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arXiv:1806.00234 · Physical Review A

Mass-energy and anomalous friction in quantum optics

Matthias Sonnleitner, Stephen Mark Barnett

Published Oct 4, 2018• 45 citations
arXivHTMLPDF

Abstract

The usual multipolar Hamiltonian for atom-light interaction features a nonrelativistic moving atom interacting with electromagnetic fields which inherently follow Lorentzian symmetry. This combination can lead to situations where atoms appear to experience a friction force, when in fact they only change their internal mass-energy due to the emission or absorption of a photon. Unfortunately, the simple Galilean description of the atom's motion is not sufficient to distinguish between a change in momentum due to acceleration and a change in momentum due to a change in internal mass-energy. In this work we show how a low-order relativistic correction can be included in the multipolar atom-light Hamiltonian. We also give examples how this affects the most basic mechanical interactions between atoms and photons.

DOI
10.1103/physreva.98.042106

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The usual multipolar Hamiltonian for atom-light interaction features a nonrelativistic moving atom interacting with electromagnetic fields which inherently follow Lorentzian symmetry. This combination can lead to situations where atoms appear to experience a friction force, when in fact they only change their internal mass-energy due to the emission or absorption of a photon. Unfortunately, the simple Galilean description of the atom's motion is not sufficient to distinguish between a change in momentum due to acceleration and a change in momentum due to a change in internal mass-energy. In this work we show how a low-order relativistic correction can be included in the multipolar atom-light Hamiltonian. We also give examples how this affects the most basic mechanical interactions between atoms and photons.
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In quantum optical problems involving the interaction of atoms with laser fields, the atoms are usually considered being stationary during the interaction. Since every photon has a momentum, the atomic momentum (motion) can be changed in the process of absorption and emission of photons. This may force a stationary atom to move or to change momentum of an already moving atom. Therefore, the dynamical behaviour of atoms can be varied by the interaction with a radiation field. For a weak driving field, the influence of this field on the atomic motion can be neglected. However, the intensities of laser fields are generally very strong, and then the motion of the atoms can be considerably changed by the laser field. Here, we discuss this aspect, especially the effect of a driving field on the motion of atoms and the atomic momentum distribution. In particular, we will consider diffraction of atoms by a standing-wave laser field due to an exchange of momentum with the photons of the wave, and radiation force on atoms driven by a running-or standing-wave laser field.
We propose a semi-classical interpretation of the geometric scalar and vector potentials that arise due to Berry's phase when an atom moves slowly in a light field.Starting from the full quantum Hamiltonian, we turn to a classical description of the atomic centre-of-mass motion while still treating the internal degrees of freedom as quantum variables.We show that the scalar potential can be identified as the kinetic energy of an atomic micro-motion caused by quantum fluctuations of the radiative force, and that the Lorentz-type force appears as a result of the motion-induced perturbation of the internal atomic state.For a specific configuration involving two counter-propagating Gaussian laser beams, we relate the geometric forces to the radiation pressure and dipole forces known from quantum optics.The simple physical pictures provided by the present analysis may help for the design and the implementation of novel geometric forces.
Multipolar quantum optics deals with the interaction of light with matter as a many-body bound system of charged particles where the coupling to electromagnetic fields is in terms of the multipolar electric polarization and magnetization. We describe two transformations applied to the conventional non-relativistic formalism, namely a gauge transformation applied directly to the fields at the Lagrangian stage and a unitary transformation applied to the old Hamiltonian. We show how such transformations lead to the same Power-Zienau-Woolley (PZW) formulation of the quantum electrodynamics (QED) of an overall electrically neutral many-body bound system of charges, including the internal motion as well as the gross dynamics of the centre of mass. Besides highlighting the utility of the multipolar formalism as a reliable and convenient platform in dealing with optical processes in atomic and molecular physics, it is shown how the analysis can also lead to the identification of the Röntgen effect arising from the gross motion of an electric dipole moment in a magnetic field and the Aharonov-Casher effect due to the motion of a magnetic dipole moment in an electric field. The importance of the two effects is pointed out in both experimental and theoretical contexts.This article is part of the theme issue 'The quantum theory of light'.
The precise control of light-matter interaction serves as a cornerstone for diverse quantum technologies, spanning from quantum computing to advanced atom optics. Typical experiments often feature multi-mode fields and require atoms with intricate internal structures to facilitate e.g., multi-photon interactions or cooling. Moreover, the development of high-precision cold-atom sensors necessitates the use of entangled atoms. We introduce a rigorous, second-quantized framework for describing multi-ΛΛΛ-atoms in a cavity, encompassing their center-of-mass motion and interaction with a two-mode electromagnetic field. A key feature of our approach is the systematic application of a Hamiltonian averaging theory to the atomic field operators, enabling the derivation of a compact and physically insightful effective Hamiltonian governing the system's time evolution. This effective Hamiltonian not only incorporates the AC-Stark and Bloch-Siegert shifts, augmented by contributions from all involved ancillary states, but also includes effects from counter-rotating terms, offering a more complete description than conventional RWA-based models. A significant finding is the emergence of a particle-particle interaction mediated by ancillary states, stemming directly from the combined quantum nature of the coupled electromagnetic field and atomic system. We illustrate the practical implications of our model through an analysis of atomic Raman diffraction, determining the time evolution for a typical initial state and demonstrating the resulting Rabi oscillations. Furthermore, our results confirm that both the atomic and optical Hong-Ou-Mandel effect can be observed within this Raman configuration, utilizing a specific two-particle input state, thereby extending the utility of Raman diffraction for quantum interference phenomena and providing a microscopic model of the effect.