Quantum electrodynamics of qubits

Journal Article · Sat Dec 15 00:00:00 EST 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.76.062106· OSTI ID:21140607

Bialynicki-Birula, Iwo; Sowinski, Tomasz ^[1]

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1. Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw (Poland)

A systematic description of a spin one-half system endowed with magnetic moment or any other two-level system (qubit) interacting with the quantized electromagnetic field is developed. This description exploits a close analogy between a two-level system and the Dirac electron that comes to light when the two-level system is described within the formalism of second quantization in terms of fermionic creation and annihilation operators. The analogy enables one to introduce all the powerful tools of relativistic QED (albeit in a greatly simplified form). The Feynman diagrams and the propagators turn out to be very useful. In particular, the QED concept of the vacuum polarization finds its close counterpart in the photon scattering off a two level system leading via the linear response theory to the general formulas for the atomic polarizability and the dynamic single spin susceptibility. To illustrate the usefulness of these methods, we calculate the polarizability and susceptibility up to the fourth order of perturbation theory. These ab initio calculations resolve some ambiguities concerning the sign prescription and the optical damping that arise in the phenomenological treatment. We also show that the methods used to study two-level systems (qubits) can be extended to many-level systems (qudits). As an example, we describe the interaction with the quantized electromagnetic field of an atom with four relevant states: one S state and three degenerate P states.

• OSTI ID: 21140607
• Journal Information: Physical Review. A, Vol. 76, Issue 6; Other Information: DOI: 10.1103/PhysRevA.76.062106; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANNIHILATION OPERATORS
DIRAC EQUATION
ELECTROMAGNETIC FIELDS
ELECTRONS
FEYNMAN DIAGRAM
MAGNETIC MOMENTS
P STATES
PERTURBATION THEORY
PHOTONS
POLARIZABILITY
PROPAGATOR
QUANTUM COMPUTERS
QUANTUM ELECTRODYNAMICS
QUANTUM MECHANICS
QUBITS
RELATIVISTIC RANGE
S STATES
SECOND QUANTIZATION
SPIN
VACUUM POLARIZATION