QUANTUM INFORMATION
Quantum information processing requires storage, control, and manipulation of information in a quantum system very much like the classical information is processed by classical bits, 0 and 1. The essential difference between a classical bit and a quantum bit (qu-bit) is that a qubit has quantum coherence for a period of time, which allows it to remain in superposition states or entangled states. The use of the entangled states is precisely what gives the unprecedented level of parallelism, and hence, advantage over classical computation schemes. The central problem towards the realization of quantum information processing systems has been the loss of coherence or decoherence in the quantum system, due to its coupling to environmental degrees of freedom. The field of quantum information is in a nascent stage, and its further progress essentially depends on a proper understanding of quantum coherence, and its control.
Various aspects of our work are summarized below: (A) Role of decoherence in quantum information, (B) Picosecond measurements in time domain and quantum control of coherence, (C) Landau’s theory of Metals and Anderson’s theory of localization, (D) Mechanisms of decoherence
A. ROLE OF DECOHERENCE IN QUANTUM INFORMATION:
The biggest challenge in quantum information science is the experimental realization of a quantum two-level system or a quantum bit (qubit) that can stay quantum mechanical for a time long enough for a number of manipulations. The time over which the qubit remains quantum mechanical is its decoherence time. From a practical point of view, experimental investigation of decoherence is important to the success of quantum information science for the following three important reasons:
(i) Measurement and Manipulation Time: In solid-state electronic systems, the time scale is known to be on the order of nanoseconds. That puts a limit on the speed (~ gigahertz) at which all manipulations have to be performed, even in these prototypes of a single qubit. The combination of low temperature in the millikelvin range and high frequency in the GHz range adds to the challenge of nanofabrication, severely restricting the experimental effort. Any limitation to decoherence at low temperatures such as the saturation is thus important to the understanding of the mechanisms of deocherence of qubits.
(ii) Scalability: Even though it would be possible to control and manipulate a single quantum two-level system, scaling to many qubits for entanglement and information processing appears to be a daunting task, as the effect of decoherence grows exponentially with the number of qubits in most models of entanglement.
(iii) Error-Correction Limit: Specifically designed error-correction codes still require that the order of magnitude of the tolerable noise level be 1.0e-5 per qubit per gate. This estimate assumes that the errors — that is, decoherence and dissipation of the individual qubits — are uncorrelated. The required number of qubits for a quantum computer n therefore depends on two factors: (a) the maximum number of qubits required to outperform the classical computer, and (b) multiplicity of the qubits for error correction. These considerations lead to an optimal number of qubits in the range of 10^3 ~ 10^6. Without error correction the precision required is 1.0e-13. Another way of manifesting the same issue is to determine the quantum gate operation time. It has to be slow enough to allow for the adiabatic evolution, and yet it has to be fast enough to beat decoherence. The current error-correction limit requires that the ratio of gate operation time and decoherence time has to be smaller than 1.0e-3 ~1.0e-6.
Understanding decoherence is the first step toward the realization of reliable quantum logic devices, and it necessarily precedes the steps of characterization and control of decoherence of the qubits. Even though the design of the qubits can be very complicated, both the techniques and the understanding of decoherence in simpler systems such as metallic wires and dots could prove to be essential in controlling and manipulating a solid-state qubit.
B. PICOSECOND MEASUREMENTS IN TIME DOMAIN AND QUANTUM CONTROL OF COHERENCE
Nanotechnology is a field best described as a democratic amalgam of many branches of science and engineering, stretching from physics, chemistry, biology to aerospace, mechanical and computer engineering. With a scope as broad as this, it holds potential for the creation of practical quantum computers, synthesis of designer molecules atom by atom, sorting of proteins and DNAs – or quite simply, fixing atomic and molecular problems by atomic and molecular means: devices and objects that can be fabricated, controlled and manipulated on the molecular scale atom. Naturally, the atomic- and molecular-scale nanostructures have their own scales for time and frequency. The manipulation and control have to be done precisely in these characteristic frequency and time scales, should the exploration and exploitation of any new behavior be desired. Toward this end, techniques must be developed to enable measurement and control on the appropriate frequency and time scales. The characteristic time scales (dwell time, resonance time, relaxation time and coherence time) of typical nanostructures lie in the picosecond-nanosecond regime.
The behavior of nanometer-scale structures is dominated by quantum mechanics . Quantum mechanics manifests in these structures because the characteristic length scale for “the fundamental property” of quantum mechanics — that is, quantum coherence — is on the order of few nanometers to microns . Understanding of the behavior of structures smaller than this length scale will require real-time measurements that are done on the appropriate time scale of nanoseconds to picoseconds.
We are developing a time-domain measurement technique that will enable dynamic exploration of nanoscale structures in the picosecond range, the relevant timescale for quantum coherence and relaxation. Quantum mechanics dominates the behavior of nanoscale systems as the characteristic length for quantum coherence becomes comparable to the system size. Even more fundamental is the coherence time, which is typically on the order of nanoseconds.
Currently, we are performing time-domain measurements of interference effects: (i) Aharonov-Bohm oscillation, (ii) conductance fluctuation and (iii) weak localization, which have been studied by magnetic-field-based measurements for almost two decades. Our goal is to draw upon the advances and insights from a variety of fields to create a suite of alternative techniques and apply them to study dynamical aspects of quantum coherence with interference effects. The main motivation is the measurement of low temperature decoherence time without using magnetic-field-based techniques. Building upon our earlier work in this area carried over the last decade, we will attempt to experimentally address the current problem of treating decoherence and interference effects in a single theoretical framework. Another aspect of our work in time domain involves the development of schemes to control coherence in time domain with picosecond pulses.
C. LANDAU’S THEORY OF METALS AND ANDERSON’S THEORY OF LOCALIZATION
In condensed matter physics, metals are usually understood as Fermi liquids. In this picture, there is a unique many-body ground state at T=0 in which electrons occupy all levels up to the Fermi surface according to the exclusion statistics. Low-lying excitations from this ground state are understood in terms of quasi-particles with long lifetimes. These quasi-particles can be considered unbounded non-interacting particles with only a few effective parameters entering the various equilibrium physical quantities such as thermodynamic density of states, spin susceptibility and specific heat. These quantities are expressed in terms of their free-electron values and the Landau parameters. An effective Landau theory of the disordered interacting electron systems is obtained through modified Landau expressions in terms of new renormalization parameters of the effective interaction coupling. This formalism has been successful in explaining many observed physical properties.
The concept of localization of electrons in a random potential or Anderson localization, based on a single-electron picture, forms the microscopic foundation of disordered metals and insulators. In presence of finite disorder, the system is described in terms of an effective coupling identified with the inverse conductance. The conductivity or diffusion constant D is renormalized, and, in strong disorder, the system evolves towards an insulating state, becoming an Anderson insulator at T=0. Inclusion of electron-electron interaction completes and modifies Anderson localization in an apparently rich framework of renormalized perturbation theory.
Landau’s Fermi-liquid description starts from the unique many-body ground state at T=0. The inelastic scattering rate (~ dephasing rate, 1/tauphi) of the quasi-particles vanishes as T approaches 0 due to the lack of phase space for scattering. Quantum localization effects in low-dimensional disordered conductors, described by the scaling theory, rely additionally on a power-law dependence as T approaches 0. The power law divergence of 1/tauphi at T=0 has been confirmed by the perturbative calculation of 1/tauphi due to electron interaction. If the dephasing rate is finite at T=0, then there will be delocalization of the wave packet associated with the dephasing of the constitutive electron wave functions, precluding quantum localization. The experimental study of electron decoherence at low temperature, in particular, the low temperature saturation aspect is therefore extremely important to the fundamental theories of metals and insulators.
D. MECHANISMS OF DECOHERENCE
An electron has two distinct degrees of freedom, charge and spin. These two degrees of freedom define the electron wave function, its coherence as well as its decoherence. The charge degree of freedom contributes to decoherence due to its coupling to a randomly fluctuating electric field—-or rather, a fluctuating vector potential—-either intrinsic or extrinsic. Likewise, the spin degree of freedom contributes to decoherence by its coupling to a randomly fluctuating magnetic field along the interfering electron path. Inside a nominally-pure, metallic conductor, fluctuating magnetic fields could arise due to localized spins from the presumably-unavoidable magnetic impurities. Because the interaction between the electron spin and the magnetic impurity spin is very complex, understanding the electron decoherence time in the absence of magnetic impurities is a fundamentally important problem.
Given the conceptual and formal difficulties with the understanding of the intrinsic mechanism of electron-electron interaction, it is natural to search for other extrinsic mechanisms that might cause temperature independent decoherence at low temperatures. Despite extensive theoretical suggestions and associated experimental checks, the catalogue of possible extrinsic mechanisms continues to grow. The primary reason is that even with a single source of decoherence, such as magnetic impurity spins, it is possible to have many different mechanisms, which require different types of measurements to rule them out. Elsewhere, we have provided extensive checks for the effects of electron heating, high-frequency noise, two-level defects, and magnetic impurities, and we have found that the observed saturation in our samples is not due to any of these mechanisms. Recently, we reported the results of a different type of measurement performed at high fields, which rules out an entire class of mechanisms based on magnetic impurity spins.
In recent experiments, we have measured electron decoherence time in a series of pure gold wires, 18 nm thick and 30 nm wide. At fields up to 15 tesla, large enough to polarize any concentration of magnetic impurity spins, conductance fluctuation measurements show almost no temperature dependence of the decoherence time below 300 mK, both in the correlation field for interference and in the root-mean-square value of the fluctuations. Combined with previous low-field weak localization measurements on samples from similar material, our experiment suggests that the ubiquitous saturation of decoherence time in these samples is not due to any mechanism based on magnetic impurity spins.
Current time-domain and quantum information experiments are performed by Robert Badzey, Minghai Li, Duru Cuturela and P. Mohanty.
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SPINTRONICS
Electronics and information processing with spins promise to be anything but conventional. In spin-based electronics, information is injected, stored, transferred, or manipulated with the spin degree of freedom. The realization of its importance—-and the ensuing excitement—-stems from the fact that successful incorporation of spins into conventional semiconductor technology will allow to combine both information storage and information manipulation within a single platform. Recent discovery of a number of spin-based phenomena such as giant magnetoresistance has also marked the beginning of a new era with spintronics, and spin-based quantum information processing.
We are developing a spin-mechanical device to control and detect spin currents by nanomechanical torque. Our hybrid nano-electro-mechanical device, which contains a nanowire with a ferromagnetic-nonmagnetic interface, is designed to measure or induce spin polarized currents. Since spin carries angular momentum, a spin flip or spin transfer process involves a change in angular momentum—and hence, a torque—-which enables mechanical measurement of spin flips. Conversely, an applied torque results in spin polarization & spin current.
Spin transport and nanomechanics form the underlying basis of our spin-mechanical device, which is capable of detecting, controlling and creating both spin transport and spin population. The central concept of its function is rather simple: spin carries angular momentum and a change in the angular momentum due to spin transport creates a torque, which can be detected by a nanomechanical torsion oscillator. The experiments are performed in millikelvin temperatures in extremely sensitive environment.
Work done by Guiti Zolfagharkhani, Alexei Gaidarzhy, P. Mohanty (Boston) in collaboration with Stefan Kettemann (University of Hamburg), Peter Fulde (Max-Planck, Dresden), Claudio Chamon (Boston), and Chris Bauerle and Laurent Samindayar (Grenoble, France)