(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

In this review we look at the concepts and state-of-the-art concerning the strong coupling of surface plasmon-polariton modes to states associated with quantum emitters such as excitons in J-aggregates, dye molecules and quantum dots. We explore the phenomenon of strong coupling with reference to a number of examples involving electromagnetic fields and matter. We then provide a concise description of the relevant background physics of surface plasmon polaritons. An extensive overview of the historical background and a detailed discussion of more recent relevant experimental advances concerning strong coupling between surface plasmon polaritons and quantum emitters is then presented. Three conceptual frameworks are then discussed and compared in depth: classical, semi-classical and fully quantum mechanical; these theoretical frameworks will have relevance to strong coupling beyond that involving surface plasmon polaritons. We conclude our review with a perspective on the future of this rapidly emerging field, one we are sure will grow to encompass more intriguing physics and will develop in scope to be of relevance to other areas of science.

https://iopscience.iop.org/article/10.1088/0034-4885/78/1/013901/pdf

Strong coupling between surface plasmon polaritons and emitters: a review

The Jaynes-Cummings model (JCM), a soluble fully quantum mechanical model of an atom in a field, was first used (in 1963) to examine the classical aspects of spontaneous emission and to reveal the existence of Rabi oscillations in atomic excitation probabilities for fields with sharply defined energy (or photon number). For fields having a statistical distributions of photon numbers the oscillations collapse to an expected steady value. In 1980 it was discovered that with appropriate initial conditions (e.g. a near-classical field), the Rabi oscillations would eventually revive, only to collapse and revive repeatedly in a complicated pattern. The existence of these revivals, present in the analytic solutions of the JCM, provided direct evidence for discreteness of field excitation (photons) and hence for the truly quantum nature of radiation. Subsequent study revealed further non-classical properties of the JCM field, such as a tendency of the photons to antibunch. Within the last two years it ha...

The Jaynes-Cummings Model

The recent development of techniques to produce optical semiconductor cavities of very high quality has prepared the stage for observing cavity quantum-electrodynamic effects in solid-state materials. Among the most promising systems for these studies are semiconductor quantum dots inside photonic crystal, micropillar or microdisk resonators. We review the progress so far in obtaining true quantum-optical strong-coupling effects in semiconductors. We discuss the recent results on vacuum Rabi splitting with a single quantum dot, emphasizing the differences from quantum-well systems. Finally, we propose nonlinear tests for the true quantum limit and speculate about applications in quantum information devices.

Vacuum Rabi splitting in semiconductors

Achieving coherent quantum control over massive mechanical resonators is a current research goal. Nano- and micromechanical devices can be coupled to a variety of systems, for example to single electrons by electrostatic or magnetic coupling, and to photons by radiation pressure or optical dipole forces. So far, all such experiments have operated in a regime of weak coupling, in which reversible energy exchange between the mechanical device and its coupled partner is suppressed by fast decoherence of the individual systems to their local environments. Controlled quantum experiments are in principle not possible in such a regime, but instead require strong coupling. So far, this has been demonstrated only between microscopic quantum systems, such as atoms and photons (in the context of cavity quantum electrodynamics) or solid state qubits and photons. Strong coupling is an essential requirement for the preparation of mechanical quantum states, such as squeezed or entangled states, and also for using mechanical resonators in the context of quantum information processing, for example, as quantum transducers. Here we report the observation of optomechanical normal mode splitting, which provides unambiguous evidence for strong coupling of cavity photons to a mechanical resonator. This paves the way towards full quantum optical control of nano- and micromechanical devices.

Observation of strong coupling between a micromechanical resonator and an optical cavity field

The spectral and temporal response of an optical cavity resonantly coupled to an ensemble of barium atoms has been investigated experimentally. The empty-cavity trnasmission resonances are found to split in the presence of the atoms and, under these conditions, the cavity's temporal response is found to be oscillatory. These effects may be viewed as a manifestation of a vacuum-field Rabi splitting, or as a simple consequence of the linear absorption and dispersion of the intracavity atoms.

Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations.

We report the first observation of continuous-wave two-photon lasing in the optical regime, and demonstrate that its initiation requires the injection of a trigger pulse into the laser resonator. Successful operation of the two-photon laser relies on the use of a novel gain medium consisting of laser-driven, two-level atoms and the use of a high-finesse optical cavity to isolate the two-photon gain from competing processes. Threshold conditions for laser action are in good agreement with recent theoretical predictions.

Realization of a continuous-wave, two-photon optical laser.

We have measured the emission spectrum of two-level-like Ba atoms driven by two strong, equal-amplitude fields with frequency separation 2\ensuremath{\delta}. The spectrum consists of a series of peaks with an essentially constant spacing \ensuremath{\delta} and alternating linewidths. These features differ qualitatively from the characteristic triplet spectrum observed in the case of strong monochromatic excitation. Certain features of the observed spectrum such as its comblike structure can be motivated in terms of the energy spectrum of atom--bichromatic-field product states. Other features, such as the alternating linewidths, require more subtle analysis.

Resonance fluorescence of two-level atoms under strong bichromatic excitation.

A feature associated with continuous-wave two-photon optical gain has been observed in the absorption spectrum of an ensemble of barium atoms driven by a strong near-resonant optical field. In the dressed-atom picture, the observed gain is attributable to inverted two-photon transitions with nearly resonant intermediate states. A cw optical two-photon laser utilizing this gain appears feasible.

Observation of a two-photon gain feature in the strong-probe absorption spectrum of driven two-level atoms.

Observations of qualitatively different coherent transient phenomena associated with bichromatic optical excitation are reported. The effects demonstrated include the control of atomic dynamics through a variation of the initial relative phase of the driving fields and the polarization of population within atom-field dressed states. The dynamics observed are fundamentally more complex than those characteristic of monochromatically driven atoms.

Qilin Wu

Papers

Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations.

Realization of a continuous-wave, two-photon optical laser.

Resonance fluorescence of two-level atoms under strong bichromatic excitation.

Observation of a two-photon gain feature in the strong-probe absorption spectrum of driven two-level atoms.

Phase-sensitive dynamics of bichromatically driven two-level atoms.