Early quantum optics 1900-1970 Blackbody radiation Planck 1900: EM wave amplitudes/energies work as though they were quantized Photoelectric effect: Einstein 1905: They are quantized: photons Quantum electrodynamics Quantum field theory for E, B (Feynman etc, 1940’s-1960’s) Vacuum fluctuations and zero point energy Quantum optics as a discipline begins with laser invention (1960) Quantum uncertainties in number, phase, position of photons.

New quantum optics 1970-present Squeezed states to redistribute uncertainties of phase, numbers of photons Photon entanglements to test quantum ideas Quantum cryptography, “teleportation” of photon or single atom states

Vacuum zero point energy A vacuum is a collection of simple harmonic oscillators. E and B are its excitations, and play roles like x, v in SHO. Energy levels for each mode in a vacuum: Zero point energy represents fluctuations in E, B that are part of a vacuum.

Casimir effect predicted in 1948: Two parallel mirrors are brought close to each other. Only certain frequencies are allowed inside the cavity(boundary conditions). Pressure from more vacuum fluctuations outside than inside!

Casimir force is real Forces on parallel plates observed to within 15 % of theory! Sphere-plate version to within 1% of theory

Vacuum zero point energy How much of this energy is there in the universe? New ultraviolet catastrophe! finite volume has infinite zero point energy.

New ultraviolet catastrophe! “This problem, also known as the ‘cosmological constant problem’ because of its obvious connection with the introduction of a cosmological constant in Einstein gravitation equations, has remained unsolved during the twentieth century, despite considerable efforts for proposing solutions. It has the status of a paradox, lying just at the crucial interface between quantum theory and gravity, and pointing at the necessity of substantial reformulations in the present theoretical formalism.” Serge Reynaud et al, 2000

Quantum Optics: Experiment 1 to remember Double slit illumination: Quantum superposition in single-photon experiments Each photon is in a superposition of “through top slit” and “through bottom slit” states. Old experiment and debate: can we know which slit the photon (electron) went through and get interference?

Image formation one photon at a time! Single photons know how to do ray optics

Experiment 2 to remember Quantum superposition in single-photon experiment Delayed choice experiment. Put shutter in (or not) randomly, but after the time “the photon should have passed the beamsplitter” (classically). Analysis after experiment When shutter in:   no interference When shutter out: fringes

Quantum entanglement of two particles Momentum-entangled particle pair emission. (e.g electrons) Suppose pair (a,b) or (a’,b’) momentum must be conserved (zero total p) Can we “know which slit” a particle went through by measuring the directions of particle b, b’?

How photon entanglement is achieved Nonlinear downconversion in low symmetry crystal. UV photon 2 visible photons of same l (green), or 2 photons of different l (red/blue) z Total momentum is conserved (hence y-z momentum of pair is zero)

Experiment 3 to remember (1998) Entangled photons created at crystal, go to camera D1 and D2. D1 can be at point A or B, either f or 2f from the lens. Lens is 2f from double slit. z Entanglement: photon 1 acts as though it were time-reversed copy of photon 2, since they have opposite momentum components !

“Weird” observations Photons at D1, FT position (A), show the fringes, even though their partners went through the slits! z Moving D1 to imaging position (B) (2f from lens) lets us see which slit they go through. This makes the 2-slit pattern at D2 disappear …. even though we classically “they’ve hit D2 before D1”. review article

General If we measure (or could measure) in any way “which slit” they go through, all interference vanishes “Quantum eraser”: if we absorb or detect photon 1 in such a way that it cannot possibly give information about which slit photon 2 went through, then we get interference patterns for photon 2. So how can we be sure to achieve an interference pattern on the screen at the left? z