When a coherent field is combined with the phase-matched output of an atomic ensemble, the second-order correlation function of the total field can exhibit superbunching or antibunching. Homodyning the reference field with the atomic emission can amplify the nonclassical characteristics of the atomic emission. A theoretical description of these phenomena is presented. It is pointed out that, even if the number of excitations in the ensemble is much less than unity, truncating a factorized state to have at most two excitations can lead to errors in calculating the second-order correlation function. We also include the effects of dephasing produced by Rydberg-Rydberg interactions and show how they modify the bunching and antibunching that occur in the absence of atom-atom interactions. It is shown that the particle separation probability distribution and the joint particle separation probability distribution play critical roles in determining the effects of dephasing.
When a coherent field is combined with the phase-matched output of an atomic ensemble, the second-order correlation function of the total field can exhibit superbunching or antibunching. Homodyning the reference field with the atomic emission can amplify the nonclassical characteristics of the atomic emission. A theoretical description of these phenomena is presented. It is pointed out that, even if the number of excitations in the ensemble is much less than unity, truncating a factorized state to have at most two excitations can lead to errors in calculating the second-order correlation function. We also include the effects of dephasing produced by Rydberg-Rydberg interactions and show how they modify the bunching and antibunching that occur in the absence of atom-atom interactions. It is shown that the particle separation probability distribution and the joint particle separation probability distribution play critical roles in determining the effects of dephasing.
A review is given of recent theoretical studies devoted to the problem of generating radiation fields that exhibit the opposite of the well-known bunching of photons observed in light from thermal sources, the so-called antibunching effect. It is made clear that this phenomenon reflects the corpuscular nature of light and, hence, cannot be interpreted in terms of classical electrodynamics, needing, instead, the quantum-mechanical formalism for its description. It is shown in some detail that nonlinear interaction mechanisms like multiphoton absorption and parametric three-wave interaction are suited to change the photon statistical properties of incident (in most cases coherent) light such that the output field will be endowed with antibunching properties. Special emphasis is given to the problem of correctly specifying the dimensions of the mode volume occurring in the usual single-mode treatment of the field, which is, in fact, of great practical interest, since the magnitude of the antibunching effect is determined by the inverse average number of photons contained in that volume. In a later section it is pointed out that destructive interference with a coherent reference beam provides a means of (a) effectively enhancing photon antibunching that is already present in a high-intensity field, through reduction of the intensity, and (b) transforming phase fluctuations produced in a Kerr medium into antibunching-type intensity fluctuations. On the other hand, there exists a way of directly generating light with antibunching properties, the physical mechanism being resonance fluorescence from a single atom. The main features of this technique, both theoretical and experimental, are outlined, including a discussion of the first experimental results obtained a few years ago.
We investigate the photon statistics of an ensemble of coherently driven non-interacting two-level atoms in the weak driving regime. As it turns out, the system displays unique emission characteristics that are strongly in contrast to the emission of classical oscillating dipoles. By deriving the second-order autocorrelation function, we show that extraordinary two-photon correlations are obtained, ranging from strong antibunching to superbunching. These features are enhanced by disorder in the emitter positions, and the control parameter is the number of excitations in the system. We observe the appearance of bunching and antibunching when the light is scattered by the atoms predominantly coherently, i.e., mimicking classical Rayleigh scattering, whereas thermal photon statistics is obtained when the light is scattered via spontaneous decay, a well-known quantum effect. The underlying mechanism is the interplay between coherent scattering, which exhibits spatial fluctuations due to interference, and dissipation in the form of isotropic spontaneous decay.
We demonstrate the existence of nonclassical correlations in the radiation of two atoms, that are coherently driven by a continuous laser source. The photon-photon correlations of the fluorescence light show a spatial interference pattern not present in a classical treatment. A feature of this phenomenon is that bunched and antibunched light is emitted in different spatial directions. The calculations are performed analytically. It is pointed out that the correlations are induced by state reduction due to the measurement process when the detection of the photons does not distinguish between the atoms. It is interesting to note that the phenomena show up even without any interatomic interaction.
Superradiance, i.e., spontaneous emission of coherent radiation by an ensemble of two-level atoms in collective states introduced by Dicke in 1954, is one of the enigmatic problems of quantum optics. The startling gist is that even though the atoms have no dipole moment they radiate with increased intensity in particular directions. Following the advances in our understanding of superradiant emission by atoms in entangled W-states we examine the quantum statistical properties of superradiance. Such investigations require the system to have at least two excitations in order to explore the photon-photon correlations of the radiation emitted by such states. We present specifically results for the spatially resolved photon-photon correlations of systems prepared in doubly excited W-states and give conditions when the atomic system emits nonclassial light. Equally, we derive the conditions for the occurrence of bunching and even of superbunching, a rare phenomenon otherwise known only from nonclassical states of light like the squeezed vacuum. We finally investigate the photon-photon cross correlations of the spontaneously scattered light and highlight the nonclassicalty of such correlations. The theoretical findings can be implemented with current technology, e.g., using ions in a linear rf-trap, atoms in an optical lattice or quantum dots in a cavity.
Resonance fluorescence arises from the coherent interaction of laser light with a two-level system and constitutes a quantum light source exhibiting single-photon emission and antibunching, making it a fundamental building block for future quantum networks. Our recent work [Nat. Commun.16, 6453 (2025)10.1038/s41467-025-61884-x] demonstrates that under continuous-wave excitation and in the absence of pure dephasing, the single-time joint state of resonance fluorescence and the two-level system can be described by a pure entangled state. Here, we analyze the cross-correlation and auto-correlation properties of the quantum optical field generated by the interference of resonance fluorescence with laser light at the resonance excitation frequency. Simulation results indicate that by varying the intensity or phase of the interfering laser light, the higher-order coherence of the post-interference quantum optical field transitions from anti-bunching to super-bunching behavior, consistent with recent theoretical and experimental advances by mean-field engineering. This approach offers a complementary framework to characterize and manipulate the multiphoton quantum optical fields.
Interactions between Rydberg atoms can result in a dipole blockade for which the probability Pn to have n atomic excitations is reduced significantly when $n\ensuremath{\ge}2$. Ideally, this allows one to create a single collective Rydberg excitation in an atomic ensemble with P1=1. A single-photon source is realized by mapping this atomic excitation into a propagating light field. Even if ${P}_{n}\ensuremath{\ne}0$ for $n\ensuremath{\ge}2$, a single-photon source can be approximated if interaction-induced dephasing damps the contributions from multiply excited collective states into the preferred spatial field mode. Two quantities that can be used as figures of merit for these single-photon sources are the second-order correlation function g(2) associated with the phase-matched field emitted by the sample and the second-order correlation function g(A) associated with the atoms. Here we demonstrate that interaction-induced dephasing can lead to significant differences between g(2) and g(A) even if ${P}_{2}\ensuremath{\ll}{P}_{1}\ensuremath{\approx}1$. Theoretical expressions are derived for these quantities and it is shown that ${g}^{(2)}\ensuremath{\le}{g}^{(A)}$. It is also shown that there is a distinct advantage for minimizing g(2) and g(A) by using adiabatic pulsed fields rather than constant amplitude fields to excite the ensemble. These results maybe useful for optimizing Rydberg single-photon sources.