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International Journal of Modern Physics B

Phase correlation of ensemble of quantum emitters and timed Dicke state

Jae Seok Yoon, Suc-Kyoung Hong, Seog Woo Nam, Hyung-Jin Yang

Published Jun 10, 2016• 1 citation
Publisher

Abstract

We study the phase-correlated state which is introduced by the instantaneous excitation of an ensemble of identical two-level quantum emitters and its relation with the Dicke states. Under weak coupling regime, the time evolution of the phase-correlated system of the emitters is also derived to see the characteristics of the collective spontaneous emission of the emitters. It is found that the effective coupling of the ensemble in the phase-correlated state with the emitted field is directly determined by the collective phase of the system. Hence, the collective phase is considered for several specified distributions in brief.

DOI
10.1142/s0217979216501460

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We study the phase-correlated state which is introduced by the instantaneous excitation of an ensemble of identical two-level quantum emitters and its relation with the Dicke states. Under weak coupling regime, the time evolution of the phase-correlated system of the emitters is also derived to see the characteristics of the collective spontaneous emission of the emitters. It is found that the effective coupling of the ensemble in the phase-correlated state with the emitted field is directly determined by the collective phase of the system. Hence, the collective phase is considered for several specified distributions in brief.
We present a theoretical analysis of the intensity correlation functions for the spontaneous emission from a planar ensemble of self-assembled quantum dots. Using the quantum jump approach, we numerically simulate the evolution of the system and construct photon-photon delay time statistics that approximates the second-order correlation functions of the field. The form of this correlation function in the case of collective emission from a highly homogeneous ensemble qualitatively differs from that characterizing an ensemble of independent emitters (inhomogeneous ensemble of uncoupled dots). The signatures of collective emission are observed also in the case of an inhomogeneous but sufficiently strongly coupled ensemble. Different forms of the correlation functions are observed in the intensity autocorrelations and in cross correlations between various spectral ranges, revealing the quantum state projection associated with the detection event and the subsequent interaction-induced redistribution of occupations. The predicted effect of collective dynamics on the correlation functions appears under various excitation conditions. Thus, we show that the second-order correlation function of the emitted field provides a sensitive test of cooperative effects.
The spontaneous emission of a set of NNN identical two-level atoms interacting with a quantized electromagnetic field is studied. The atoms are assumed to be close together compared to the mean wavelength of the emitted radiation, and their initial state is either a Dicke state or a superposition of the ground and excited state for each atom. Approximate expressions are obtained for transition probabilities, expectation values, and correlations as functions of time. The spontaneous emission for a very large separation of the atoms is also studied. In this case the directional properties of the emitted radiation, as well as the time within which the atoms decay to their ground state, depend on the position of each atom.
Abstract This work introduces a theoretical framework to model the collective dynamics of quantum emitters in highly non-Markovian environments, interacting through the exchange of photons with significant retardations. The formalism consists on a set of coupled delay differential equations for the emitter’s raising/lowering operators σ i ± , supplemented by input–output relations that describe the field mediating the interactions. These equations capture the dynamics of both linear (bosonic) and nonlinear (two-level) emitter arrays. It is exact in some limits—e.g. bosonic emitters or generic systems with up to one collective excitation—and can be integrated to provide accurate results for larger numbers of photons. These equations support a study of collective spontaneous emission of emitter arrays in open waveguide-QED environments. This study uncovers an effect we term cascaded super- and sub-radiance, characterized by light-cone-limited propagation and increasingly correlated photon emission across distant emitters. The collective nature of this dynamics for two-level systems is evident both in the enhancement of collective emission rates, as well as in a superradiant burst with a faster than linear growth. While these effects should be observable in existing circuit QED devices or slight generalizations thereof, the formalism put forward in this work can be extended to model other systems such as network of quantum emitters or the generation of correlated photon states.
When a quantum system is put into an excited state, it will decay back to the ground state through a process termed spontaneous emission.It is generally assumed that spontaneous emissions between different individual emitters will not be coherent with each other; to produce coherent light, one would need population inversion and stimulated emission.In this work, we show that an optically thin ensemble of 11 000 radiating atoms spontaneously organizes to produce spatially coherent light.The reason for this coherence is collective coupling of the individual emitters via Dicke superradiance and subradiance (as opposed to amplification through stimulated emission).
We discuss the evolution of the quantum state of an ensemble of atoms that are coupled via a single propagating optical mode. We theoretically show that the quantum state of N atoms, which are initially prepared in the timed Dicke state, in the single excitation regime evolves through all the N-1 states that are subradiant with respect to the propagating mode. We predict this process to occur for any atom number and any atom-light coupling strength. These findings are supported by measurements performed with cold cesium atoms coupled to the evanescent field of an optical nanofiber. We experimentally observe the evolution of the state of the ensemble passing through the first two subradiant states, leading to sudden, temporary switch-offs of the optical power emitted into the nanofiber. Our results contribute to the fundamental understanding of collective atom-light interaction and apply to all physical systems, whose description involves timed Dicke states.
Fully-excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength λλλ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of non-interacting atoms with mutual separations much larger than λλλ. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.