consists of a continuum of states, as would be appropriate for a macroscopic lead. Only one state in each quantum dot is considered, which amounts to the assumption that the tunneling parameters connecting our two states to any neglected state are much less than the energy differences with that state. The Hamiltonian of the system can be written as the sum of two terms, H = H0 + Hc. The first term, H0, represents the dynamics of the simple two-state system, H0 = ε1d † 1d1 + ε2d † 2 d2 + V (d† 1d2 + d†
Theory and experiment have not fully resolved the apparent dichotomy , which has agonized physics for the past eighty years: on the one hand, the description of microsystems by quantum mechanics and, on the other, the description of macrosystems by classical dynamics or statistical mechanics. Derivations of the time-irreversible Liouville equation for an open quantum system, based on projecting out its environment, have narrowed the gap between the quantum and classical descriptions. Yet our `classical' intuition continues to be confronted by quantum-mechanical results like the Einstein--Podolsky--Rosen paradox that challenges the classical notion of locality, or the quantum Zeno effect which suggests that the isolation of a system is not the only way to preserve its quantum state. There are two key concepts in any discussion of such issues. The first, which is responsible for the most salient nonclassical properties, is entanglement , that is partial or complete correlation or, more generally, inseparability of the elements comprising a quantum ensemble . Even after their interaction has ceased, this inseparability, originating from their past interaction, can affect the state of one element when another element is subject to a nonunitary action, such as its measurement, tracing- out, or thermalization. The second key concept is decoherence of open quantum systems, which is the consequence of their entanglement with their environment, a `meter' or a thermal `reservoir', followed by the tracing-out of the latter. Despite new insights into entanglement and decoherence, there are still no complete, unequivocal answers to the fundamental questions of the transition from quantal to classical behaviour: how do irreversibility and classicality emerge from unitarity as systems and their environments become increasingly complex ? At what stage does system--meter entanglement give rise to a classical readout of the meter? Is there an upper limit on the size or complexity of systems displaying entanglement? Major developments have opened new vistas into controlled entanglement , which is the resource of quantum information processing. However, these developments have mainly focused on ensembles of simple two- and three-level systems that are thoroughly isolated from their environments. Treatments of coherence in quantum computing have mostly assumed that only a single or a few the elements of the quantum ensemble may simultaneously undergo an uncontrolled intervention---a quantum error. Decoherence-control protocols for more general types of errors are still incomplete. In order to resolve the outstanding issues of the quantum--classical transition, and study the control of entanglement and decoherence without the foregoing restrictions, we must venture into the domain of Quantum Complex Systems (QUACS), either consisting of a large number of inseparable elements or having many coupled degrees of freedom. Our conviction is that fundamental understanding and manipulation of entanglement within QUACS or their entanglement with the environment or a meter, call for the creation of a new conceptual framework or paradigm, that would encompass phenomena common to cold atoms in laser fields, large molecules, Josephson junctions, quantum gases and solids, with the view of employing these systems for quantum information processing and computing. Progress within this paradigm should allow us to answer the questions: does entanglement play an essential role in the evolution of large collections of complex systems? What are the size and complexity limits of systems and ensembles still controllable by an external intervention? What are the most appropriate decoherence protection schemes and control algorithms? This special issue addresses the challenge of understanding in depth and manipulating the basic quantum properties of optical, atomic, molecular and condensed-matter QUACS, and large ensembles thereof. In view of the interdisciplinary character of this issue, we find it expedient to look at the presented articles not only according to the physical objects they describe, but also from a unifying standpoint. Several unifying themes may be discerned: memory effects in dephasing and relaxation; protection of quantum information by its distribution throughout the ensemble; control of decoherence and entanglement by time-dependent interventions or measurements; manifestations of entanglement in scattering off statistical ensembles; measurment-induced dynamics. The concerted discussion of the topics outlined above should help us advance the new paradigm that addresses our abilities to diagnose and manipulate the entangled states of complex quantum objects and their robustness against decoherence. These abilities are required for quantum information (QI) applications in matter--wave interferometry in molecular, semiconducting or superconducting systems. On the fundamental level, this book may help establish the notion of dynamical information exchange between quantum systems and chart in detail the route from unitarity to classicality. Further developments within the outlined paradigm should yield novel, advantageous QI processing schemes and high-sensitivity interferometers, owing to decoherence suppression and effective control of many degrees of freedom. In the long run, these strategies may prove to be the first step towards the (hitherto unattempted) use of entanglement in nanotechnology, metrology and chemistry, with potentially remarkable novel applications.
Quantum reservoir engineering leverages dissipative processes to achieve desired behaviour, with applications ranging from entanglement generation to quantum error correction. Therein, a structured environment acts as an entropy sink for the system and no time-dependent control over the system is required. We develop a theoretical framework for active reservoir engineering, where time-dependent control over a quantum system is used to manipulate its environment. In this case, the system may act as an entropy sink for the environment. Our framework captures the dynamical interplay between system and environment, and provides an intuitive picture of how finite-size effects and system-environment correlations allow for manipulating the environment by repeated initialisation of the quantum system. We illustrate our results with two examples: a superconducting qubit coupled to an environment of two-level systems and a semiconducting quantum dot coupled to nuclear spins. In both scenarios, we find qualitative agreement with previous experimental results, illustrating how active control can unlock new functionalities in open quantum systems.
Coherence is a familiar concept in physics. It is the driving force behind wavelike phenomena such as the diffraction of light. Moreover, wave-particle duality implies that all quantum objects can exhibit coherence, and this quantum coherence is crucial to understanding the behaviour of a plethora of systems. In this paper, which is written at an undergraduate level, we shall briefly introduce what is meant by coherence in a well-known classical setting, before going on to describe its quantum version. We will show that coherence is important in describing the properties of solid-state nanosystems and especially quantum dots. Simple experiments that reveal the coherent nature of matter-and how this leads to some very powerful applications-will be described. Finally, we shall discuss the fragility of coherence and shall introduce a method for describing decoherence in open quantum systems.
Since information has been regarded as a physical entity, the field of quantum information theory has blossomed. This brings novel applications, such as quantum computation. This field has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineering, to the physical sciences. Thus, we now have an interdisciplinary field where great efforts are being made in order to build devices that should allow for the processing of information at a quantum level, and also in the understanding of the complex structure of some physical processes at a more basic level. This thesis is devoted to the theoretical study of structures at the nanometer-scale, "nanostructures," through physical processes that mainly involve the solid-state and quantum optics, in order to propose reliable schemes for the processing of quantum information. Initially, the main results of quantum information theory and quantum computation are briefly reviewed. Next, the state-of-the-art of quantum dots technology is described. In so doing, the theoretical background and the practicalities required for this thesis are introduced. A discussion of the current quantum hardware used for quantum information processing is given. In particular, the solid-state proposals to date are emphasised. A detailed prescription is given, using an optically-driven coupled quantum dot system, to reliably prepare and manipulate exciton maximally entangled Bell and Greenberger-Horne-Zeilinger (GHZ) states. Manipulation of the strength and duration of selective light-pulses needed for producing these highly entangled states provides us with crucial elements for the processing of solid-state based quantum information. The all-optical generation of states of the so-called Bell basis for a system of two quantum dots (QDs) is exploited for performing the quantum teleportation of the excitonic state of a dot in an array of three coupled QDs. Theoretical predictions suggest that several hundred single quantum bit rotations and controlled-NOT gates could be performed before decoherence of the excitonic states takes place. In addition, the exciton coherent dynamics of a coupled QD system confined within a semiconductor single mode microcavity is reported. It is shown that this system enables the control of exciton entanglement by varying the coupling strength between the optically-driven dot system and the microcavity. The exciton entanglement shows collapses and revivals for suitable amplitudes of the incident radiation field and dot-cavity coupling strengths. The results given here could offer a new approach for the control of decoherence mechanisms arising from entangled "artificial molecules." In addition to these ultrafast coherent optical control proposals, an approach for reliable implementation of quantum logic gates and long decoherence times in a QD system based on nuclear magnetic resonance (NMR) is given, where the nuclear resonance is controlled by the ground state "magic number" transitions of few-electron QDs in an external magnetic field. The dynamical evolution of quantum registers of arbitrary length in the presence of environmentally-induced decoherence effects is studied in detail. The cases of quantum bits (qubits) coupling individually to different environments ("independent decoherence"), and qubits interacting collectively with the same reservoir ("collective decoherence") are analysed in order to find explicit decoherence functions for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: this sensitivity is a characteristic of both types of coupling (collective and independent) and not only of the collective coupling, as has been reported previously. A non-trivial behaviour - "recoherence" - is found in the decay of the off-diagonal elements of the reduced density matrix in the specific situation of independent decoherence. The results lead to the identification of decoherence-free states in the collective decoherence limit. These states belong to subspaces of the system's Hilbert space that do not become entangled with the environment, making them ideal elements for the engineering of "noiseless" quantum codes. The relations between decoherence of the quantum register and computational complexity based on the new dynamical results obtained for the register density matrix are also discussed. This thesis concludes by summarising and pointing out future directions, and in particular, by discussing some biological resonant energy transfer processes that may be useful for the processing of information at a quantum level.