Introduction Ever since 1916/17 when Einstein argued [45] [46] that spontaneous emission must occur if matter and radiation are to achieve thermal equilibrium, physicists have believed that spontaneous emission is an inherent quantum mechanical property of atoms and that excited atoms inevitably radiate. This view, however, overlooks the fact that spontaneous emission is a consequence of the coupling of quantized energy states of atoms with the quantized radiation field, and is a manifestation of quantum noise or of emission ‘stimulated’ by ‘vacuum fluctuations’. An infinity of vacuum states is available to the photon radiated by an excited atom placed in free space, leading to the effective irreversibility of such emissions. If these vacuum states are modified, as for example by placing an excited atom between closely spaced mirrors or in a small cavity (essentially the Casimir effect), spontaneous emission can be greatly inhibited or enhanced or even made reversible. Recent advances in atomic and optical techniques have made it possible to control and manipulate spontaneous emission. A whole new branch of quantum optics called ‘cavity QED’ has developed since 1987 utilizing these dramatic changes in spontaneous emission rates in cavities to construct new kinds of microscopic masers or micromasers that operate with a single atom and a few photons or with photons emitted in pairs in a two-photon transition.
Introduction Ever since 1916/17 when Einstein argued [45] [46] that spontaneous emission must occur if matter and radiation are to achieve thermal equilibrium, physicists have believed that spontaneous emission is an inherent quantum mechanical property of atoms and that excited atoms inevitably radiate. This view, however, overlooks the fact that spontaneous emission is a consequence of the coupling of quantized energy states of atoms with the quantized radiation field, and is a manifestation of quantum noise or of emission ‘stimulated’ by ‘vacuum fluctuations’. An infinity of vacuum states is available to the photon radiated by an excited atom placed in free space, leading to the effective irreversibility of such emissions. If these vacuum states are modified, as for example by placing an excited atom between closely spaced mirrors or in a small cavity (essentially the Casimir effect), spontaneous emission can be greatly inhibited or enhanced or even made reversible. Recent advances in atomic and optical techniques have made it possible to control and manipulate spontaneous emission. A whole new branch of quantum optics called ‘cavity QED’ has developed since 1987 utilizing these dramatic changes in spontaneous emission rates in cavities to construct new kinds of microscopic masers or micromasers that operate with a single atom and a few photons or with photons emitted in pairs in a two-photon transition.
Ever since Einstein demonstrated that spontaneous emission must occur if matter and radiation are to achieve thermal equilibrium, physicists have generally believed that excited atoms inevitably radiate. Spontaneous emission is so fundamental that it is usually regarded as an inherent property of matter. This view, however, overlooks the fact that spontaneous emission is not a property of an isolated atom but of an atom-vacuum system. The most distinctive feature of such emission, irreversibility, comes about because an infinity of vacuum states is available to the radiated photon. If these states are modified—for instance, by placing the excited atom between mirrors or in a cavity—spontaneous emission can be greatly inhibited or enhanced.
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.
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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.
Spontaneous emission of a source, such as an atom, is often thought of as an inherent property of the source, but is a result of the interaction between the radiating source dipole and the vacuum electromagnetic field. Therefore, the radiation emitted from an atom can be altered by suitably modifying the surrounding vacuum field [1] with a cavity. This has been verified by experiments initiated in the 1980s using atoms which are passed through a cavity and show enhanced[2] or inhibited[3] spontaneous emission. This field, called cavity quantum electrodynamics (QED), is currently addressing important issues in semiconductor nanostructures, in particular, high-efficiency light-emitting diodes for communications and single photon sources for quantum cryptography. [4,5] For example, quantum cryptography has emerged as a significant field of study over the last fifteen years, because it offers the promise of private communication whose security is assured by the laws of physics. Most implementations of quantum cryptography so far have used a protocol introduced by Bennet and Brassard, which uses four different states of a quantum system (generally known as BB84) [6 ]. For example, the message can be encoded on the polarization state of single photons, with a random choice between two non-othogonal polarization bases when the photons are sent (by Alice) and recieved (by Bob). Since an eavesdropper (Eve) does not know what bases have been chosen, any measurement she makes will impose a back-action on the states of the transmitted photons, which can be easily detected. Using error correction and privacy amplification, Alice and Bob can distill the transmitted message into a secure key about which Eve knows arbitrarily little.
It is well known that spontaneous emission is not an intrinsic atomic property, but rather results from the coupling of the atom to the vacuum modes of the electromagnetic field. As such, it can be modified by tailoring the electromagnetic environment into which the atom can radiate. This was already realized by Purcell, who noted that the spontaneous emission rate can be enhanced if the atom placed inside a cavity is resonant with one of the cavity is resonant with one of the cavity modes, and by Kleppner, who discussed the opposite case of inhibited spontaneous emission. It has also been recognized that spontaneous emission need not be an irreversible process. Indeed, a system consisting of a single atom coupled to a single mode of the electromagnetic field undergoes a periodic exchange of excitation between the atom and the field. This periodic exchange remains dominant as long as the strength of the coupling between the atom and a cavity mode is itself dominant. 23 refs., 6 figs.
We revisit the problem of spontaneous emission by a two-level system in a cavity, concentrating in particular on those aspects associated with the finite propagation time of light between the atom and the cavity boundaries. We find that spontaneous emission always occurs first at the free space rate and there is then an abrupt change in these dynamics when light reflected by the cavity mirrors returns to the atom, leading to interference effects that result either in an enhancement or a reduction of this rate or in a periodic exchange of excitation between the atom and the cavity field. From this point of view, reversible spontaneous emission in terms of single-mode ``vacuum Rabi oscillations'' can be interpreted as resulting from the interference between the multimode partial waves reflected at the cavity mirrors and the instantaneously radiated light. \textcopyright{} 1996 The American Physical Society.