quantum optics of many-body systems...quantum optics of many-body systems igor mekhov université...
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Quantum optics of
many-body systems
Igor Mekhov
Université Paris-Saclay (SPEC CEA) University of Oxford, St. Petersburg State University
Lecture 2
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Previous lecture 1
Quantum atom optics quantum atomic states
classical light
Devices: beam splitters, mirrors, diffraction gratings,
cavities
light
matter
Classical optics light waves
material devices
Atom optics matter waves light forces
Quantum optics classical (hot) atoms quantum light states
Quantum optics of quantum gases
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Photons: Discreteness of energy in a single mode, NOT discreteness of classical modes
A. Kuhn, Oxford
A single photon:
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Coherent state Superfluid state
Mott insulator sub-Poissonian distribution
nonclassical statistics
Previous lecture 1
Fock state Mott insulator
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Further plan
Light-matter interaction
cavity QED, vacuum Rabi oscillations, Dicke superradiance (long-range interaction) Manipulation of matter-waves by light
light forces for cooling and trapping Quantum matter waves
second quantization of matter fields Quantum gases in optical lattices
superfluid, Mott insulator states
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Light-matter interaction
Single-mode cavity, two-level atom(s)
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Light-matter interaction
left right
Cavity QED (quantum electrodynamics): Two-level atom coupled to a single mode cavity
Atomic excited (e) and ground (g) states
Analogy for ultracold atoms: Double-well potential (left and right wells)
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Full Hamiltonian: atom, light, and dipole interaction terms
atom transition operators:
Using identity:
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Interaction part:
Dipole transition matrix element:
Electric field for a single mode and fixed coordinate
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Interaction with a two-level atom
Standard spin (Pauli) operator
Light-matter coupling constant
raising and lowering operators
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Bloch sphere
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Jaynes-Cummings model, rotating wave approximation
left right
Quantum potential? Quantum optical lattices? T. Esslinger, A. Hemmerich (2015, 2016)
Cold atoms: Josephson oscillations
Can it be an operator?
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Vacuum Rabi oscillations
Light-matter entanglement
Coupling only between the pairs of levels
oscillations
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Initial conditions: atom in the excited state, no photons
Population inversion
In general, multi-frequency oscillations
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Initial vacuum field
Vacuum Rabi oscillations What is quantum? – They start with no photons present: due to the vacuum fluctuations Reversible spontaneous emission
Vacuum Rabi frequency
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Initial coherent field
Collapse and revival
Due to the discreetness of photons
Analogous effects in quantum atom optics: due to the discreteness of quantum mater waves
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Seeing the matter wave discreteness in a nondestructive way
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Dressed states Strong coupling
Weak coupling
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Many-atom effects, superradiance
Angular momentum:
- maximal
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Dicke states
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Long-range correlation: do not depend on the position, maximal for M = 0
N/2 excitations are symmetrically shared between all atoms
Entanglement
Long-range interaction (global)
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How a global interaction can compete with short-range one?
Alternating coupling constants Many modes
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Classical view: coupled oscillators
Linear problem
Nonlinear pendulum
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Weak field: “vacuum” Rabi oscillations Strong field: Rabi oscillations Strong field degrades collective effects
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1
2
3
4
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Matter wave superradiance (W. Ketterle)
Overdamped regimes: Purcell effect and superradiance
Collective enhancement of spontaneous emission
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Light forces acting on atoms
k k
Spontaneous emission in an arbitrary direction In average: recoil momentum
Force (dissipative, absorptive):
Emission rate:
Excited state population
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Doppler shift for a moving atom
Weak light field (no saturation of the atomic transition), slow atomic motion:
Doppler cooling
limit
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Diffraction/ beam splitting by light
Initial wave:
Interaction:
Interchange with integer number of photons leads to the diffraction of the atomic wave Two peaks: beam splitter
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Trapping, collimating, reflecting
Induced dipole moment:
Interaction energy:
Dipole force:
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Dipole force:
Depends on the detuning
Beam
Potential
Trap, lens
Mirror
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Atomic interferometer
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More advanced cooling schemes
Sisyphus cooling
Velocity selective coherent population trapping (VSCPT): dark states
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Evaporative cooling
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Cavity cooling Relaxation provided by the cavity (instead of spontaneous emission) Off-resonant Does not depend on the level structure Promising for molecules Macroscopic particles
Trapping a single atom by a field of a single photon (G. Rempe)
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Optomechanics Cooling a massive object down to its ground state (Fock state of motion) Squeezing of motion Entanglement Quantum “optics” of phonons a single mechanical mode of a macroscopic object