Jaynes-Cummings Hamiltonian

Jaynes-Cummings Hamiltonian
Claudiu Genes Max Planck Institute for the Science of Light (Erlangen, Germany) Lecture 7: Jaynes-Cummings Hamiltonian Laser theory Quantum Physics of Light-Matter Interactions, SS19, FAU

Optical cavities How to test the presence of these modes? Place a quantum emitter in it. Combining this with complexity – collective dynamics plays a big role

Optical cavity My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Optical cavity Electric field operator
My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Zero point electric field per photon

Optical cavity Electric field operator
Operator creating excitations in a given delocalized mode Electric field operator My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Zero point electric field per photon

Optical cavity Multiple resonances
Lorentzian profile – enhanced density of optical modes around resonances Quasi-mode My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. frequency Cavity mode linewidth

Optical cavity Coherent light source
My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction 2 equivalent approaches My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction Eliminate vacuum modes – master equation for the cavity mode My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction Eliminate vacuum modes – master equation for the cavity mode My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Cavity intensity decay rate

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction Eliminate vacuum modes – master equation for the cavity mode My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Collapse operator

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction Eliminate vacuum modes – master equation for the cavity mode My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction Eliminate vacuum modes – master equation for the cavity mode My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Driving field amplitude

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction Keep vacuum modes – quantum Heisenberg Langevin equations (quantum stochastic approach) My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction quantum Heisenberg Langevin equations Heisenberg equations of motion My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. and

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction quantum Heisenberg Langevin equations Heisenberg equations of motion My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. and Formal solution

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Effective decay

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Driving plus noise term Effective decay

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction Result My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction Result Input noise correlations My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Optical cavity Coherent light source Leakage of cavity photons modelled as an exchange interaction Result Input noise correlations My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Input-output relations

quantum electrodynamics with two-level systems
Cavity quantum electrodynamics Cavity quantum electrodynamics with two-level systems My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Atom in cavity- Jaynes Cummings dynamics
The Jaynes-Cummings Hamiltonian My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Master equation of cavity-emitter system
The full master equation with the total Hamiltonian My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The Jaynes-Cummings Hamiltonian Matrix elements My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The Jaynes-Cummings Hamiltonian Matrix elements Up to two excitations My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The Jaynes-Cummings Hamiltonian Matrix elements Leads to photon blockade (as we‘ll see later) Up to two excitations My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Polaritons (single excitation subspace) My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Polaritons (single excitation subspace) Eigenvalues My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Polaritons (single excitation subspace) Eigenvalues On resonance My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The polariton transformation Diagonalization of the Hamiltonian Diagonalization of the Linblad term My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The full master equation with the total Hamiltonian My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The full master equation with the total Hamiltonian My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Let’s derive equations of motion for averages

Linear regime Low excitation regime: two driven coupled oscillators

Strong coupling Low excitation regime: two driven coupled oscillators
Emergence of strong coupling Decay rates Frequencies My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Strong coupling Low excitation regime: two driven coupled oscillators
Emergence of strong coupling My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The Purcell effect Bad cavity regime Decay rates Frequencies

The Purcell effect Bad cavity regime Cooperativity (or Purcell factor)
Decay rates Frequencies My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Photon blockade Photon blockade

Photon blockade My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The laser (quantum theory)

Source: youtube: How a laser works
My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Source: youtube: How a laser works

Model 1 The laser Fast relaxation pump Lasing transition
Incoherent pump My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Model 1 The laser Fast relaxation pump Lasing transition
Effective inverse decay – incoherent pumping model Incoherent pump ...like decay from the ground to the excited state My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

If pump larger than natural decay rate – we have population inversion
The laser Model 1 Fast relaxation pump Lasing transition Effective inverse decay – incoherent pumping model Incoherent pump ...like decay from the ground to the excited state My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. If pump larger than natural decay rate – we have population inversion

The laser Incoherent pump Question: is there non-zero amplitude light coming out of the cavity if the pump is strong enough? My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The laser Incoherent pump Question: is there non-zero amplitude light coming out of the cavity if the pump is strong enough? Solving the problem for averages My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The laser Incoherent pump Question: is there non-zero amplitude light coming out of the cavity if the pump is strong enough? Cavity loss Solving the problem for averages My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The laser Incoherent pump Question: is there non-zero amplitude light coming out of the cavity if the pump is strong enough? Cavity loss Solving the problem for averages Gain (medium polarization) My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The laser Incoherent pump Question: is there non-zero amplitude light coming out of the cavity if the pump is strong enough? Cavity loss Solving the problem for averages Gain (medium polarization) My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Population inversion term

The laser We can use collective operators but the problem is not directly solvable Incoherent pump overall medium polarization My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The laser We can use collective operators but the problem is not directly solvable Incoherent pump How to proceed: factorization of operators in the macroscopic limit My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The laser Incoherent pump We can use collective operators but the problem is not directly solvable How to proceed: factorization of operators in the macroscopic limit Solvable now!! My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The laser Predicted threshold Incoherent pump Laser cooperativity
Saturation photon number My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Saturation photon number Below threshold My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

Saturation photon number Below threshold My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Thermal (incoherent) light

Saturation photon number Below threshold My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Above threshold

Saturation photon number Below threshold My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Above threshold Maybe coherent light?

The laser How to proceed?

How to proceed? Model 1 The laser Eqs for operators (including atomic
and cavity input noise) Derive first order and second order coherence properties for light field Model 1 Incoherent pump

How to proceed? Model 2 Model 1 The laser after
Eqs for operators (including atomic and cavity input noise) Derive first order and second order coherence properties for light field Model 1 Incoherent pump Eliminate atomic degrees of freedom and derive statistics of photons inside cavity

The laser Source: Wikipedia Thermal Poissonian

The laser Model 2 Lasing transition

The laser after Excited or ground state atom Excited state atom

The laser after (incorporates action of the atom onto cavity field –
a photon might have been emitted into the cavity mode)

a photon might have been emitted into the cavity mode) Rate of pumping atoms into the cavity

a photon might have been emitted into the cavity mode) ...or not Rate of pumping atoms into the cavity

The laser after Reduced master equation for the cavity field

The laser after Reduced master equation for the cavity field gain

The laser after Question: - what is the action of a single atom initially prepared in the excited state onto the cavity field?

The laser after Question: - what is the action of a single atom initially prepared in the excited state onto the cavity field? Answer:

The laser Derivation – solve the following master equation for the time interval My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information.

The laser Derivation – solve the following master equation for the time interval

The laser Solution

The laser Solution Photon statistics: - diagonal elements

The laser Photon statistics: - diagonal elements

The laser Photon statistics: - diagonal elements Below threshold
My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Thermal

The laser Photon statistics: - diagonal elements Below threshold
Above threshold My main research field is quantum optics. If I were to give a simple definition of quantum optics, I would say that it is a field that ….at the quantum level. However, armed with these tools and driven by pure intellectual curiosity I often find myself driven towards fields that are necessarly within my expertise. In consequence, some of the research discussed today will show some connection to solid-state systems, as quantum transport, quantum metrology and information. Thermal Poissonian

The laser Linewidth

Jaynes-Cummings Hamiltonian

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Jaynes-Cummings Hamiltonian

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