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"Quantum Optics 1, Single Photons" introduced students to the fundamental principles of light quantization as well as the standard Quantum Optics formalism. All of the examples were taken from single photon phenomena, including quantum technology applications.
In the same vein, "Quantum Optics 2, Two Photons and More" will teach students how to use the Quantum Optics formalism to describe entangled photons, a unique property at the heart of the second quantum revolution and its applications to quantum technologies. Learners will also discover how the Quantum Optics formalism can be used to describe classical light, whether coherent like laser light or incoherent like thermal radiation. Using a many photons description, one can derive the so-called Standard Quantum Limit (SQL), which applies to classical light, and understand how new types of quantum states of light, such as squeezed states of light, allow one to beat the SQL, one of quantum metrology's achievements. Several examples of quantum technologies based on entangled photons will be presented, beginning with quantum communication and moving on to quantum teleportation and quantum cryptography. Quantum Computing and Quantum Simulation will also be covered, as well as some insights into the recently proposed Noisy Intermediate Scale Quantum (NISQ) computing, which raises the prospect of demonstrating, In the near future, the actively sought quantum advantage, i.e. the ability to perform calculations exponentially faster than with classical computers, will be realised.
Syllabus :
1. Quasi-Classical states of radiation : Single mode case
- Quantum Optics formalism in a nutshell
- Quasi-classical state: Definition and elementary properties
- Average field. Dispersion
- Photon number
- Photoelectric signals: fully classical
- Transformation on a beam splitter
- Single mode laser: an emblematic example
- Freely propagating beam: shot noise
- The standard shot noise formula: photocurrent fluctuations
2. Multimode Quasi-Classical states of radiation
- Multimode quantum optics in a nutshell
- Multimode quasi-classical states: Poisson distribution of photons
- Quasi-classical wave packet; case of less than one photon
- Quasi-classical wave packet on a beam splitter
- Beat note between two laser beams; heterodyne detection
- Incoherent multimode radiation; classical vs quantum average
- Beyond classical light
3. Squeezed Light : Beating the statndard quantum limit
- Balanced homodyne detection
- Quadrature components
- Complex plane representation: quadratures, field
- Squeezed state: definition, properties
- Measurements below the SQL
- Squeezing is fragile
- Beating the SQL in a Mach-Zehnder interferometer
- Beating the SQL in Gravitational Waves detection
- A genuine quantum technology
4. Entanglement : A revolutionary concept
- Polarized one photon wave packet: an almost ideal two-level system
- Pairs of photons entangled in polarization
- How to understand the EPR correlations?
- Bell’s inequalities: the possibility to settle the debate experimentally
- Experiments: local realism untenable
5. Entanglement based quantom technologies
- Quantum Key Distribution for cryptography: Ekert protocol
- QKD in the real world: need for quantum repeaters
- Bell states, Bell measurement: a basic tool in quantum information
- Quantum teleportation
- Quantum simulation
- Programmable quantum computing
