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= Cavity Quantum Electrodynamics = Cavity quantum electrodynamics (Cavity QED) is the study of the interaction between light confined in a reflective cavity and atoms or other particles, under conditions where the quantum nature of photons is significant. It provides a platform to test fundamental quantum effects: state superposition and entanglement, complementarity, measurement postulates and decoherence.

== Background == Cavity QED has its origins in the study of spontaneous emission of excited state atom. Spontaneous emission is not a property of an isolated atom but of an atom-vacuum system. Irreversibility of this process comes from the fact that the radiated photon has infinite vacuum states to occupy. Thus, modifying these vacuum states by imposing a boundary condition the rate of spontaneous emission can be modified. Thus, placing the excited atom between mirrors or in a cavity can inhibit or enhance the spontaneous emission. It was first noted by Edwar Mills Purcell in a seminal abstract for the 1946 APS March meeting. Besides the rate modification of spontaneous emission, the atomic levels shift (Lamb Shift) due to the interaction of the atom with the vacuum field in the cavity.

Theory
The Hamiltonian of a two-level atom in a cavity is given by:

$$\hat{H}=\hbar \omega_{eg} \hat{\sigma}_z + \hbar \omega_c  \hat{a}^{\dagger}\hat{a} +\frac{ \hbar \Omega}{2}(\hat{a}\hat{\sigma}_{+}+\hat{a}^{\dagger}\hat{\sigma}_{-} )$$Here this Hamiltonian represents a two-level atom with energy difference $$\hbar \omega_{eg}$$ is interacting with a single mode of a cavity with frequency $$\omega_c$$. This is the Jaynes-Cummings model. It explains the dynamics of a closed system. With lossy cavities the number of available modes increases and due to loss of the photons, atoms decay into ground states.

Experiments
Early observations of modification in spontaneous emission rate paved the road for cavity QED. In 70s and 80s advances were made in experimental techniques to prepare, control and observe the spontaneous emissions of the atoms. These studies were done in weak coupling regime where the photon loss from the cavity is much greater than the emission rate from the atom. Since the photon emitted by the atom is lost it does not interact again with the atom whereas in the strong coupling regime where the Q factor of the cavity is high, and the photon losses are low the emitted photon interacts with the atom again. This coupling reveals the basic quantum properties of the atom-vacuum system. Thus, the spontaneous emission becomes reversible and gives rise to vacuum Rabi oscillations.

Following are some seminal experiments that built the foundation of the field.

=== Observation of the vacuum induced Lamb shift using Ramsey interferometry === In their work in 1993, Serge Haroche's group observed light shift produced on circular Rydberg states by very weak non-resonant microwave fields in a single cavity mode. When photons are stored in a cavity mode non-resonant with the atomic transitions, a radiative shift adds up to the Lamb shift which evolves into a light shift, proportional to field intensity.

Experimental setup
A beam of Rubidium atoms is created from an oven. Then the atoms are prepared in the circular Rydberg state with principal quantum number $$n=51$$. This beam is passed through a cavity ($$C$$) and its interaction with the cavity is probed via Ramsey interferometry using two separated oscillatory fields applied using cavities ($$S_{R}$$) sandwiching the cavity $$C$$. The atomic states are detected by ionization in an electric field and counting the resulting electrons by using an electron multiplier. The ionizing electric field is switched between ionization thresholds of the $$n=51$$ and  $$n=50$$ levels (136 and 148 V/cm). A small coherent field is injected in the cavity in $$V_{c}$$ mode.

Measurement
The atoms are prepared in an equal superposition state of $$n=50 \; (|g\rangle)$$ and $$n=51 \; (|e\rangle)$$ levels: $$\frac{|e\rangle+|g\rangle}{\sqrt{2}}$$ using the first cavity $$S_{R}$$ (performing $$\pi/2$$ pulse). After the atom enters the cavity containing N photons, the collective state of the atom-vacuum system will be $$|\psi\rangle=\frac{|e;N\rangle+|g;N\rangle}{\sqrt{2} }$$. In the far-resonance case where the frequency of the cavity field is detuned from the resonance frequency of the atom, the energy of the excited level is shifted a bit. Thus, when the atoms traverse through the cavity ($$C$$) this state will acquire a phase shift due to the energy shifts.

The accumulated average phase is $$(N+ \frac{1}{2}  ) \frac{\Omega^{2}}{\delta}\sqrt{2\pi}\frac{w}{v} $$. Where;


 * $$\Omega$$ = Vacuum Rabi frequency


 * $$\delta$$ = Detuning in the cavity field
 * $$w$$ = Width of the atom beam
 * $$v$$ = Velocity of the atoms

The phase can be measured after the atoms pass through the second cavity $$S_{R}$$ (performing $$\pi/2$$ pulse) and then detecting $$|e\rangle$$ and $$|g\rangle$$ states.

So, for N=0 there is a residual phase shift. It comes from the vacuum cavity-induced Lamb shift of the excited state. To observe it multiple measurements are performed for various values of atom-cavity detuning in the absence of any injected field inside the cavity.

Results
The lamb shift caused by the cavity then can be extrapolated after considering factors like thermal effects, mirror ellipticity etc.

Observation of normal mode splitting for the atom-cavity system by measuring its spectral response
A direct spectroscopic observation of vacuum Rabi splitting has been made.

Nobel Prize in Physics
The 2012 Nobel Prize for Physics was awarded to Serge Haroche and David Wineland for their work on controlling quantum systems. Haroche shares half of the prize for developing a new field called cavity quantum electrodynamics (CQED) – whereby the properties of an atom are controlled by placing it in an optical or microwave cavity.