It was first realized by Purcell (1) that the spontaneous emission rate of a quantum system can be enhanced or suppressed by placing it in a resonant radiofrequency cavity. Spontaneous emission as it was first theoretically described by Einstein (2) is not a pure property of matter. It is described by matter coupled to quantized radiation field modes, which can be manipulated in an artificial structure such as a cavity. Cavity quantum electrodynamics (QED) is used to describe such effects that intimately depend on the fact that light is made of photons. Cavity QED has been extensively studied in atoms and the experimental proof was awarded with the Nobel Prize in 2012 (3). It has been applied to cooling of single atoms and for the detection of single atoms and creating and studying states with few photons and few atoms (4). In more recent developments these ideas have been extended to manipulate electronic states (5) and vibrations in molecules (6, 7). In PNAS, Flick et al. (8) introduce recent theoretical developments for the application of cavity QED to molecules and suggest possible novel applications to photochemistry. These include nonadiabatic dynamics of molecules in cavities, the modification of molecular properties, and the integration of QED with density functional theory.
A quantized electromagnetic field mode can be described as a harmonic oscillator whose coordinate is the electric field displacement (Fig. 1 A ). The zero point energy translates into a nonvanishing field intensity ⟨ e 2 ⟩ in the ground state | 0 ⟩ (vacuum fluctuations). The electric vacuum field increases for a small cavity volume e c = ℏ ω c V ϵ 0 , [1]
Fig. 1.
( A ) Illustration of the standing wave cavity mode and the resulting field quantization (Fock states). ( B ) Combined matter-field states (dressed states, | ± , n ⟩ …
[↵][1]1To whom correspondence should be addressed. Email: smukamel{at}uci.edu.
[1]: #xref-corresp-1-1
It was first realized by Purcell (1) that the spontaneous emission rate of a quantum system can be enhanced or suppressed by placing it in a resonant radiofrequency cavity. Spontaneous emission as it was first theoretically described by Einstein (2) is not a pure property of matter. It is described by matter coupled to quantized radiation field modes, which can be manipulated in an artificial structure such as a cavity. Cavity quantum electrodynamics (QED) is used to describe such effects that intimately depend on the fact that light is made of photons. Cavity QED has been extensively studied in atoms and the experimental proof was awarded with the Nobel Prize in 2012 (3). It has been applied to cooling of single atoms and for the detection of single atoms and creating and studying states with few photons and few atoms (4). In more recent developments these ideas have been extended to manipulate electronic states (5) and vibrations in molecules (6, 7). In PNAS, Flick et al. (8) introduce recent theoretical developments for the application of cavity QED to molecules and suggest possible novel applications to photochemistry. These include nonadiabatic dynamics of molecules in cavities, the modification of molecular properties, and the integration of QED with density functional theory.
A quantized electromagnetic field mode can be described as a harmonic oscillator whose coordinate is the electric field displacement (Fig. 1 A ). The zero point energy translates into a nonvanishing field intensity ⟨ e 2 ⟩ in the ground state | 0 ⟩ (vacuum fluctuations). The electric vacuum field increases for a small cavity volume e c = ℏ ω c V ϵ 0 , 1
Fig. 1.
( A ) Illustration of the standing wave cavity mode and the resulting field quantization (Fock states). ( B ) Combined matter-field states (dressed states, | ± , n ⟩ …
↵1To whom correspondence should be addressed. Email: smukamel{at}uci.edu.
In this work, we provide an overview of how well-established concepts in the fields of quantum chemistry and material sciences have to be adapted when the quantum nature of light becomes important in correlated matter-photon problems. We analyze model systems in optical cavities, where the matter-photon interaction is considered from the weak- to the strong-coupling limit and for individual photon modes as well as for the multimode case. We identify fundamental changes in Born-Oppenheimer surfaces, spectroscopic quantities, conical intersections, and efficiency for quantum control. We conclude by applying our recently developed quantum-electrodynamical density-functional theory to spontaneous emission and show how a straightforward approximation accurately describes the correlated electron-photon dynamics. This work paves the way to describe matter-photon interactions from first principles and addresses the emergence of new states of matter in chemistry and material science.
Abstract Inhibition and enhancement of spontaneous emission rate, first proposed by Purcell, is discussed in terms of altered density-of-modes in various types of solid-state cavities and the Purcell factor is derived for two-level atomic system. The conditions for observing Purcell factor and experimental findings in micropillars embedded with Quantum Dots (QD)s are discussed. The strong interaction between photons and matter in the form of QD excitons, dispersion relations for ground and excited states separated by Rabi splitting are discussed. Experimental photoluminescence spectra showing anticrossing of exciton lines and cavity lines by temperature and other tuning methods are used to illustrate the strong light-matter interaction. The Jayness–Cummins model based on second quantization is presented to point out Rabi oscillation, Purcell effect, and other novel features. Microcavity structures for observing cavity quantum electrodynamics effects are mentioned. Microcavity lasers predicting thresholdless operation for unity spontaneous emission coupling factors are discussed.
Cavity qed is the domain of quantum optics which studies the behaviour of single atoms and photons coupled together in an electromagnetic resonator. During the last ten years, various spectacular effects have been observed on such systems, either on the atom’s or on the field’s properties. The presence of a cavity around an atom can produce an alteration of the atomic radiative rates which has been observed in several experiments. Ideally, cavity qed deals with two-level atoms coupled resonantly or nearly resonantly to a single cavity mode. This is of course a simplification of real situations, in which atoms have many levels and the cavity sustains more than one mode. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect.
The earliest studies on the subject of spontaneous emission from an excited atom via interaction with the vacuum modes of the radiation field go back to the early days of quantum mechanics. In view of the fundamental nature of the vacuum fluctuations, it was long thought that spontaneous emission could not be controlled. However, in 1946 Purcell noted that the spontaneous emission rate of the atom inside a resonant cavity can be substantially enhanced (or suppressed) over its free-space value. This is due to the dramatic change of the density of modes of the vacuum field in a cavity. The enhancement and suppression of spontaneous emission in resonant and off-resonant cavities were observed experimentally in the 1980s. It was also realized in the 1950s and 1960s that coherent driving fields can dramatically change the characteristics of the spontaneous emission. The Autler-Townes doublet and Mollow three-peak spectrum are the examples of such behavior. A dramatic narrowing of the spectral peaks were discovered in driven multilevel atomic systems in the early 1990s. The role of atomic coherence in quenching spontaneous emission fluctuations in the context of laser physics was studied in the 1980s, via the correlated spontaneous emission laser (CEL). In this case atomic coherence results in the correlation of two spontaneous emission noise events so that the spontaneous emission quantum noise is eliminated in the relative linewidth. Later, it was “discovered” that the spontaneous emission can be suppressed through quantum interference between decay channels. Properly stated, this was rediscovered since it was first discovered and explained by Lamb in the 1940s. If the dipoles of two transitions from one upper level to two lower levels are parallel, the spontaneous emission in an ordinary vacuum can be cancelled. In a nonuniform vacuum, e.g., a cavity, the quenching of spontaneous emission can be achieved, even for the orthogonal dipoles.
The interaction of light with matter is at the heart of quantum optics, which itself enables insight into the fundamental aspects of quantum mechanics. First experimental access to this research field has been realized by coupling atoms to light. Here, the transition between discrete energy states of the atom is associated with the absorption and emission of a photon, a single quantum of the electromagnetic field. As a central aspect of quantum optics, the light-emitter interaction can be significantly enhanced by placing the emitter in optical cavity that is on resonance with the emitter. In recent years, this has led to a rapidly evolving research field known as cavity quantum electrodynamics (CQED). In CQED two different regimes are distinguished: the strong and the weak coupling regimes. In the strong coupling regime, the emitted photon is reflected from the cavity mirrors and eventually reabsorbed by the emitter. In contrast, the weak coupling regime describes the irreversible emission, where the photon leaks out of the cavity before it can be reabsorbed. Both the weak and strong coupling regimes enabled fundamental experiments for a better understanding of quantum optical phenomena. \n \n \n \nCQED grants access to the quantum world and hence offers potentially revolutionizing applications, particularly in the field of quantum information processing. A central aspect for the successful implementation of quantum applications is the system's scalability. Unfortunately, placing atoms deterministically inside a cavity remains technologically elaborate and hence minimizes the prospect of scaling a atom-CQED system. \n \nA possibility to address this issue is to implement CQED in the solid state, where sophisticated fabrication strategies allow miniaturization and scalability of the system. Particularly the development of self-assembled quantum dots (QD) in semiconductors represent a promising route. QDs can be considered as artificial atoms that mimic the atomic two-level system. These structures interact strongly with light and therefore have the potential for replacing atoms in CQED. As a central advantage, QDs are naturally trapped, which greatly simplifies the deterministic incorporation into the cavity. \n \nIn recent years, many efforts have been made to couple self-assembled QDs to microcavities. Generally, the successful implementation of CQED requires a cavity with a high quality factor Q and a low mode volume. In a majority of the approaches, the high Q/small mode volume cavities were monolithically defined around the QD, embedding the QD at a fixed position inside the cavity. Both the weak and strong coupling regimes have been reached with these systems. However, for future applications they suffer from several disadvantages. The fixed position of the QD inside the cavity minimizes the prospects for spectral tunability and spatial positioning the QD inside the cavity. Furthermore, prospects for further increasing of the cavity Q-factor and minimization of the mode volume remain limited in these systems. \n \nIn this thesis the mentioned disadvantages are addressed by developing a fully tunable miniaturized Fabry-Pérot microcavity with low mode volume. The design enables both spatial positioning of the emitter inside the cavity and spectral tunability. Successful coupling of a single QD to the microcavity is demonstrated including the strong coupling regime. Further a new approach to decrease the cavity mode volume is presented, where we demonstrate weak coupling is achieved
In 1946, E. M. Purcell predicted that the radiative lifetime of an emitter is not an intrinsic property but can be modified by structuring the surrounding electromagnetic field [36]. By inserting a semiconductor quantum dot (QD) in an optical cavity, one can accelerate or inhibit its spontaneous emission. In the present article, we show that the QD spontaneous emission can be deterministically controlled to fabricate bright sources of quantum light. QDs in cavities: basics, motivation, first demonstrations Light-matter coupling We note f the ground state of the QD and e its excited state. For a cavity mode close to resonance with the QD optical transition, we consider only the states with 0 or 1 photon in the cavity mode. The states ∣ e, 0〉 and ∣ f, 1〉 are coupled through light–matter interaction, with a constant g , where h g = ∣〈 e, 0∣ Ed ∣ f, 1∣, with d the dipole of the optical transition e → f and E the electric field at the QD position. Each of the states ∣ e, 0 > and ∣ f, 1 > are also coupled to continua of states: continuum of the free-space optical mode, phonons of the semiconductor matrix, etc. [4]. Here, we consider only the coupling to the continuum of the free-space optical mode, related to the cavity losses, with a constant γ c . When g << γ c , the photon emitted by the recombination of an exciton efficiently escapes outside the cavity. The QD optical transition radiative recombination rate can be accelerated (Purcell effect) or inhibited.