Journal of Modern Optics

Strong-field Theory of Dressed Atoms and Dressed Photons

L. Lo Cascio, Franco Persico

Published Jan 1, 1992• 3 citations

Abstract

We consider a two-level atom in a strong laser field, described by the Jaynes-Cummings Hamiltonian in the rotating-wave approximation, yielding the well known dressed states. Diagonalization of the total Hamiltonian is attained by introducing dressed-atomic and photon operators. The quantum theory of measurement of finite duration is used to explore the nature of the physical observables corresponding to the dressed operators. A measuring apparatus is contrived in order to observe the bare-atomic population and the bare-photon number in a dressed state of the system. It is shown that, if the duration of the measurement is longer than the Rabi period of the system, the apparatus leads to observation of the dressed-atomic population and of the dressed-photon number rather than of the corresponding bare quantities for which it was designed. Conceptual and practical consequences of this result are discussed.

DOI: 10.1080/713823347

Related papers

Further considerations on the nature of dressed states

G. Compagno, Roberto Passante, Franco Persico

Introduction . In this final chapter we review two topics of the literature concerning dressed atoms which are of conceptual relevance and capable of shedding some light on the physical meaning and significance of atomic dressing. The first section is devoted to some recent work in connection with the quantum theory of measurement. We include the measuring apparatus in the Hamiltonian along with an appropriate apparatus-atom coupling. We argue that the theory of measurement of finite duration provides us with a tool for detecting the spectral composition of the virtual cloud surrounding an atom. In fact, we show that in a measurement of duration T on a two-level atom fully dressed by the vacuum fluctuations, as discussed in Chapters 6 and 7, the apparatus perceives the atom as dressed only by photons of frequency larger than T -1 . In the case of a two-level atom dressed by a single-mode field populated by real photons, discussed in Chapter 5, we show that if T is smaller than the inverse Rabi frequency ħΔ -1 , the atom is perceived by the apparatus as bare; on the contrary, if T is larger than ħΔ -1 , the atom is perceived as dressed. The time scales for the two cases of dressing, by vacuum fluctuations or by a real single-mode field, are very different, but the similarity of the effects indicates a common physical aspect of the two kinds of dressing.

Cambridge University Press eBooksAug 3, 19950 citations

Dressed Atoms and the Quantum Theory of Measurement

G. Compagno, Roberto Passante, Franco Persico

A gedanken experiment is discussed to measure the population of a two-level atom interacting with a single-mode radiation field. The atom-field system is taken to be in the dressed ground state. The measuring apparatus consists of a classical pointer linearly coupled to the atom. It is shown that the result of the measurement depends strongly on the duration τ on the measuring process. For τ shorter than the time of the vacuum fluctuations creating the virtual photon cloud around the atom, the pointer perceives the atom as bare. In the opposite case the atom is perceived by the pointer as dressed or partially dressed. The insight gained in the nature of the virtual photon cloud, in the meaning of the quantum detection process and in the preparation of partially dressed states, is discussed in the light of this result.

Europhysics Letters (EPL)Jun 15, 199013 citations

Atoms dressed by a real e.m. field

G. Compagno, Roberto Passante, Franco Persico

Introduction . The second part of the book is dedicated to the dressed atom, and it begins with this chapter, which deals mainly with the quantum-dynamical description of an atom dressed by a real electro-magnetic field. Here the emphasis is on the adjective ‘real’, by which we mean that the field is in an excited state populated by real photons and not just by the zero-point photon background. Due to the coupling discussed in the first part of the book, atom-photon correlations are established which admix, shift and split the levels of the system atom plus radiation field. The admixed and correlated states are called dressed-atom states. In Section 5.2 we obtain the Hamiltonian for an atom in a cavity with perfectly reflecting walls. The cavity selects a discrete set of field modes, and this leads us naturally to consider the simplest possible nontrivial atom-field system: the Jaynes-Cummings model describing a two-level atom coupled to a single-mode system. In Section 5.3 we develop the theory, based on a unitary transformation, to dress a two-level atom by a mode of the cavity populated by real photons. A necessary preliminary for dealing with more complicated atom-field models is the theory of spontaneous emission in free space, which is discussed in Section 5.4 in a Wigner-Weisskopf framework.

Cambridge University Press eBooksAug 3, 19951 citation

Eigenstates of the driven Jaynes-Cummings system

P. M. Alsing, D.-S. Guo, Markus Lindberg +2 more

The eigenstates of the Jaynes-Cummings Hamiltonian (the dressed atomic states) are widely used to describe the interaction between a single two-level atom and a single mode of the electromagnetic field. They provide a particularly useful basis when the secular approximation is justified. For an atom interacting fog with n photons in a cavity, the secular approximation requires that the n-photon Rabi frequency 2 n g be much larger than the atomic and cavity linewidths. Normally this condition is met when n is large and the coupling constant g is much smaller than the atomic and cavity linewidths. In this paper we allow g to be larger than the linewidths, and we allow the photon number to be small. We show that when the cavity is driven by a coherent field, the usual secular approximation cannot be used. The natural basis states become are now the eigenstates of the Jaynes-Cummings Hamiltonian plus the external field interaction. We solve this eigenvalue problem by separating the field and atomic parts of the Hamiltonian using a displacement and squeeze in the Hilbert-space of the field. We find that the Rabi frequencies are renormalized downwards as the strength of the driving field is increased. They eventually vanish at a critical field strength. At this critical field strength we observe a spontaneous symmetry breaking in the steady-state solution of the master equation for a single atom interacting with a driven cavity mode.

Annual Meeting Optical Society of AmericaJan 1, 19900 citations

Dressed-state analysis of three-level quantum-jump experiments

Martin Ligare

Recent experiments with single atomic ions isolated in electromagnetic traps have demonstrated abrupt changes in observed fluorescence intensities, which have been interpreted as evidence for quantum jumps as the atom changes energy levels. This presents the seeming paradox of discontinuously changing observables from a system whose dynamical evolution is governed by the continuous optical Bloch equations. In this paper I present an analysis of the dynamics of a model three-level atom interacting with two laser fields in terms of the dressed states of the atom-laser system. These dressed states are eigenstates of a Hamiltonian which includes laser-atom interactions, and thus they simplify the discussion of the time evolution of the combined laser-atom system. This dressed-state description is particularly useful in the regime in which both laser intensities are strong enough to saturate their respective transitions. I calculate the radiative lifetimes of the different species of dressed states and the branching ratios for decay to other dressed states, and demonstrate the consequences of these quantities for the observed fluorescence pattern. The calculated duration of bright and dark periods shows a pronounced dependence on the detunings of the lasers.

Physical Review AMay 1, 198814 citations

Response of a two-level atom to a classical field and a quantized cavity field of different frequencies

C. K. Law, Joseph H. Eberly

We consider a two-level atom interacting simultaneously with a classically described cw laser field and a quantized cavity field. The classical field is assumed strong, and the cavity field is regarded as a quantum probe of its dressed states. The two fields have different frequencies and amplitudes, but we show that an effective time-independent Hamiltonian can be obtained via two rotating-frame transformations. There is a different effective Hamiltonian in each of an infinite sequence of ``probe resonance zones'' associated with the subharmonic Rabi sidebands of the dressed states. In the mth zone, the Hamiltonian has the same form as the m-photon Jaynes-Cummings Hamiltonian. We consider both time-dependent and time-averaged atomic response and make comparisons with recent findings in the case that both fields are fully classical.

Physical Review AJun 1, 199129 citations