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Natal Workshop 2015 RADIATION EMISSION FROM ACCELERATED ATOMS REINALDO DE MELO E SOUZA In collaboration with: P.A.M. Neto and F. Impens INTRODUCTION • Accelerated charges emit radiation. INTRODUCTION • Accelerated charges emit radiation. • Does neutral atoms without permanent dipole moment irradiate when accelerated? INTRODUCTION • Accelerated charges emit radiation. • Does neutral atoms without permanent dipole moment irradiate when accelerated? • Answer must be yes. (Dynamical Casimir effect) INTRODUCTION • In this presentation we shall analyze the radiation emited from an atom in a prescribed trajectory. INTRODUCTION • In this presentation we shall analyze the radiation emited from an atom in a prescribed trajectory. • We show that for atoms in the grounded state acceleration is necessary however not sufficient for emission. INTRODUCTION • In this presentation we shall analyze the radiation emited from an atom in a prescribed trajectory. • We show that for atoms in the grounded state acceleration is necessary however not sufficient for emission. • We evaluate the angular distribuition of the radiation. INTRODUCTION • In this presentation we shall analyze the radiation emited from an atom in a prescribed trajectory. • We show that for atoms in the grounded state acceleration is necessary however not sufficient for emission. • We evaluate the angular distribuition of the radiation. • Strongly dependent on the frequency of motion. INTRODUCTION • In this presentation we shall analyze the radiation emited from an atom in a prescribed trajectory. • We show that for atoms in the grounded state acceleration is necessary however not sufficient for emission. • We evaluate the angular distribuition of the radiation. • Strongly dependent on the frequency of motion. • When an atom is in an excited state, we evaluate how the motion influences the spontaneous emission rate. FORMALISM • In the dipolar approximation, the hamiltonian describing an atom at rest interacting with an electromagnetic field is given by: atomic center of mass position atomic dipole operator electric field operator FORMALISM • In the dipolar approximation, the hamiltonian describing an atom at rest interacting with an electromagnetic field is given by: • When an atom is moving, there is a magnetic dipole moment in the laboratory frame FORMALISM • In the dipolar approximation, the hamiltonian describing an atom at rest interacting with an electromagnetic field is given by: • Alternatively, the electric field in the rest frame is a superposition of lab frame electric and magnetic fields (Lorentz boost). FORMALISM • In the dipolar approximation, the hamiltonian describing an atom at rest interacting with an electromagnetic field is given by: • Alternatively, the electric field in the rest frame is a superposition of lab frame electric and magnetic fields (Lorentz boost). Röntgen current • In the lab fame (NRel regime): FORMALISM • Atom in the grounded state and field in the vacuum state. • In first order of perturbation theory, the probability of emission of radiation is given by |s > = atomic internal state. 1 photon with wave vector k and polarizationλ. FORMALISM • Atom in the grounded state and field in the vacuum state. • In first order of perturbation theory, the probability of emission of radiation is given by |s > = atomic internal state. In order to emit radiation the atom must go to an excited state! 1 photon with wave vector k and polarizationλ. FORMALISM • Atom in the grounded state and field in the vacuum state. • In first order of perturbation theory, the probability of emission of radiation is given by • The center of mass is treated as a classical variable. • Neglegible width of the packet. FORMALISM • Atom in the grounded state and field in the vacuum state. • In first order of perturbation theory, the probability of emission of radiation is given by • The center of mass is treated as a classical variable. • Neglegible width of the packet. • Given the center of mass motion we can evaluate the radiation emission. RADIATION EMISSION FOR HARMONIC MOTION • We take the motion • For simplicity we treat two-level atoms. excited grounded RADIATION EMISSION FOR HARMONIC MOTION • We take the motion • For simplicity we treat two-level atoms. • In the long time limit, there is emission only of photon with frequencies . RADIATION EMISSION FOR HARMONIC MOTION • We take the motion • For simplicity we treat two-level atoms. • In the long time limit, there is emission only of photon with frequencies . • This can be intuitively grasped: SCATTERING FROM MOVING PLATE • When an wave incides upon a conducting plate at rest, the reflected wave has the same frequency. SCATTERING FROM MOVING PLATE • When an wave incides upon a conducting plate oscillating with frequency , we obtain sidebands. SCATTERING FROM MOVING PLATE • The vacuum field can be thought of as virtual electromagnetic plane waves travelling through space. SCATTERING FROM MOVING PLATE • The vacuum field can be thought of as virtual electromagnetic plane waves travelling through space. • When we have reflected photons with negative frequency. SCATTERING FROM MOVING PLATE • The vacuum field can be thought of as virtual electromagnetic plane waves travelling through space. • When we have reflected photons with negative frequency. • Incident virtual photon becomes real photon. (Bogoliubov transformation). SCATTERING FROM MOVING PLATE • Spectral distribution of photons emited by an oscilating plate. http://www.lkb.ens.fr/Dynamical-Casimir-effect-for-a?lang=en SCATTERING FROM MOVING PLATE • Spectral distribution of photons emited by an oscilating plate. • Only photons with . SCATTERING FROM MOVING PLATE • Spectral distribution of photons emited by an oscilating plate. • Only photons with . • For a single two-level atom: • Only incident photons with frequency are abosbed. SCATTERING FROM MOVING PLATE • Spectral distribution of photons emited by an oscilating plate. • Only photons with . • For a single two-level atom: • Only incident photons with frequency are abosbed. M.I. Kaganov, Electrons, Phonons, Magnon Mir (1981) RADIATION EMISSION FOR HARMONIC MOTION • We take the motion • For simplicity we treat two-level atoms. • In the long time limit, there is emission only of photon with frequencies . RADIATION EMISSION FOR HARMONIC MOTION • We take the motion • For simplicity we treat two-level atoms. • In the long time limit, there is emission only of photon with frequencies . • The angular distribution of radiation emission is RADIATION EMISSION FOR HARMONIC MOTION • Profile depend upon comparision between Ω e ω0. Ω = 1.01 ω0 Ω = 5 ω0 RADIATION EMISSION FOR HARMONIC MOTION • Since , our result is of order v2/c2! RADIATION EMISSION FOR HARMONIC MOTION • Since , our result is of order v2/c2! • Our hamiltonian is correct only until order v/c! RADIATION EMISSION FOR HARMONIC MOTION • Since , our result is of order v2/c2! • Our hamiltonian is correct only until order v/c! RADIATION EMISSION FOR HARMONIC MOTION • Energy balance. Energy received by the field: ħ (Ω-ω0) Energy received by the internal degree of the atom : ħω0 RADIATION EMISSION FOR HARMONIC MOTION • Energy balance. Energy received by the field: ħ (Ω-ω0) Energy received by the internal degree of the atom : ħω0 Energy loosed by the atomic center of mass: ħΩ. RADIATION EMISSION FOR HARMONIC MOTION • Energy balance. Energy received by the field: ħ (Ω-ω0) Energy received by the internal degree of the atom : ħω0 Energy loosed by the atomic center of mass: ħΩ. • Exactly the expected for a packet in an harmonic well. RADIATION EMISSION FOR HARMONIC MOTION • Energy balance. Energy received by the field: ħ (Ω-ω0) Energy received by the internal degree of the atom : ħω0 Energy loosed by the atomic center of mass: ħΩ. • Exactly the expected for a packet in an harmonic well. • However, our description of the center of mass was entirely classical. ANALOGY WITH THE PHOTOELECTRIC EFFECT • In the photoelectric effect, light incident on a metal eject electrons from it. ANALOGY WITH THE PHOTOELECTRIC EFFECT • In the photoelectric effect, light incident on a metal eject electrons from it. • Although its explanation constitutes one of the most success of the corpuscular theory of radiation, it is not necessary to quantize the electromagnetic field to explain it. ANALOGY WITH THE PHOTOELECTRIC EFFECT • In the photoelectric effect, light incident on a metal eject electrons from it. • Although its explanation constitutes one of the most success of the corpuscular theory of radiation, it is not necessary to quantize the electromagnetic field to explain it. • Radiation emission from accelerated atoms has some parallels with the photoelectric effect once we perform the following associations: Radiation Emission Center of mass Photoelectric effect Incident Radiation ANALOGY WITH THE PHOTOELECTRIC EFFECT • In the photoelectric effect, light incident on a metal eject electrons from it. • Although its explanation constitutes one of the most success of the corpuscular theory of radiation, it is not necessary to quantize the electromagnetic field to explain it. • Radiation emission from accelerated atoms has some parallels with the photoelectric effect once we perform the following associations: Radiation Emission Center of mass ω0 Photoelectric effect Incident Radiation Work function ANALOGY WITH THE PHOTOELECTRIC EFFECT • In the photoelectric effect, light incident on a metal eject electrons from it. • Although its explanation constitutes one of the most success of the corpuscular theory of radiation, it is not necessary to quantize the electromagnetic field to explain it. • Radiation emission from accelerated atoms has some parallels with the photoelectric effect once we perform the following associations: Radiation Emission Center of mass ω0 Emitted photons Photoelectric effect Incident Radiation Work function Ejected electrons DYNAMICAL PURCELL EFFECT • From now on we will be dealing with atoms in an excited state. DYNAMICAL PURCELL EFFECT • The boundary changes the rate of spontaneous emission by an atom! (Purcell Effect) DYNAMICAL PURCELL EFFECT • The boundary changes the rate of spontaneous emission by an atom! (Purcell Effect) • We study how the motion influences the spontaneous emision. (Dynamical Purcell Effect) DYNAMICAL PURCELL EFFECT • There are three kinds of emission process. (a) excited state grounded state DYNAMICAL PURCELL EFFECT • There are three kinds of emission process. (b) DYNAMICAL PURCELL EFFECT • There are three kinds of emission process. (b) absorption of a phonon. DYNAMICAL PURCELL EFFECT • There are three kinds of emission process. (c) DYNAMICAL PURCELL EFFECT • There are three kinds of emission process. (c) emission of a phonon. DYNAMICAL PURCELL EFFECT • There are three kinds of emission process. • The emission rate is given by emission of a phonon. absorption of a phonon. FINAL REMARKS • In this work we performed a detailed analysis of the emission of radiation by accelerated atoms in vacuum. FINAL REMARKS • In this work we performed a detailed analysis of the emission of radiation by accelerated atoms in vacuum. • If an atom in a grounded state vibrate with a frequency lower than all of its transition frequencies than there is no emission. FINAL REMARKS • In this work we performed a detailed analysis of the emission of radiation by accelerated atoms in vacuum. • If an atom in a grounded state vibrate with a frequency lower than all of its transition frequencies than there is no emission. • We are investigating the role of adiabaticity in our results, providing a better conection of the microscopical and macroscopical dynamical Casimir effect. FINAL REMARKS • In this work we performed a detailed analysis of the emission of radiation by accelerated atoms in vacuum. • If an atom in a grounded state vibrate with a frequency lower than all of its transition frequencies than there is no emission. • We are investigating the role of adiabaticity in our results, providing a better conection of the microscopical and macroscopical dynamical Casimir effect. • The effects described are usually very small and more of a conceitual interest. However, if these effects will be relevant.