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IEEE International Symposium on Circuits and Systems proceedings

Equivalent circuits for two-fermion four-state quantum systems

Pier Paolo Civalleri, Marco Gilli, Michele Bonnin

Published May 1, 2009• 1 citation
Publisher

Abstract

An equivalent circuit is presented for a quantum system composed of two spin 1/2 particles. Such a circuit shows that the entire dynamics of the system, including single-particle and two-particle annihilation and creation, as well as the single particle transitions between ground and excited states, can be described as the superposition of the variables of two uncoupled resonant circuits.

DOI
10.1109/iscas.2009.5117813

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An equivalent circuit is presented for a quantum system composed of two spin 1/2 particles. Such a circuit shows that the entire dynamics of the system, including single-particle and two-particle annihilation and creation, as well as the single particle transitions between ground and excited states, can be described as the superposition of the variables of two uncoupled resonant circuits.
Nanocircuits are composed of nanoelements interacting with external electromagnetic fields which are ultimately described in terms of voltages and currents or incident and reflected waves. Hence the necessity of describing their quantum performance in terms of circuit quantities. We present equivalent circuits for the small signal performance of a population of non-interacting spin 1/2 particles about passive and active equilibria induced by external pumping between the ground and the excited state, that describe respectively e.g. nuclear magnetic resonance and reflection amplification.
We propose a scheme for simulating 3+1, 2+1, 1+1 Dirac equation for a free spin-1/2 particle with superconducting josephson circuits consisting of five qubits, four qubits, two qubits respectively. In 3+1D and 2+1D, the flux qubit1 driven by a resonant pulse is in the superposition state of its own two eigenstatesis, and it is used as a bus to induce the (blue)red-sideband excitation consisting of a magnetic pulse acting resonantly on two levels of the flux qubit2 and the energy levels of one phase qubit, which yields two (Anti)Jaynes-Cummings interactions with one driving pulse and reduces the damage of the driving pulses to the system consequently. Numerical results show that decoherence time is several times longer than transition time supposing set appropriate experimental parameters. Therefore experiments verifying the dynamics of electron and neutrino, such as Zitterberwung effect in 3+1, 2+1 and 1+1 dimensions, can be implemented by microelectronic chips composed of the qubits as artificial atoms.
We show that virtual particles, despite being unobservable, can be described by quantum operators which can be interpreted under certain conditions as valid qubit quantum states. For a single virtual fermion, we prove that such a state is a separable mixed two-qubit state with a well-defined finite temperature. For spin-1 virtual bosons, we find them to be associated with four-qubit operators which can be interpreted as quantum states for some gauges. We also study the creation of virtual pairs of fermions, where the pair is shown to be associated with an entangled four-qubit operator, and show the corresponding quantum circuit. Finally, we prove that renormalization does not structurally affect these results. These findings represent interesting connections between quantum field theory, quantum information, and quantum thermodynamics.
The development of nanostructures as components of macroscopic electrical circuits puts into evidence the necessity of providing integrated models of the entire system. The most natural approach is to represent such nanostructures by equivalent circuits to be imbedded in the model of the macroscopic structure. In the paper we discuss to which extent such a task can be accomplished and in particular how it fits the available circuit software for numerical simulations. We present as a meaningful example the circuit model for an atom, described as a two-state quantum system, coupled with a single mode cavity in a n-photon state; such a simple system describes a quantum oscillator realized by the interaction of the electromagnetic field with matter.
The authors describe S=1/2 Ising-like magnetic chains completely in terms of domain walls. They formulate domain wall creation and annihilation operators as fermion operators and calculate the domain wall content of the ground state and of excited states. From exact results for finite chains and from the solution in the one-domain wall subspace they find that a single domain wall behaves like a free particle in a well. The transition between the two equivalent ground states of Ising-like S=1/2 chains is found to be dominated by quantum diffusion: the approach of the magnetization to the asymptotic behaviour is algebraic and not exponential. The analogy of this observation to interface fluctuations in the two-dimensional classical system is pointed out. For domain walls in the presence of impurities they study the phase shift and the transmission coefficient as well as the exact energy spectrum of finite impure lattices. To visualize the domain wall scattering they also demonstrate their real-time dynamics.
There are several reasons for circuit modeling of quantum systems: the first is to establish a bridge between quantum and classical worlds, inasmuch this is possible, the second is to provide a unified view of quantum systems interacting with a macroscopic environment on the point of view of observations done on the latter, the third is the possibility of using circuit simulators to describe the performance of complex quantum systems. We discuss here the construction of equivalent circuits for coupled Fermi oscillators.