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AIP conference proceedings

Quantum 1/f effect in spin decoherence rates and quantum computing

Peter H. Handel

Published Jan 1, 2001• 1 citation
Publisher

Abstract

The quantum 1/f effect is a fundamental new aspect of quantum mechanics, quantum electrodynamics, and quantum field theory in general, with practical importance in most high-technology applications. It is based on the reaction of material currents to their spontaneous emission of infra-quanta such as photons, gravitons, transversal phonons, spin waves, etc. It is the result of decoherence of entangled states of particles and their spontaneous bremsstrahlung, a consequence of infrared-divergent interactions between particles and their field. It is the quantum manifestation of classical turbulence and it represents the most fundamental form of quantum chaos. It is described by the simple universal formula of conventional and coherent quantum 1/f noise, important in engineering, science and technology. It provides a new physical meaning to the notion of “constant current,” in time and space, similar to the 1937 definition of elastic processes by Bloch and Nordsieck. Finally, it is an interesting aspect of the concrete way in which matter generates its forms of existence, for instance time and space. Quantum 1/f spin decoherence rates, known to severely limit the performance of quantum computers, are shown here to be also affected by the quantum 1/f effect. Indeed, the elementary spin-flip process has a bremsstrahlung amplitude, leading to a non-stationary state with 1/f quantum fluctuations, and a disentangled system of non-localized low-frequency photons with negative conditional entropy. Thus, decoherence is due to the entangled system’s interaction with the rest of the world, as is its quantum 1/f fluctuation which can be expressed in qubits. Increasing the spin-excess n is one way to reduce these fluctuations. In general, we find that both decoherence and its quantum 1/f noise could be controlled by better insulating the system in a new way.

DOI
10.1063/1.1388686

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The quantum 1/f effect is a fundamental new aspect of quantum mechanics, quantum electrodynamics, and quantum field theory in general, with practical importance in most high-technology applications. It is based on the reaction of material currents to their spontaneous emission of infra-quanta such as photons, gravitons, transversal phonons, spin waves, etc. It is the result of decoherence of entangled states of particles and their spontaneous bremsstrahlung, a consequence of infrared-divergent interactions between particles and their field. It is the quantum manifestation of classical turbulence and it represents the most fundamental form of quantum chaos. It is described by the simple universal formula of conventional and coherent quantum 1/f noise, important in engineering, science and technology. It provides a new physical meaning to the notion of “constant current,” in time and space, similar to the 1937 definition of elastic processes by Bloch and Nordsieck. Finally, it is an interesting aspect of the concrete way in which matter generates its forms of existence, for instance time and space. Quantum 1/f spin decoherence rates, known to severely limit the performance of quantum computers, are shown here to be also affected by the quantum 1/f effect. Indeed, the elementary spin-flip process has a bremsstrahlung amplitude, leading to a non-stationary state with 1/f quantum fluctuations, and a disentangled system of non-localized low-frequency photons with negative conditional entropy. Thus, decoherence is due to the entangled system’s interaction with the rest of the world, as is its quantum 1/f fluctuation which can be expressed in qubits. Increasing the spin-excess n is one way to reduce these fluctuations. In general, we find that both decoherence and its quantum 1/f noise could be controlled by better insulating the system in a new way.
The conventional Quantum 1/f (Q1/f) Effect is present in any scattering cross section or process rate involving charged particles or current carriers. The present paper shows how bremsstrahlung and decoherence at all frequencies yield macroscopic quantum interference, resulting in probability density fluctuations at all frequencies in the outgoing scattered beam, that are observed as fundamental base-band 1/f noise and as 1/f frequency fluctuations, or phase noise close to carrier, in materials, devices, and resonant or non-resonant systems. We emphasize the role of the phenomenon of quantum decoherence showing that the fundamental, universal 1/f noise is both a phenomenon of decoherence and of the infrared divergence of quantum electrodynamics. This eliminates the last persisting misunderstandings of the Q1/f Theory and of this new field of Infra-quantum Physics. On this basis we give the first universal engineering formulas, applicable for the ultra-low noise optimization of all Hi-Tech applications, of the materials, devices and systems of modern industry, microelectronics, nanotechnology, highest stability resonators, oscillators and clocks, MEMS, and any resonant and non-resonant sensors. Q1/f noise, i.e, the coherent and conventional Q1/f Effects, is a new fundamental aspect of quantum physics, as basic as space and time. In resonators and oscillators, fundamental frequency fluctuations come usually from 1/f fluctuations in the dissipation.
Most sensors traduce various environmental, industrial, or laboratory parameters into electrical signals. Quantum sensing pushes this to the ultimate limit of achievable sensitivity, detectivity, resolution, and stability. Quantum mechanics sets these limits through the uncertainty principle. It causes the ubiquitous 1/f noise, as we show here for LiNbO3. Quantum 1/f theory, known as the quantum theory of the fundamental 1/f noise phenomenon, is a new aspect of quantum mechanics, that governs the nonlinear interaction of particle and field, introducing the new notions of "physical cross sections" (PCS) and "physical process rates" (PPR). These contain the fundamental macroscopic quantum 1/f fluctuations. They yield the usually defined PCS and PPR with infrared radiative corrections, when the expectation value is taken over the low-frequency photon states of negative entropy. The physical charged particle, such as an electron, contains both the bare particle and its electromagnetic field. The latter is in a coherent state, where the phase of the electromagnetic field oscillators is determined. Heisenberg’s uncertainty principle then requires that the energy must be uncertain, leading to nonstationary states describing the particle. The particle’s resulting fractional current fluctuations in large devices always have the spectrum 2α/πf, where α=1/137 is the fine structure constant.
Quantum 1/f noise is the manifestation of the coherent and conventional quantum 1/f effects (Q1/fE). The conventional Q1/fE is a fundamental quantum fluctuation of physical cross sections σ and process rates Γ, caused by the bremsstrahlung (recoil) energy and momentum losses of charged particles, when they are scattered, or accelerated in any way. The closely related coherent Q1/fE is present in any current carried by many particles. It is caused by the energy spread characterizing any coherent state of the electromagnetic field oscillators. According to the Heisenberg's uncertainty principle, because an approximation of the phase or position variable is known, exact knowledge of the energy is precluded. This energy spread results in nonstationary energy values, or fluctuations in the energy of the oscillators. To find the spectral density of these inescapable basic fluctuations, which are known to characterize any quantum state, which is not an energy eigenstate, we use an elementary physical derivation based on Schrödinger's definition of coherent states, which can be supplemented by a rigorous derivation from a well-known quantum-electrodynamical branch-point propagator. The example of a simple harmonic oscillator is also useful for illustrating the uncertainty that arises due to Q 1/f Noise. Clearly illustrating the relation between the uncertainty principle and Q 1/f noise.
The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the qubits. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, the noise that the quantum device demonstrates has a 1/ f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review, the current state of the theory of the decoherence due to the qubit interaction with the fluctuators is discussed. The effect of such an environment on two different protocols of the qubit manipulations, free induction and echo signal, is described. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently, the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function alone. We describe the effect of the fluctuators using the so-called spin-fluctuator model. Being quite realistic, this model allows one to exactly evaluate the qubit dynamics in the presence of one fluctuator. This solution is found, and its features, including non-Gaussian effects, are analyzed in detail. We extend this consideration to systems of large numbers of fluctuators, which interact with the qubit and lead to the 1/ f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
We are in the midst of a renaissance in the study and interpretation of fundamental quantum mechanics, from quantum coherence and quantum entanglement to the quantum measurement process. This stems partly from the impressive advances in experimental techniques that are making yesterday's gedanken experiment today's reality. Another reason quantum coherence and entanglement have come to the forefront is the emerging and tantalizing field of quantum information science. The ability to store information in quantum systems may someday yield devices that process quantum superpositions of inputs in parallel or improve communication through the `wiring' implicit in quantum entanglement. Indeed, quantum computing has the remote prospect of revolutionizing the way we store and process information. This has become particularly important in the face of impending limits on the miniaturization of conventional computers due to quantum effects. Of course, all real systems face limits imposed by decoherence, or the environmentally-induced destruction of quantum coherence. Here, superpositions of quantum states suddenly become probabilistic mixtures of states when they interact with the environment or when the system parameters are fluctuating. Decoherence theory is commonly interpreted as a way to quantify the elusive boundary between quantum and classical worlds and almost always precludes the existence of complex quantum superpositions, except at extremely short time scales. In practice, it is very important to study how decoherence appears in particular quantum systems and try to fight against it. In this special issue of Journal of Optics B: Quantum and Semiclassical Optics , we highlight recent results in the exciting area of quantum coherence and entanglement, including generating interesting and complex quantum states, characterizing coherence and entanglement in these systems, and triumphing over relevant decoherence processes. We hope this issue will not only act as a bookmark in the ongoing study of fundamental quantum mechanics, but will also help guide the rapid developments in quantum information science.