Evolution of microwave quantum states in terms of measurable ordered moments of creation and annihilation operators

Abstract

The detection of microwave states is complicated by strong thermal noise, which is inevitably introduced by linear amplifiers. We show how to extract from measured data normally or anti normally ordered moments of photon creation and annihilation operators, the set of which contains complete infor mation on the quantum state of an electromagnetic field. Equations for the evolution of the quantum state are derived in terms of moments. Using this approach, we consider in detail issues of decoherence and ther malization of microwave quantum states. Results are illustrated using the examples of Fock, coherent, squeezed, thermal, and even and odd coherent states (Schrödinger cat states).

On Quantum Operations of Photon Subtraction and Photon Addition

“…The photon creation and annihilation operators are extensively used in quantum optics [3] because many physical operators and characteristics are be expressed through them, for instance in terms of the moments tr[̺(a † ) m a n ], Refs. [4][5][6]. Conditional transformations of quantum states in a measurement are conventionally described by a mapping I : (Ω, F ) → O that is also referred to as instrument [2,[7][8][9].…”

“…The photon creation and annihilation operators are extensively used in quantum optics [3] because many physical operators and characteristics are be expressed through them, for instance in terms of the moments tr[̺(a † ) m a n ], Refs. [4][5][6].…”