Download RADIATION EMISSION FROM ACCELERATED ATOMS

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.